Talk:Anatoly Karatsuba/Archive 1

First fast computational method?
At present all statements are referenced. The corresponding paper was published by well-known journal and was out in Springer. I don't understand, wht in the free enciclopedia must be reflected only one, and not very professional opinion. Where was a publication fon Neumann (before A.A. Karatsuba publication in 1960)? Why Gauss never told he invented Fourier transforms (he was born before Fourier and was died after Fourier)? There are many other qiestions. I should it woulf be preferably and more tolerant to present different opinions. Especially, if they are published.Mathtruth (talk) 10:00, 14 April 2013 (UTC)

I believe that the (unreferenced!) statement that "[Karatsuba] authored the first fast computational method" is incorrect. It isn't clear what exactly is considered a "fast computational method" here. Is merge sort (known at least in the 1940s to Neumann) a fast method? Is FFT (known to Gauss in 19th century according to ) a fast computational method? In my opinion both are fast algorithms - they are significantly faster than naive O(n^2) algorithms for the same tasks. What is certain is that Karatsuba did invent the first fast multiplication method, we can cite Knuth's TAOCP on that. So I suggest changing "the first fast computational method" to "the first fast multiplication method" in the article. -- X7q (talk) 14:11, 2 April 2011 (UTC)

There is a problem here: what to consider as a source of a method? For example, the paper of Heidemann&Burrus 1985 refered to a work of Gauss where (by my opinion) there is no any mothod like FFT, or DFT, or even ordinary Fourier transform. However, the paper Heidemann&Burrus contains a form of FFT. If you will read this paper attentively, you will notice that the authors write actually that, if to add a formula from Gauss work with some other formulas you will get the FFT. May be, this is a right statement. However, any math.result, including any algorithm just consist from such "addition" or supplement of old known formulas and results by certain other formulas and results to get something new what never been before. That is this is not argument in the Gauss favour.

How to understand did Mr.X a fast algorithm(not only about FFT or Quick Sort)? The answer is very easy. First of all, you should consider only originals, but not retelling by other persons. When you will consider the original work (written by Gauss and von Neumann, but not by Burrus and Heidemann and modern authors), you should study the formulas presented there. If you will find an algorithm there, you should to calculate the complexity bound using the definition of bit complexity. After that you will get the answer.Riemann&#39;sZeta (talk) 15:11, 2 April 2011 (UTC)

Actually, here at wikipedia we do rely on what you called "retelling by other persons": see WP:No original research and WP:Verifiability. Heidemann & Burrus tell me that Gauss invented FFT in 19th century. Knuth tells me that Neumann invented merge sort in 1945. Who can you cite to support your claims? -- X7q (talk) 15:20, 2 April 2011 (UTC)

What do you mean: who can you cite? Open any math.book or textbook, about FFT, it is written there, Cooley and Tukey are authors, not Gauss. Open any books, the sorting algorithms will be separate from computational algorithms there.

There is also another problem here. There are "computational algorithms" (the effectivity is measured by the bit-complexity of a calculation, by definition), there are also algorithms with other measures (like algebraic, Kolmogorov etc. complexities). What is the measure of "Merge Sort" algorithm in question? In a computational algorithm, you must obtain as an output a result with accuracy till n digits, where n tends to +\infty The first algorithm that was analyzed from the viewpoint of its complexity, was, probably, the Euclidean algorithm for computing the greatest common divisor of two integers. Its complexity was measured by the total number of steps-divisions in this algorithm. The bounds for complexity of the algorithm were obtained Reynaud (rough estimate, 1811), Pierre-Joseph-Étienne Finck (an estimate which is close to the optimal one, 1841) and Gabriel Lamé (the optimal estimate, 1844). What does it mean? Gabriel Lame did an algorithm with optimal complexity bound (there are nothing like that at present for computational algorithms)! However, although the algorithm computes the greatest common divisor of two integers, this is not a "computational algorithm" (and not fast computational algorithm).

I afraid, Heidemann and Burrus are not Gauss friends and collegues, they are not mathematicians, so I don't think, their opinion is a very competent one. Anyway, everybody should have own opinion on the basis of original work of Gauss. As for Merge Sort --- I already formulate my question. What is the measure of effectivity of a Sorting algorithm? Isn't it a number of steps of such an algorithm?Riemann&#39;sZeta (talk) 16:18, 2 April 2011 (UTC) — Preceding unsigned comment added by Riemann'sZeta (talk • contribs) 16:16, 2 April 2011 (UTC)


 * This is WP:OR (and is total nonsense besides); see Talk:Fast Fourier transform. — Steven G. Johnson (talk) 17:40, 2 April 2011 (UTC)

I don't understand what means — Steven G. Johnson, if he means that total nonsense is to compare Merge Sort and the Karatsuba mathod --- he is right, as I believe. To estimate the effectivity of a fast computational algorithm we use the bit complexity, what is impossible to use for the sorting algorithms, where we have the operation of comparison > or <. These are two different families of algorithms, and it's incorrect statement of the problem --- to compare them.

The second point. X7q wrote, that Donald Knuth told or wrote that in 1945 von Neumann invented Merge Sort algorithm. Where is the reference to the original work of von Neumann? If you write certain information in encyclopedia, be so kind, give the reference to the original work, not to the rumors.Riemann&#39;sZeta (talk) 20:20, 4 April 2011 (UTC)

Merge sort and FFT
I believe the statements that Merge Sort was from 1945 and FFT is from 19th century are also unreferenced!!! There are no references to the original work of von Neumann from 1945 (the reference to book of Knuth from 1998 isn't available, this is an algorithm from 1998, not from 1945, you must indicate the published work from 1945 in the case if the talk is about priority!). the Gauss work has no description of the FFT, it has a description of ordinary manipulations with trigonometric series, and a very special case for N=12 (only the person who doesn't understand what is it ---algorithm which must include the description of the first step and OF THE $$n$$-TH STEP --- can consider this manipulations as an "algorithm"). Not speaking about the fact that both processes are not computational algorithms. At the same time, one should notice, that all fast sorting algorithms and the FFT arose after 1960 and they are based on the A.A. Karatsuba idea, which was called later Divide and Conquer.Riemann&#39;sZeta (talk) 13:24, 15 April 2011 (UTC)


 * You have already started talks about the origin of those algorithms at Talk:Merge_sort and Talk:Fast_Fourier_transform. I believe further discussion should happen at those two places, not here. So far, no one supports you at those two talk pages. -- X7q (talk) 17:27, 15 April 2011 (UTC)

Why is this article so long?
This is a very interesting Wikitext of A.A. Karatsuba,  where  his results in mathematics  and  interesting facts about his life are very well described. I think that the length of the Wikitext of A.A. Karatsuba is no more than Wikitexts dedicated to other great scientists. — Preceding unsigned comment added by 149.157.204.198 (talk) 13:03, 30 April 2013 (UTC)

I believe that the length of the Wikitext of A.A. Karatsuba is no greater than Wikitexts devoted to other such famous scientists and cultural figures.Sagr1904 (talk) 09:21, 30 April 2013 (UTC)

Why does the article go so deep into the mathematical details of every result Karatsuba showed? It should quickly summarize the most important results, and then readers can follow links to the named theorems to learn more, if they wish. --DFRussia (talk) 22:20, 25 January 2012 (UTC)


 * I agree. Moreover, we really need secondary sources to establish the notability of individual research papers.  The Karatsuba algorithm is certainly notable, but detailed information on that algorithm belongs on the web page for that algorithm.


 * And essentially all of the biographical information was unsourced and needed to be deleted (although it can be re-inserted, perhaps abbreviated, given appropriate sources).


 * Unfortunately, a review of the history of this page, its Talk page, and pages on related algorithms reveal that a fan of Karatsuba has been promoting him on Wikipedia without an understanding of Wikipedia's policies, and has been resistant to any change of behavior. — Steven G. Johnson (talk) 17:14, 9 March 2012 (UTC)

This article was created by many collegues of A.A. Karatsuba from different countries and it's long enough because the amount of notable Karatsuba results is so great. But many biographical WIKI-pages (dedicated not only to scientists, but for example to artists and actors) are much more long than A.A. Karatsuba page.

About sources. For example, we read on the Kolmogorov page "Around the same years (1936) Kolmogorov contributed to the field of ecology and generalized the Lotka–Volterra model of predator-prey systems.In his study of stochastic processes (random processes), especially Markov processes, Kolmogorov and the British mathematician Sydney Chapman independently developed the pivotal set of equations in the field, the Chapman–Kolmogorov equations.Later on, Kolmogorov changed his research interests to the area of turbulence, where his publications beginning in 1941 had a significant influence on the field. In classical mechanics, he is best known for the Kolmogorov–Arnold–Moser theorem (first presented in 1954 at the International Congress of Mathematicians). In 1957 he solved a particular interpretation of Hilbert's thirteenth problem (a joint work with his student V. I. Arnold). He was a founder of algorithmic complexity theory, often referred to as Kolmogorov complexity theory, which he began to develop around this time." Were are the references here?--- Nothing.

The same in all biographical WIKI-pages. So, this is a false argument of Stevenj. Moreover, it's easy to prove that User Stevenj has private, non-objective relation to A.A. Karatsuba. In his first editing of A.A. Karatsuba article he deleted at first just such reference (source out) from the paper of French mathematician Jean-Paul Delahaye (http://fr.wikipedia.org/wiki/Jean-Paul_Delahaye) who writes some papers about interesting results in the journal "Pour La Science" and who call the Karatsuba algorithm "the most useful result in mathematics" --- Stevenj, writing about outsourcing deleted this fragment of the WIKI-text FIRSTLY!

I believe, unfortunately, Stevenj is not an expert in the field of number theory, But I have a hard impression that he has a private, non-objective attitude to the A.A. Karatsuba and the Stevenj actions are explained not by its hypocritical cares about politics of Wikipedia. On other pages he tried to defense absolutely wrong statements about the FFT and Merge sort algorithms without any competent sources. When I tried to discuss about it on these pages, the authors of the pages adviced me to write my own Wiki-texts, not preventing to express their point of view. But the same Stevenj prevents to other people express THEIR POINT OF VIEW on Wikipages and to people who much more competent in this subject! In the text dedicated to A.A. Karatsuba there are a lot of references to work of other modern number-theorists including living at present Iwaniec, Friedlander, Moser etc. All of them (and many others, including E.Bombieri and H.Montgomery) participated in the memorial volumes in Number Theory dedicated of A.A. Karatsuba. May be, Stevenj should ask about notability of A.A. Karatsuba works Hugh Montgomery and Enrico Bombieri? I am sure, they confirm such a notability!

Stevenj writes that Wikipage about A.A. Karatsuba  "has been promoting him on Wikipedia" --- A.A. Karatsuba was died at 08.09.2008. What promotion needs a dead mathematician?

The reasons of Stevenj are false!It is he is trying to downplay the value of some mathematicians, and exaggerate the significance and contribution of the others. This is the reason for his activities. However, he can write about their favourits separate article in Wikipedia --- no need to delete and spoil our article!91.79.207.7 (talk) 11:46, 10 March 2012 (UTC)


 * There are indeed other articles on Wikipedia that have sourcing problems, but we try to improve things one article at a time; problems elsewhere are not excuses for re-inserting unsourced material here. Nor do I claim that the material cannot be sourced and cannot be notable, just that it wasn't, and needs to be appropriately sourced and follow WP:NPOV before re-insertion.  Moreover, details of notable mathematical results should be placed in context in the appropriate mathematical article, and simply linked to in the biographical article, as pointed out by DFRussia above.


 * The reason I looked into this article in particular is that I noticed a pattern of similar problematic edits by multiple (WP:SOCK?) accounts and IPs [ e.g. Riemann'sZeta, 83.149.209.253 Algoritmist, 91.79.192.32, AliceNovak, Ekaratsuba (who linked to and may be this daughter of Karatsuba?) ], concentrated at Anatolii Alexeevitch Karatsuba, Divide and conquer algorithm, Karatsuba algorithm, and Fast Fourier transform (FFT), pushing a slanted point of view of Karatsuba's work which contradicts multiple authoritative sources. This motivated me to try and clean up the damage.


 * As explained on Talk:Divide and conquer algorithm, numerous sources cite other examples preceding Karatsuba's work as examples of "divide and conquer" algorithms. For example, as explained on Talk:Fast Fourier transform, it is widely accepted in the literature that Gauss developed a divide-and-conquer FFT algorithm circa 1805.


 * Regarding Delahaye's "most useful result in mathematics" quote, the reason I removed this (rather hyperbolic) quotation is that it needs more context to make sure we are describing it accurately. What result was he referring to specifically, and in what way did he mean it was the "most useful"?  Frankly, given the pattern of your edits, I don't trust an ambiguous quotation like this without more context, and I was unable to obtain the cited article from my library.  (e.g. was Delahaye referring to the concept of divide-and-conquer algorithms in general, which you then attributed to Karatsuba in contradiction with much of the computer-science literature?)


 * Wikipedia articles do not exist to allow editors to express "THEIR POINT OF VIEW". See WP:NPOV and WP:V and WP:RS.  You need to find reputable published sources for a given point of view (and also to establish notability of individual research papers -- see WP:PRIMARY).  — Steven G. Johnson (talk) 14:29, 10 March 2012 (UTC)

Karatsuba's discovery
I see no reason at all why all this dispute takes place. Of course, minor (or even major) editing of this article is possible and maybe inevitable but Karatsuba is so well known that it is ridiculous to question his achievements. I suggest that the full version of this article is put back so it can be seen by everybody. Minor discussions are possible of course. I think it is ridiculous to question the authority of Kolmogorov for instance. Before Karatsuba's discovery Kolmogorov, as correctly described in the article, believed that multiplication of numbers as people do at school is optimal. He was so impressed by Karatsuba's new method that he cancelled his seminar. What other evidence is necessary? Gentlemen, you are piling questions and accusations, but I do not see any sense in that. I suggest the article is put back.Tiger1tiger (talk) 18:33, 16 March 2012 (UTC)


 * Some of the edits made in the past tried to claim that Karatsuba has invented the first "fast algorithm" and divide & conquer paradigm. I disagree with that. What about merge sort invented in 1940s by Neumann? What about FFT which was known to Gauss according to Heideman & Burrus, 1984? These are also D&C algorithms, much faster than naive algorithms for same tasks. Why must we disregard these discoveries and praise Karatsuba instead? -- X7q (talk) 19:49, 16 March 2012 (UTC)


 * I agree that Karatsuba was the first to invent a fast multiplication algorithm. Kolmogorov, Knuth and other sources state this, noone's arguing about this. But I do not know of any sources which attribute to Karatsuba the discovery of "fast algorithms", an ill-defined term without proper context, and divide & conquer. Without sources this shouldn't be on wikipedia. Regardless of whether it is true or not, wikipedia's goal isn't to discover the truth, but to present what is already published in reliable sources. -- X7q (talk) 20:07, 16 March 2012 (UTC)

Very useful link, a lot of information!91.79.162.132 (talk) 22:03, 31 May 2012 (UTC)

I think without relatively full formulations of Karatsuba's results the page will be not so informative. The biographic information is also interesting. In this area sources may be not documental, but for example personal memories.85.141.140.51 (talk) 07:57, 30 April 2013 (UTC)
 * Note that periodically re-inserting all of the problematic material (see above) as an anonymous IP accomplishes nothing; it will just get immediately reverted. The sourcing and other problems need to be corrected, and probably discussed in Talk first, before this material can be included in any form.  — Steven G. Johnson (talk) 23:32, 31 May 2012 (UTC)


 * I agree with the removal of this material. This is a biography and should contain biograhical material not detailed mathematically content. Even Albert Einstein has no extended mathematical notation. What is needed here is more well-referenced biographical material. Stuartyeates (talk) 23:40, 31 May 2012 (UTC)


 * But somebody deleted also all biographical material about A.A. Karatsuba! Enimies? If to look at talks of wiki-administrators? above: not honest position is evident!213.173.227.110 (talk) 20:35, 15 June 2012 (UTC)


 * The biographical material was not sourced, as was explained above. — Steven G. Johnson (talk) 16:56, 26 April 2013 (UTC) This material was sourced when you deletd it! I add three (3) sources, 2 of them translated into English and published by Springer, the main is:http://link.springer.com/article/10.1134%2FS0081543813030012

Proceedings of the Steklov Institute of Mathematics April 2013, Volume 280, Issue 2 Supplement, pp 1-22 Scientific achievements of Anatolii Alekseevich Karatsuba, M. E. Changa, S. A. Gritsenko, E. A. Karatsuba, M. A. Korolev, I. S. Rezvyakova, D. I. Tolev.Mathtruth (talk) 23:32, 1 May 2013 (UTC)

Way forward
I would suggest to compromise. There are several publications about AA Karatsuba, in particular this one by Springer. It provides enough material about Karatsuba and his work to create a reasonable Biography page, something intermediate between current and longer versions. As about the math, well, it certainly does not hurt to include a few key equations, but not that much. I agree that works by Karatsuba himself were published in peer-reviewed journals or books by respectable publishers. Therefore, all these publications can be also used for sourcing, especially in the page about AA Karatsuba. But remember, this is a biography page. Math belongs to other pages, and everyone is welcome to improve these pages, but only as long as they follow the rules. My very best wishes (talk) 18:06, 30 April 2013 (UTC)
 * In answer: there are not equal rules for everybody here, unfortunately. As one told me, when the A.A. Karatsuba collegague tried to do a separated math.page dedicated to certain mathproblem, the same administrators deleted it or tried to use it to advertise their friends (with their results).Mathtruth (talk) 22:59, 1 May 2013 (UTC)

Why the present text was protected? It's not enough and wrong in some details. Could you explain me, what is the Wikipedia politics? Who is such a Wikipedia God to approve the text? Please, let us to edit the text and to do more compact but useful text, not like the present one!Mathtruth (talk) 22:55, 1 May 2013 (UTC)

All material has sources: I add three (3), 2 of them translated into English and published by Springer, the main is:http://link.springer.com/article/10.1134%2FS0081543813030012 Proceedings of the Steklov Institute of Mathematics April 2013, Volume 280, Issue 2 Supplement, pp 1-22 Scientific achievements of Anatolii Alekseevich Karatsuba, M. E. Changa, S. A. Gritsenko, E. A. Karatsuba, M. A. Korolev, I. S. Rezvyakova, D. I. Tolev.Mathtruth (talk) 23:32, 1 May 2013 (UTC)

Look at the Wikipedia rules: you ruin it!
I read in the Wiki-rules: '''On pages that are experiencing edit warring, temporary full protection can force the parties to discuss their edits on the talk page, where they can reach consensus. Isolated incidents of edit warring, and persistent edit warring by particular users, may be better addressed by blocking, so as not to prevent normal editing of the page by others.'''

'''When protecting a page because of a content dispute, administrators normally protect the current version, except where the current version contains content that clearly violates content policies, such as vandalism, copyright violations, or defamation of living persons. Since protecting the most current version sometimes rewards edit warring by establishing a contentious revision, administrators may also revert to an old version of the page predating the edit war if such a clear point exists. Pages that are protected because of content disputes should not be edited except to make changes which are uncontroversial or for which there is clear consensus (see above).'''

Administrators should not protect or unprotect a page to further their own positions in content disputes.

Mathtruth (talk) 23:43, 1 May 2013 (UTC)

How to block a troll ?
How to block a troll? The information in the article confirmed by published papers (not by one paper, but by some different papers by differet authors). However, there is somebody, who permanently delete the article not taking into account these references. Please, help us!Mathtruth (talk) 10:04, 14 April 2013 (UTC)


 * See the Why is this article so long? discussion below. Simply re-inserting the same problematic material will merely get reverted.  Using new Wikipedia accounts to re-insert the same material is not helpful: see also WP:SOCK. — Steven G. Johnson (talk) 16:53, 26 April 2013 (UTC)

There are many long and useless articles in Wikipedia. Look at articles dedicated to actors and sportsmen. This article is very important. Please save it!193.233.208.56 (talk) 12:28, 29 April 2013 (UTC)


 * The criterion for inclusion in Wikipedia has little or nothing to do with editor's judgements of usefulness. It is purely determined by sourcing.  See WP:NOTE and WP:RS.   For example, the biographical material "you" (whoever you are; switching accounts but making the same edits is prohibited WP:SOCK behavior, BTW) keep re-inserting is unsourced.   And the long list of scientific-article summaries is only sourced to the original articles; we need third-party sources to establish notability of individual scientific publications, and in any case the corresponding information should normally go into the corresponding mathematical article rather than into a biographical article, as discussed below.   But I'm not sure why I bother responding, as all of this was already discussed below, and "you" are merely re-inserting the same material over and over without addressing (or even acknowledging) any of the problems. — Steven G. Johnson (talk) 16:06, 29 April 2013 (UTC)--- all material has sources, I add 3, published in English in Springer 2, the main source is :http://link.springer.com/article/10.1134%2FS0081543813030012

Proceedings of the Steklov Institute of Mathematics April 2013, Volume 280, Issue 2 Supplement, pp 1-22 Scientific achievements of Anatolii Alekseevich Karatsuba, M. E. Changa, S. A. Gritsenko, E. A. Karatsuba, M. A. Korolev, I. S. Rezvyakova, D. I. Tolev.

Hello, Stevenj| I received from Wikipedia the following letter: "Hello Mathtruth, Welcome to Wikipedia! You've joined the English-language version of the free encyclopedia that anyone can edit." Do you agree with these Wikipedia ideas? Why you are writing above "unsourced" ? Have you seen the published bu Springer paper: http://link.springer.com/article/10.1134%2FS0081543813030012 Proceedings of the Steklov Institute of Mathematics April 2013, Volume 280, Issue 2 Supplement, pp 1-22 Scientific achievements of Anatolii Alekseevich Karatsuba, M. E. Changa, S. A. Gritsenko, E. A. Karatsuba, M. A. Korolev, I. S. Rezvyakova, D. I. Tolev? It's written by 6 specialists in number theory and numerical analysis and published in the well-known journal by well-known Publishing House. This is a source for information. Unfortunately, the Wiki-paper is not optimally written and doesn't reflect all results of such distinguished scientist as A.A. Karatsuba. But, it will be edit and added by other Wiki-users, as I hope. I don't see a problem, do you?Mathtruth (talk) 18:34, 29 April 2013 (UTC)


 * That 2013 paper is a useful source of biographical information, albeit in a relatively obscure journal, but WP:NOTE policy is usually that multiple sources are expected, and a conflict of interest may apply here if you are one of the authors of that paper. However:


 * Biographical information needs to be sourced with inline citations, so that it is known which of the information can be sourced to that paper. Simple blanket re-insertion without inline cites is not appropriate&mdash;the "Studies and Work" section that you keep re-inserting had zero citations.  Nor is a single source sufficient to establish notability of exhaustive detail (which elementary school he went to, etcetera).
 * An exhaustive summary of Karatsuba's papers is still not appropriate in a biographical article, for the reasons discussed below (math results belong in math articles, primary sources are discouraged, and multiple sources (by different authors) are required to establish notability of individual mathematical results).
 * Dubious claims that the Karatsuba algorithm is the first divide and conquer algorithm, which is contradicted in detail by numerous authoritative sources (e.g. Knuth cites several prior examples), still do not belong in the article. (Your 2011 article doesn't explicitly say that it wasItalic text the first divide-and-conquer algorithm either, although it could be read as implying it, but that could be a translation problem, or simply an error in the original.  The same article makes the claim that FFT algorithms were developed on the "basis" of Karatsuba's result, which is also flatly contradicted by numerous reputable sources which date FFTs back two centuries. WP:FRINGE claims have a high bar for inclusion in WP, and these conflicts with established literature undermine the reliability of the 2013 article as a source.)
 * Blanking the page, blanket re-insertion of material that had been removed after discussion, and switching between multiple accounts to make the same edits are all violations of Wikipedia policy and practice and will tend to be reverted/blocked on sight. Just because "anyone can edit" doesn't mean you can edit without regard for Wikipedia policies.
 * — Steven G. Johnson (talk) 20:00, 29 April 2013 (UTC)

About claims that A.A. Karatsuba invented first fast algorithm: I read some material, it depends on how to define what is it fast algorithm. If this is a bit complexity by Kolmogorov, than A.A. Karatsuba did the first fast algorithm. But if you define it in another way --- there were many fast algorithms before (seems first fast algorithm which was defined by the number of steps was invented in the 19th century). About "divide and conquer" --- it's the same. This termin is used often for problems with subdivisions, not for fast algorithms a la Kolmogorov. But if this is fast computational "divide and conquer" difining by bit complexity a la Kolmogorov --- the Karatsuba algorithm was the first one. About FFT and Gauss. I think, there are specialists in Fourier transforms, and one needs to ask them, what they are think about this hypothesis (that Gauss did the first FFT). I think, the both opinions can be reflected in Wikipedia.Mathtruth (talk) 23:32, 1 May 2013 (UTC)


 * I reverted the added text since WP:CONSENSUS has clearly not been followed; repeted additions without discussion at the talk page may lead to the protection of the page.--Ymblanter (talk) 16:21, 30 April 2013 (UTC)


 * Hello Steven and Ymblanter. I read your arguments. Honestly speaking, you don't support the Wikipedia politics, by my opinion. This is a free enciclopedia, and the text is written about one of the best Russian mathematicians ever, as I think. Your argument that the opinion of some reputable sources or somebody who you consider as an authoritative scientist (I remark, I didn't find in the Knuth books what about you are telling above, so you can not refer to Knuth, if these claims, which you are prescribed to him, haven't been published) contrudict to the opinion of some other very reputable scientists (see paper "Scientific achievements of Anatolii Alekseevich Karatsuba") and that is why we can not place this information in the Wikipedia article doesn't correspond not only the Wikipedia politics, but also to common sense. Every political/life/scientific/cultural event causes different opinions, and to publish only one of them --- it's from totalitarian regimes. It's against any freedom and any common sense. Yous use such expressions like "obscure journal" about one of the best Russian mathematical journals, so you simply don't know the truth. You don't know, but you try to prevent and to distroy our topic refereeing to Wikipedia politics what has absolutely different basis. If you will try not to consider the sources you refereed as an absolute truth, but try to consider all of them on equal basis, you will understand that this is a norm that A.A. Karatsuba students and colleagues write best for Wikipedia what they know. At the same time, let somebody else write in another topic that Gauss invented Fourier transforms (I afraid, the  opinion of very reputable French mathematicians about this will not coincide with opinion of your "reputable sources"). The Wikipedia politics are absolutely supported in the A.A. Karatsuba article, excluding your first point (biographical). You are right, we should find the published source of this information, or to delete it. All other results are supported by published (I repeat) in one from the best Russian journals, refereed by AMS and Zentralblatt etc. and it;s not so appropriate, I afraid, to offend the authors of this issue who are the best world number theorists including such American number theorist like Brian Conrey. If A.A. Karatsuba would be alive, we wouldn't be try to present his results so precisely and in full volume. So, I can not be agree with you that the present paper contradicts to Wikipedia politics, it's just in the limits of the Wiki-politics (if to look at this objectively). Please, try to be objective! It need to further editions --- it's true. If you will not prevent us to do it, we will do it successfully, as I hope. Every success  for you in science, Best Mathtruth (talk) 20:04, 1 May 2013 (UTC)
 * Note that I am not a party in the dispute, I just check that all parties stick to the policies. Would you please address the proposal at the bottom of this page.--Ymblanter (talk) 21:53, 1 May 2013 (UTC)
 * What do you mean "stick to the policies"? If somebody deleted my text. but inserted his/her own text and you protected this bad version so that nobody would be able to edit it, it's OK by your opinion? Such a Wikipedia politics?Mathtruth (talk) 23:32, 1 May 2013 (UTC)
 * Would you please mind reading WP:CONSENSUS as I repeatedly advised you on the previous occasions. Thank you.--Ymblanter (talk) 08:44, 2 May 2013 (UTC)
 * The consensus is possible if the other side wants to reach it and honestly discusses all points. Unfortunately the present situation is another one: Stevej wrote:

''The same article makes the claim that FFT algorithms were developed on the "basis" of Karatsuba's result, which is also flatly contradicted by numerous reputable sources which date FFTs back two centuries. '' But this is never contradicts to these sources! FFT Cooley-Tukey algorithm (and also some other persons did the same method) was prepared in 1965, the sources you cited (I will tell you below about their content) appear for the first time 20 years later!!! So the authors of the FFT (modern version) did know A.A. Karatsuba method when they did their FFT, but didn't know anything else! Just your source with the Cooley paper confirmed this. they didn't know anything about Gauss. So, claiming that they did their FFT on the basis of the Karatsuba idea is right and correct. Moreover, you cited three sources as a "reputable" ones. However, only one of them is a publication (of Cooley), another two are not published and do not come via refereeing process. In the Cooley paper, he doesn't claim that Gauss made FFT, he wrote that there is "essentials of the FFT" (but this is not a method, at all). The paper of Johnson, Burrus and Heideman also claims that you should add an equation of Gauss by some other equations to get the FFT. May be, by your opinion it means that Gauss knew the FFT, by my opinion --- it means the opposite, he didn't make FFT. Anyway, I repeat, the modern FFT from 60-es based on the A.A. Karatsuba idea, the authors didn't know anything else at that time!Mathtruth (talk) 09:21, 2 May 2013 (UTC)

Whabout A.A. Karatsuba results in number theory?
As about all other A.A. Karatsuba text in number theory --- I don't understand you, you don't want to revert the previous text? However you never had any claims on the content. You want that many editors would write this text (or some other things) about A.A. Karatsuba results from the begining? But this is an absurd requirement! As about volume of this text --- it's not so great --- look at the Wikipedia page for Steven Jobs. Advices of some administrators to create separate pages for main number theoretic results (connected with A.A. Karatsuba studies) would be good, if they wouldn't be edited by some persons who begin to advertise there somebody else who they believe a "notable" (but for us, he was worse than the last student of A.A. Karatsuba). Let us to do a good (and not so big) page about A.A. Karatsuba! Who does prevent you to do a good page with description of results for another mathematician? For everybody,whose results inspire you in your work! As for me, I would read such Wikipedia pages about modern mathematicians with great interest. I see a great hypocrisy when you speak about notability of A.A. Karatsuba works and believe that the text is too great, but all Wikipedia texts about sportsmen, actors, singers etc. are filled with such "valuable" information as the story of marriages, divorces, children, grandparents etc. which has no relation to their activity at all. Don't you see here a contradiction?Mathtruth (talk) 18:42, 9 May 2013 (UTC)

What do you want?
OK. You ruin the Wikipedia rules since the text we placed doesn't coincide with your opinion (by the way, are you number theorists?) about A.A. Karatsuba work. Our text which was created by many specialists in number theory and cybernetics and which you deleted some hours ago corresponeded to all Wikipedia rules: it was sourced, it was shorted etc. But this was not enough for you. So, what do you want then? What text will be good for you? The text you protected can not be good for anybody who knows significance and valuability of A.A. Karatsuba works in number theory and computational mathematics. What can be consensus with you, if you don't tell us your further requirements? Your previous requirements about published sources were fulfiled. What else do you want? Tell us honeslty!Mathtruth (talk) 00:55, 2 May 2013 (UTC)

1.Ymblanter protected not "currenly version", but the previous one!

2.Stevenj and Ymblanter ignored the following Wiki-rule:"Administrators should not protect or unprotect a page to further their own positions in content disputes." Mathtruth (talk) 23:43, 1 May 2013 (UTC)
 * I do not have any position in the dispute, please do not list me as involved. You just repeatedly ignore WP:CONSENSUS, and I protected the [age to force you finally to discuss its content (previously you were only interested in inserting your own text, reverting, not so much in discussing). I do not have any particular interest in this page.--Ymblanter (talk) 08:41, 2 May 2013 (UTC)

I am sorry, but you protected the text of StevenJ, not my one, so you are not objective in the discussion. I never ignored WP:CONSENSUS when I am in the Inet. You can see that I try to discuss every point. However, the consensus is possible if another side try to reach it. I introduced 3 additional sources, one of them coveres fully all discussional points. I tried to short the text, deleting some lines and many references to do the text more short, but what to do the other side in this discussion? Only reverted and protected his short and bad version which is absolutely not appropriate to the A.A. Karatsuba contribution to science. Please, tell me, is it possible to apply to somebody who must watch how Wiki-administrators make their duties and who can deal with unfair acivity of certain administrator?Mathtruth (talk) 08:53, 2 May 2013 (UTC)
 * Depends what you want to do. If you want to really reach consensus for the content of the article, this page is the best place, but please also reply to others, do not just state your opinion as the last word. If nobody would react say withing two days, the page gets unblocked, and you can make your changes. If others react but you disagree and can not come to consensus WP:DRN is the place to proceed. If you just want to complain against my actions, WP:ANI is at your service (do not forget no notify me if you go this way). Concerning my revert, you cited the policy above: Since you were clearly edit-warring and introducing your text at every instance, and others clearly objected, I had to revert your additions and protect the page - otherwise you would just get your hand, and you were not so much interested in discussing content.--Ymblanter (talk) 09:09, 2 May 2013 (UTC)

I answered to StevenJ in the "How to block a troll" when he put their questions. However, I don't understand why did you protect StevenJ text, if you are so "not involved"? If you are really not involved, I ask you to demonstrate it and to deletefrom the present blocked by you text "Anatolii Alexeevitch Karatsuba" the sentence of StevenJ:"Karatsuba's multiplication algorithm is an example of what is now termed a divide and conquer algorithm; it was subsequently surpassed in asymptotic performance by the Schönhage–Strassen algorithm." There is a ground for it: this statement isn't condirmed by any source. Do I right understand you, that if nobody will react, we can revert the former big text and to continue to edit it?Mathtruth (talk) 09:52, 2 May 2013 (UTC) H
 * If there is consensus to delete this sentence, I (or someone else) will delete it. If nobody reacts to your suggestions say within two days, yes, you can provisionally take it for consensus and go ahead editing the article.--Ymblanter (talk) 09:57, 2 May 2013 (UTC)
 * What exactly in that sentence do you think there is no source for? There are numerous references on the Schönhage–Strassen algorithm page confirming that it has O(N * logarithmic) complexity, which is asymptotically faster than the O(N1.585...) complexity of Karatsuba multiplication.  And numerous references are given on the Divide and conquer algorithm that there are many divide-and-conquer algorithms, of which Karatsuba is one example, including examples that pre-date Karatsuba.  (Someone with very similar editing patterns to Mathtruth, possibly a WP:SOCK account, already argued about this on that and other pages and failed to convince anyone.) — Steven G. Johnson (talk) 14:00, 2 May 2013 (UTC)


 * It's possible to convince in true math. results only math. literate people who are open-minded.

However, in this O you wrote for the Schönhage–Strassen algorithm complexity bound is so great constant that this algorithm is practically useless. On the other side the the Schönhage–Strassen algorithm is a generalization of A.A. Karatsuba method. That is if A.A. Karatsuba wouldn't be exist, never been Schönhage–Strassen algorithm. But not only Schönhage and Strassen could do the algotihm like their one. They have been the first (because they contacted with Kolmogorov, who visited Schönhage in Germany, Strassen was three times in Moscow etc). But in other situation the authors of this generailzation could be other people (like Toom, Cook etc.). The basis for all of them is the A.A. Karatsuba result (which was a big surprise for A.N. Kolmogorov and for all other scientists at that time). You sentence diminish the A.A. Karatsubacontribution, making it a "feedthrough event" between some algorithms, it gives the impression that Schönhage and Strassen did their result independently and better than A.A. Karatsuba, and you wanted just it, did you? I am sure there are no published sources where it would be written that Toom or Schönhage–Strassen algorithm "surpassed" the A.A. Karatsuba algorithm. Because the importance of the A.A. Karatsuba algorithm in the history of mathematics is much greater than all its generalizations. The same about "divide and conquer". Your offensive line about A.A. Karatsuba work is meaningless: Of course, the car is superior to the cart, but the one who invented the wheel is more important, than who constructed a car. Because the wheel can be used not only in vehicles. The same about Newton's laws. All further inventions can not diminish their importance. It's strange to speak about that, say "Einstein equations" surpassed Newton ones! You don't think?Mathtruth (talk) 10:07, 3 May 2013 (UTC)


 * Utterly false that Schonhage-Strassen is not practically useful. I'm not sure why you think it is an insult to Karatsuba that subsequent authors improved on his result; it doesn't change the fact that he was the first (for multiplication).  Nor why it is a slur to place his results in the context of subsequent work.  — Steven G. Johnson (talk) 17:25, 3 May 2013 (UTC)

I absolutely don't understand you. You wrote the following: no consensus is needed for Stevenj to introduce something. But for me to introduce and even to delete a line which offensively represents one of the most brillant results of A.A. Karatsuba, a consensus is necessary! Everybody must be agree with that what I need to write or to delete in Wikipedia. But other persons (very selected--- by whom, by God?) can do everything what they want, write everything without any sources, without any common sense, simple everything what they want. And you tell methat you are not involved? Sorry, you are.Mathtruth (talk) 10:27, 2 May 2013 (UTC)
 * Everything that Ymblanter wrote is true, including the bit about WP:ANI being the place to complain about their actions. Stuartyeates (talk) 10:39, 2 May 2013 (UTC)
 * The 50K text you were repeatedly adding was several times added last year and rejected (and the article had to be protected several times), this is why adding it without consensus was not acceptable. Concerning the sentence by Stevenj, my understanding that this is not (yet) a recurring issue.--Ymblanter (talk) 11:25, 2 May 2013 (UTC)


 * The text was rejected "several times" as you noted by the same person or two persons without any serious grounds and against all Wikipedia rules.

They simply don't want to recognize a great contribution of A.A. Karatsuba to science that is why they delete the text dedicated to this scientist. This is not a ground. If they like other scientists, they have possibility to create pages abou them and their results. But why to delete work of other people? This article abot A.A. Karatsuba is sourced, and by publsihed and refreed (AMS, Zentralblatt) papers. There are no any wrong statement in it.Mathtruth (talk) 09:44, 3 May 2013 (UTC)


 * Actually, Ymblanter, various (probably WP:SOCK) accounts have been trying to remove that sentence in favor of exaggerated claims that Karatsuba invented the first divide-and-conquer algorithm, or even the "first fast algorithm" (not fast multiplication algorithm, "fast algorithm" period) for years now, arguing the case on multiple pages, repeatedly failing to convince other editors. See, for example, here, and this, and this, and this, and this (on this page).  See also many edits in the history of this article: for example, this, this, and this. — Steven G. Johnson (talk) 14:10, 2 May 2013 (UTC)


 * Stevenj, your words " Ymblanter, various (probably WP:SOCK) accounts have been trying to remove that sentence in favor of exaggerated claims that Karatsuba" tells that you put this unvalid and unsourced line to downplay the A.A. Karatsuba results? And you really believe this is a "honest game"?

As I already expalined you above, it depends on what to call "fast algorithm". If fast algorithm defined by bit complexity a la Kolmogorov --- in fact, A.A. Karatsuba did the first fast algorithm. And what you call exaggerated claims, doesn't correpsond to realty. Even the fact that people multiply two n-digit integers during 4 thousands years with the bit complexity (of Klomogorov definition) n^2, and A.A. Karatsuba invented how to do it faster, is a greatest mathematical victory. You are unfair to A.A. Karatsuba. What to call fast algorithm, which algorithms have been before Karatsuba etc. it's a problem, it's in the limit of discussion. But anyway the claimes that A.A. Karatsuba did 1) the first fast algorithm (defined by bit complexity a la Kolmogorov ) is true; 2) the first divide and conquer (if to mean fast divide and conquer defined by bit complexity a la Kolmogorov and defined by Kolmogorov what means "to compute") is true 3) The FFT is based on A.A. Karatsuba idea (modern version of FFT was prepared 20 years before paper of Heideman,Johnson, Burrus about Gauss computations was publsihed) is true. All these claims at least have grounds. And waht grounds do you have to delete all the text about A.A. Karatsuba where reflected not only his great results in computations, but also his great results in number theory? I think this page is interesting for all  number theorists and students in number theory! Tell honestly, why you don't like A.A. Karatsuba article and prevent to pout this sourced and edited by many people text into Wikipedia?Mathtruth (talk) 09:44, 3 May 2013 (UTC)


 * In computer science, people analyze complexity of algorithms in the context of different abstract machines; it is false that only bit complexity (ala Turing machines) is used. Even if we only consider bit complexity on 1-bit Turing machines,  merge sort is asymptotically faster than naive sort, FFTs are asymptotically faster than naive summation, the Euclidean algorithm is asymptotically faster than naive search, and so on.  It is easily verified that a "fast algorithm" in computer science typically refers informally to algorithms that are asymptotically faster than their predecessors: if you search the literature, you can easily find "fast sorting algorithms", "fast GCD algorithms", and so on.  Arbitrarily restricting the definition of "fast algorithm" to multiplication algorithms is nonstandard.


 * Various Wikipedia articles clearly state that Karatsuba's algorithm was the first fast algorithm for multiplication (compared to the naive algorithm). But this is not enough for you: you apparently will only be satisfied by the claim that this was the "first fast algorithm" period, or the "first divide and conquer algorithm."  These claims are exaggerated.  Nor is it a slur on Karatsuba, as you somehow seem to think, to state the uncontestable fact that asymptotic improvements in multiplication complexity were subsequently found by other authors.  (By the way, it is utterly false to claim that Schonhage-Strassen is a "practically useless" algorithm.  FFT-based multiplication is used in practice by many practical arbitrary-precision arithmetic libraries, such as the GMP library.)


 * As divide and conquer algorithm is defined in computer science, Karatsuba multiplication is not the first such algorithm. We have ample references (e.g. Knuth and Cormen/Leiserson/Rivest) giving examples of other divide-and-conquer algorithms (e.g. merge sort, FFTs) that pre-date Karatsuba.


 * It is true that FFTs were re-discovered independently of Gauss (several times, in fact), most famously by Cooley and Tukey in 1965, and Gauss's contribution was only noticed afterwards. That doesn't change the fact that Gauss clearly described an FFT algorithm circa 1805, a fact that is universally acknowledged and uncontroversial in the FFT literature today (as I've already given several references for).  Nor is it true that Cooley and Tukey based their work on Karatsuba's.  Neither their original paper nor a historical note they published in 1967 mentions Karatsuba's work (although the 1967 paper does point out several other predecessors including Danielson and Lanczos in 1942 and Runge in 1924).  Moreover, Cooley and Tukey's 1965 paper did cite one other paper as inspiration, and that was a 1958 paper by I. J. Good describing what is now called the Prime-factor FFT algorithm.  Even if you pretend Gauss (and Danielson/Lanczos and Runge) don't exist, the Good paper by itself already pre-dates Karatsuba's work.
 * — Steven G. Johnson (talk) 17:17, 3 May 2013 (UTC)
 * As before, you are playing unhonest game.

Firstly, the fact that the Schonhage-Strassen algorithm is implemented in certain libraries doesn't speak that it is widely (and somewhere) used. I confirm, without A.A. Karatsuba idea would never been the Schonhage-Strassen algorithm, but the opposite event is possible.

The sources that you mentioned as sources claiming Gauss did the first FFT --- they do not claim it! They claim only that certain elements of the FFT have been found in the Gauss works! This is also a, what you call, "dubious claim" since before, in the Fourier time, nobody seen something like a variant of the FT in Gauss' works, and one needs to discuss it by mathematical community, especially by Fourier analysis specialists. This is just what I call unhonest game, you tell us that there is certain information somewhere, but it's wrong, in these sources in fact it is written absolutely other claims and statements!

Your claim, that Cooley and Tuckey never refereed to A.A. Karatsuba work, is not a ground to state, they didn't know it. Kolmogorov did a lectures devoted to this discovery during 1960--1965, including the lecture in 1962 in Stokholm at the World mathematical congress and everybody knew it to 1965. If I. J. Good or anybody else really did FFT (not something like that but the method) in 1958, or earlier, and it was really published, it would be known already to A.N. Kolmogorov, but he never mentioned it. And by the way, if it was dome before Cooley +Co, why they published their FFT? Why many years they were called as firat authors of the FFT?

As for Merge sort, the first publication with this algorithm is dated by 1963, not earlier. I think, you know about it, just because of this fact you never refer to the original paper, but refer to Knuth (I remark I haven'seen what published Knuth about it). May be to write the Wikipedia article it's enough, but this is not enough for serious discussion in mathcommunity, one needs to have original publication not further "retelling". Not speaking about the fact that sorting is out of limits of fast computational algorithms (with bit complexity by Kolmogorov).

May be, the Kolmogorov definition is nonstandard for you, but we are writing it every time especially to be indicated about what fast algorithms we speak. As for  But this is not enough for you: 'you apparently will only be satisfied by the claim that this was the "first fast algorithm" period, or the "first divide and conquer algorithm." These claims are exaggerated.' I can tell you: these claims are not exaggerated. But the last editions of the A.A. Karatsuba Wikipedia article doesn't contain these claims. Where have you seen there, that it would be written about first fast algorithm or even about FFT? We omit these problems, they need to be discussed widely by mathematical community. May be, the mathcommunity will decide, I am right, you are wrong, who knows? But before, I will not write about the problem of the priority here, but you also must not write that A.A. Karatsuba algorithm was one from the examples --- may be it was just the first? So, I have not intension to write at the Wikipedia article about A.A. Karatsuba that his algorithm was the first fast algorithm, and will not mention "divide and conquer", but you leave the text of the article as it is written by us (taking into account the absence of these claims so unpleasant for you), and will not delete it and not introduced wrong claims that it was not the first algorithm and its generalization surpassed it. If you agree with such position, I ask the administrators to take out the blocking.Mathtruth (talk) 06:29, 4 May 2013 (UTC)


 * Nest time unhonest game, StevenJ! I didn't find a free text of the Good paper (it's really publication, here you are right!), but I found Cooley-Tuckey paper, where they wrote about this Good result as about an elegant algorithm to calculate Fourier series, but they point that their algorithm is FAST. What means Good's algorithm was not a fast algorithm. So Good didn't FFT! And you wrote us, he did.

However, my suggestions are the same: we will not mention that fact thast the Karatsuba algorithm was the first fast algorithm, and you will let us to edit the rest text as we want, and will not delete it and to revert to your bad (present) version. Mathtruth (talk) 06:46, 4 May 2013 (UTC)


 * Good's algorithm was and is asymptotically faster than naive DFT summation. That is why it is now called a "prime-factor FFT" (PFA) by all reputable sources (including the 1967 review article I linked above, but also in recent reviews such as this book).  I'm sorry you don't have access to Good's paper, but if you read Good's paper there is an explicit formula near the end explaining that it reduces the number of arithmetic operations from ~n2 to ~n&times;(sum of relatively prime factors of n), which is an asymptotic improvement for appropriately chosen n.  Whether Kolmogorov knew of this result is irrelevant.  The Cooley-Tukey algorithm has practical implementation advantages that make it more popular than PFA.  But in any case, it is universally acknowledged in the literature that versions of the Cooley-Tukey algorithm were actually discovered by multiple authors, starting with Gauss in the 19th century and again by multiple authors in the first half of the twentieth century.  Unlike what you've said, the literature does not state that Gauss only discovered "elements" of FFTs; in fact, it says "Thus, Gauss' algorithm is as general and powerful as the Cooley-Tukey common-factor algorithm and is, in fact, equivalent to a decimation in-frequency algorithm adapted to a real data sequence".  I mentioned Good only to provide another data point, and to refute your assertion that Cooley & Tukey's work was based on or inspired by Karatsuba, which has no basis in the literature.   The reason why Cooley & Tukey's name is attached to the algorithm is partly historical accident and partly because they deserve credit for popularizing the approach and explaining and analyzing it more clearly than their predecessors.


 * Even though FFTs were discovered in 1805, by the way, no one claims that they were the first fast algorithm either.  Algorithms asymptotically faster than their predecessors (which is essentially what people in computer science mean by "fast algorithm", although the term "fast" is mostly an informal descriptor), whether on Turing machines or in some other complexity model, date back thousands of years—for example, Euclid's GCD algorithm.  I just focus on the FFT example because I happen to know the literature on it very well, the history of FFT algorithms has been heavily studied, and they are universally acknowledged to be divide-and-conquer algorithms, so they are the easiest refutation of your arguments.


 * You don't get to "edit an article the way you want" if what you want to do is to insert exaggerated claims that are contradicted by vast amounts of well-established literature, or to flout other Wikipedia guidelines, or to make Wikipedia a soapbox for your personal advocacy. Nor is editing a game of "I won't write this if you won't write that" ... the Wikipedia article should reflect what is well-established in the literature, according to the sourcing and notability guidelines. — Steven G. Johnson (talk) 17:30, 4 May 2013 (UTC)


 * I wrote you above that I have no intension to introduce what you called exaggerated claims. All lines of the A.A. Karatsuba article is sourced and sutisfy to all Wikipedia guidelines, including [WP:RS|sourcing]] and notability guidelines. The administrators asked me to come to comsensus with you that's why I tried to recognize from you the conditions of such  a consensus. The article

in the present form 1) doesn't claim the Karatsuba algorithm was the first fast algorithm or frist divide and conquer algorithm; 2) I already don't remember about FFT (there are some lines about it or not), but I will delete any mentions of the FFT from the article, if it has it. Why you don't agree to recover the article which satisfy all Wikipedia requirements? You wrote You don't get to "edit an article the way you want" --- why if this way does correpond to all Wikipedia rules including [WP:RS|sourcing]] and notability guidelines? Mathtruth (talk) 10:00, 5 May 2013 (UTC)

The previous article was very informative and interesting. 109.252.152.234 (talk) 13:47, 5 May 2013 (UTC)


 * Your latest version still contains exaggerated claims, e.g. that The Karatsuba method was later named «Divide and conquer algorithm», the other names of this method, depending on the area of its application, are Binary Splitting, the Dichotomy Principle etc., which falsely implies that this was the original divide-and-conquer algorithm. The following sentence, The fact that this idea was not known before was remarked by D. Knuth, falsely seems to imply (although the antecedent of "this" is ambiguous) that Knuth agrees that Karatsuba's algorithm was the origin of the divide-and-conquer approach, when in fact Knuth explicitly gives multiple other examples of the principle prior to 1960 (e.g. Knuth explicitly says that von Neumann developed merge sort in 1948).  Similarly, you write on the basis of Karatsuba's idea thousands of fast algorithms were constructed, of which the most known are its direct generalizations, such as Schönhage–Strassen algorithm, the Strassen algorithm of matrix multiplication and the Fast Fourier transform (see also the Cooley–Tukey FFT algorithm).  Again, claiming that all subsequent divide-and-conquer algorithms were developed on the basis of Karatsuba's ideas (and are simply "generalizations") is a gross exaggeration, because the divide-and-conquer principle pre-dates Karatsuba, and especially since one of your examples, that of FFT algorithms, actually pre-dates Karatsuba (as is well-established in the literature).  The fact that you got this outlandish claim published in an relatively obscure journal doesn't outweigh the enormous weight of publications, from famous textbooks (e.g. Knuth, Cormen-Leiserson-Rivest, ...) to highly cited papers, that state otherwise and provide historical citations as evidence.  — Steven G. Johnson (talk) 03:29, 6 May 2013 (UTC)


 * Generally speaking, I agree with you that it's wrong to call the Karatsuba method --- "divide and conquer", because of the reason that A.A. Karatsuba method is much more than "divide and conquer". It's not me, and, as I believe, not Russian scientists who call it with such name.

But this is the fact, that somebody called it in such a name (may be, Schonhage was the first?). Another fact is (and this is just fact, you can read it in the Knuth book in the first chapter with the A.A. Karatsuba description, the Knuth PUBLISHED WORDS that this idea was not known before). All what you wrote --- this is not fact, it's only your interpretation, including that some papers derived the conclusion: Gauss made FFT. Why he (Gauss) didn't write especial paper about such transforms? Why nobody, including Fourier, who really did these transforms, never referred to Gauss? Why all specialists in Fourier analysis, never referred to Gauss? As about Merge Sort --- all unpublished words are only words. You need an original publication by von Neumann to prove it. There is the fact: the first publication with this sorting method dated by 1963. I remark, the English student of Kolmogorov Tony Hoare, who have been in Moscow just when A.A. Karatsuba did his fast multiplication method, published his Quick Sorting algorithm also in 1963 (first communicatoions about it have been even earlier). So what you read above, it's what you would want to be, to have place, but this is not true facts, only your interpretation. However, since you are such powerful person in the Wikipedia to prevent to give here another point of view including your, as I think, we should to come to consensus with you. I am going to delete all mentiones of divide and conquer, FFT and all generalizations of A.A. Karatsuba fast multiplication method (not because you are right, generally speaking, I can not understand why only one view must be presented in the Wikipedia and just your view, we simply must submit yourt pressure). As for "obscure journal" about Proceedings of Steklov institute and about other Russian journals (MathNotes, Russian Surveys etc), publsihed memorial issues dedicated to A.A. Karatsuba. May be, you are not mathematician and don't know the details, but in these issues dedicated to A.A. Karatsuba (published in 2010--2013) took part such American mathematicians like (on alphabet) Enrico Bombieri, Brian Conrey, John Frielander, Henryk Iwaniec, Hugh Montgomery. I think, may be to ask Ekaterina, to apply directly to them to ask them to explain directly to you, why A.A. Karastuba results are so notable? If you want it, we can apply to these well-known and fortunately alive mathematicians to confirm the notability of A.A. Karatsuba work in mathematics.Mathtruth (talk) 11:55, 6 May 2013 (UTC)


 * No one disagrees that Karatsuba's algorithm is a divide-and-conquer algorithm. However, it is misleading to call it the divide-and-conquer algorithm.  The term "divide and conquer" is used for a general category of algorithms, of which Karatsuba is only one (and not the first).


 * No one disagrees that Karatsuba's algorithm was the first fast multiplication algorithm. This is very different from being the first divide-and-conquer algorithm.


 * Regarding merge sort, the 1963 publication was merely a reprint of an earlier 1948 technical report. Although the earlier technical report was not published in a journal, the date of the first description is well established in the literature (see e.g. Knuth).


 * As explained all along, detailed mathematical results belong on math articles, not in biography articles. You can argue the notability of particular results on the relevant pages.


 * Anyone familiar with science and mathematics knows that results get forgotten and rediscovered all of the time, and it is quite common for some authors to be unaware of prior results from other authors, even in the same sub-field. It is especially unsurprising in the case of FFTs, since FFT algorithms only became widely useful after the advent of modern computers, and before that were an obscure and specialized technique.  Argument from incredulity is not relevant here; all that matters for Wikipedia is what reputable sources say, and an overwhelming weight of reputable sources accepts the long history of FFTs as uncontroversial.


 * We have a high bar for claims that contradict vast bodies of published literature. The Steklov proceedings are perfectly adequate as a source for biographical details.  They also help to establish notability of individual results, although a retrospective article by friends, colleagues, and family of Karatsuba is not a disinterested source.  But a low-profile journal like this is not sufficient for fringe claims (like the claim that FFTs were based on Karatsuba's ideas) that are contradicted by vast amounts of literature.  Especially when that article provides zero evidence for the unusual claims, and in fact does not even mention the competing evidence in the literature.


 * Please see the suggestion by Stuartyeates, below: rather than making massive changes to the article all at once, pick one short section and propose changes here (in a new section) to get feedback from other editors. For example, a short summary of Karatsuba's major work, or a short personal biography (birthplace, schooling, etc.).  This way, progress can be made on specific improvements. — Steven G. Johnson (talk) 02:53, 9 May 2013 (UTC)


 * — Steven G. Johnson (talk) 22:27, 8 May 2013 (UTC)
 * The main point of our disagreement with you --- you can not accept that the main idea which is in the basis of almost all fast (bit complexity) algorithms belongs just to A.A. Karatsuba, not to anybody else.

All your points are doubtful: the existence of the report of 1948 year --- nothing confirms it excluding words of somebody --- this is not a ground not only if this somebody is Knuth, but also if this somebody would be King of Great Britain etc. --- words are not enough there, you should present a publication;"divide and conquer" algorithms are valuable only if they are fast, and firat fast "divide and conquer" was constructed by A.A. Karatsuba, that Gauss made first FFT --- must confirm the specialists in Fourier analysis, what he did concreatly in this direction. FFT consists from FT, DFT and what makes it Fast, of course the A.A. Karatsuba has nothing with FT, it has relation only to first letter F in the FFT. So all your claims are doubtful, you tell us, our claims are "exaggerated", but your claims (about the authority of Gauss to FFT and for Merge Sort as the first fast algorithm "divide and conquer" are also exaggerated and mostly unsourced, especially if to look at the report "from 1948" (I think you should have specialists in coding theory in your institute, let they tell you to what year belong the codes which are used in this report "from 1948"). Not speaking about the particularities of the computer of von Neumann (it was on decimal arithmetics, not very convenient for binary splitting, isn't it?).


 * However, I repeat, we delete all claims about first fast algorithm, and about divide and conquer. About FFT it will be written, that very probably that the FFT from 1965 was based on A.A. Karatsuba idea (or was a generalization of A.A. Karatsuba idea).Mathtruth (talk) 18:54, 9 May 2013 (UTC)


 * About FFT it will be written, that very probably that the FFT from 1965 was based on A.A. Karatsuba idea &mdash; this is not what the overwhelming weight of the literature says. Wikipedia articles are not platforms for the personal opinions of the editors, they are summaries of the consensus of reputable sources.  What about this do you not understand?  — Steven G. Johnson (talk) 22:35, 9 May 2013 (UTC)


 * The problem is: we also have reputable sources which contradict to your sources. The solution of such problem can be:

1) to give possibility to present different opinions; 2)to present only YOUR OPINION which is based on sources which YOU believe as REPUTABLE ONES.Mathtruth (talk) 17:29, 12 May 2013 (UTC)

Why the A.A.Karatsuba topic is so short?
In my view, the article has a number of drawbacks. It is too short and poorly reflects the multi-faceted research activities of A.A.Karatsuba. In essence, the article is concerned only with Karatsuba's algorithm and does not say anithing about his remarcable achievements in analytic number theory. GritsenkoS (talk) 18:34, 7 June 2013 (UTC)

I agree. About A.A. Karatsuba multiplication algorithm is also written badly. It's neccessary to reblock the article and to let to edit it.91.79.163.173 (talk) 09:55, 8 June 2013 (UTC)

Scope
This article is within the scope of the wikiproject math. I am sure you have one, so add this article to it. —Preceding unsigned comment added by 137.248.75.216 (talk) 13:37, 6 August 2009 (UTC)
 * It was done in http://link.springer.com/article/10.1134%2FS0081543813030012
 * Proceedings of the Steklov Institute of Mathematics
 * April 2013, Volume 280, Issue 2 Supplement, pp 1-22
 * Scientific achievements of Anatolii Alekseevich Karatsuba,
 * M. E. Changa, S. A. Gritsenko, E. A. Karatsuba, M. A. Korolev, I. S. Rezvyakova, D. I. Tolev.Mathtruth (talk) 23:32, 1 May 2013 (UTC)

I corrected "was a mathematician" to "is a mathematician": even in the case when somebody was died he/she continues to be a mathematician since his publications continue out of print. Karatsuba is a mathematician forever.

I also corrected an absurd expression "best known" from his algorithm (for whom?) to right he is author of the first fast computational method (when something is computing with certain accuracy, with methods like sorting etc. you can not compute a function etc.), and this is his greatest contribution to the history of mathematics! 85.140.34.242 (talk) 10:09, 3 April 2010 (UTC)

193.233.212.75 (talk) 16:29, 11 June 2013 (UTC)

What else we can do?
I'm surprised that the previous long and detailed version of the paper about A.A.Karatsuba has been deleted and replaced with this very short note. A.A.Karatsuba was one of the most influential number theorists and his scientific achievements are widely known and recognized. I think that the previous paper must be restored. (D.Tolev) — Preceding unsigned comment added by Dtolev (talk • contribs) 08:59, 7 May 2013 (UTC)

This message was left on my talk page. I'm replying here. I suggest: I hope this helps. Stuartyeates (talk) 22:48, 5 May 2013 (UTC)
 * 1) Reading WP:NPA
 * 2) Reading Help:Using talk pages
 * 3) Proposing (here on the talk page) the exact text of a relatively small change to the article in the direction you want to take it and taking on board any feedback.

I suggest the following text till the Works on Number theoRY. Then I suggest to present all text as it is (on number theory), -

Anatolii Alexeevitch Karatsuba (Russian: Анато́лий Алексе́евич Карацу́ба; Grozny, January 31, 1937 — Moscow, September 28, 2008) was a Russian mathematician, who authored the first fast multiplication method: the Karatsuba algorithm, a fast procedure for multiplying large numbers.

Studies and work From 1944-1954, Anatolii Karatsuba studied at the high school № 6 for boys of the city of Grozny and completed his studies with a silver medal[1]. Already in his early years he showed exceptional talents in mathematics, being a young student he solved problems that were given to the students of the last years at school as a challenge[2].

In 1959, he graduated from Lomonosov Moscow State University, Department of Mathematics and Mechanics. In 1962 he got his PhD degree Candidate of Sciences in Physics and Mathematics, thesis «Rational trigonometric sums of special kind and their applications» (PhD supervisor N.M.Korobov), and started to work at the department of Mathematics and Mechanics of MSU. In 1966 he got his Habilitation (Doctor of Sciences in Physics and Mathematics degree), with the thesis «The method of trigonometric sums and the mean value theorems» and became a member of Steklov Institute of Mathematics (MIAN).

After 1983, he was a leading researcher in Number theory in the USSR and Russia. He was Head of Division of Number Theory in the Steklov Institute, Professor of the Division for Number Theory at Moscow State University since 1970 and Professor of Division for Mathematical analysis of Moscow State University since 1980. His research interests included Trigonometric series and Trigonometric integrals, the Riemann zeta function, Dirichlet characters, Finite-state machines, Fast Algorithms.

Karatsuba supervised the PhD studies of 15 students who obtained their PhD degrees (Cand. of Science); seven of them later obtained the second Habilitation degree (Doctor of Sciences). Karatsuba was awarded state prizes and honorary titles.

Awards and Titles

* 1981: P.L.Tchebyshev Prize of Soviet Academy of Sciences * 1999: Distinguished Scientist of Russia * 2001: I.M.Vinogradov Prize of Russian Academy of Sciences

Automata

In the paper of Edward F. Moore,[3] (n; m; p), an automat (or a machine) S, is defined as a device with n states, m input symbols and p output symbols. Nine theorems on the structure of S and experiments with S are proved. Later such S machines got the name of Moore machines. At the end of the paper, in the chapter «New problems», Moore formulates the problem of improving the estimates which he obtained in Theorems 8 and 9:


 * Theorem 8 (Moore). Given an arbitrary (n; m; p) machine S, such that every two states can be distinguished from each other, there exists an experiment of length n(n-1)/2 that identifies the state of S at the end of this experiment.

In 1957 Karatsuba proved two theorems which completely solved the Moore problem on improving the estimate of the length of experiment in his Theorem 8.


 * Theorem A (Karatsuba). If S is a (n; m; p) machine such that each two its states can be distinguished from each other then there exists a ramified experiment of length at most (n-1)(n-2)/2 + 1, by means of which one can find the state S at the end of the experiment.


 * Theorem B (Karatsuba). There exists a (n; m; p) machine, every states of which can be distinguished from each other, such that the length of the shortest experiment finding the state of the machine at the end of the experiment, is equal to (n-1)(n-2)/2 + 1.

These two theorems were proved by Karatsuba in his 4th year as a basis of his 4th year project; the corresponding paper was submitted to the journal "Uspekhi Mat. Nauk" on December 17, 1958 and published in June 1960.[4] Up to this day (2011) this result of Karatsuba that later acquired the title "the Moore-Karatsuba theorem", remains the only precise (the only precise non-linear order of the estimate) non-linear result both in the automata theory and in the similar problems of the theory of complexity of computations [].

Fast algorithms

Fast algorithms is the area of computational mathematics that studies algorithms of computing a given function with a given precision using the least possible number of bit operations. Assuming that the numbers are written in the binary system, the signs 0 and 1 of which are called "bits". One "bit operation" is defined as writing down one of the signs 0, 1, plus, minus, bracket; putting together, subtracting and multiplying two bits. Andrey Kolmogorov was the first who set up problems on the bit complexity of computations. The complexity of multiplication M(n) is defined as the number of bit operations sufficient to calculate the product of two n-digit numbers by means of the given algorithm.

Multiplying two n-digit integers by the usual school method "in a column", we obtain the upper bound M(n) = O(n^2). In 1956 A.N.Kolmogorov conjectured that the lower bound for M(n) for any method of multiplication is also of the order n^2, that is, it is impossible to calculate the product of two n-digit integers faster than by n^2 operations (the so called ``Kolmogorov n^2 conjecture). The n^2 conjecture seemed realistic, because in all the previous history people multiplied numbers with the complexity of order O(n^2), and if a faster method of multiplication existed then in all probability it would have been already discovered.

In 1960, Anatolii Karatsuba found a new method of multiplication of two n-digit numbers, now known as the Karatsuba algorithm, for which the order of complexity is M(n) = O(n^{\log_23}) = O(n^{1,58496\ldots}), thus disproving the n^2 conjecture. This result was explained by Karatsuba at the Kolmogorov seminar at Moscow State University in 1960, after which that Kolmogorov's seminar came to an end. The first paper describing the method was prepared by Kolmogorov himself,[5] where he presented two different and not connected with each other results of two of his students.

Later on the basis of Karatsuba's idea[8][9] thousands of fast algorithms were constructed [], which were implemented in practically all modern computers, not only as software, but as hardware as well.

A French mathematician and philosopher fr:Jean-Paul Delahaye[12] referred to the Karatsuba method of multiplication as the «one of the most useful results of mathematics».

Works in Number Theory

-- What do you think ? I deleted all expressions which Steven didn't like. Mathtruth (talk) 17:29, 12 May 2013 (UTC)


 * You'll notice above that I said exact text of a relatively small change to the article in the direction you want to take it not a complete rewrite. Provided that there are appropriately independent sources for it (and links aren't trashed) it looks good down to and including the awards. Stuartyeates (talk) 23:43, 12 May 2013 (UTC)


 * I don't understand what you are writing about. All our sources are independent and published in the reputable journals. What do you mean "links aren't trashed". No one from my links or opinions was ever "trashed". What do you mean "relatively small". How many lines? Ok. Let's begin with

Anatolii Alexeevitch Karatsuba (Russian: Анато́лий Алексе́евич Карацу́ба; Grozny, January 31, 1937 — Moscow, September 28, 2008) was a Russian mathematician, who authored the first fast multiplication method: the Karatsuba algorithm, a fast procedure for multiplying large numbers.

Studies and work From 1944-1954, Anatolii Karatsuba studied at the high school № 6 for boys of the city of Grozny and completed his studies with a silver medal[1]. Already in his early years he showed exceptional talents in mathematics, being a young student he solved problems that were given to the students of the last years at school as a challenge[2].

In 1959, he graduated from Lomonosov Moscow State University, Department of Mathematics and Mechanics. In 1962 he got his PhD degree Candidate of Sciences in Physics and Mathematics, thesis «Rational trigonometric sums of special kind and their applications» (PhD supervisor N.M.Korobov), and started to work at the department of Mathematics and Mechanics of MSU. In 1966 he got his Habilitation (Doctor of Sciences in Physics and Mathematics degree), with the thesis «The method of trigonometric sums and the mean value theorems» and became a member of Steklov Institute of Mathematics (MIAN).

After 1983, he was a leading researcher in Number theory in the USSR and Russia. He was Head of Division of Number Theory in the Steklov Institute, Professor of the Division for Number Theory at Moscow State University since 1970 and Professor of Division for Mathematical analysis of Moscow State University since 1980. His research interests included Trigonometric series and Trigonometric integrals, the Riemann zeta function, Dirichlet characters, Finite-state machines, Fast Algorithms.

Karatsuba supervised the PhD studies of 15 students who obtained their PhD degrees (Cand. of Science); seven of them later obtained the second Habilitation degree (Doctor of Sciences). Karatsuba was awarded state prizes and honorary titles.

Awards and Titles

* 1981: P.L.Tchebyshev Prize of Soviet Academy of Sciences * 1999: Distinguished Scientist of Russia * 2001: I.M.Vinogradov Prize of Russian Academy of Sciences

Automata

In 1957 Karatsuba proved two theorems which completely solved the Moore problem on improving the estimate of the length of experiment in his Theorem 8 [3].These two theorems were proved by Karatsuba in his 4th year as a basis of his 4th year project; the corresponding paper was submitted to the journal "Uspekhi Mat. Nauk" on December 17, 1958 and published in June 1960.[4] Up to this day (2011) this result of Karatsuba that later acquired the title "the Moore-Karatsuba theorem", remains the only precise (the only precise non-linear order of the estimate) non-linear result both in the automata theory and in the similar problems of the theory of complexity of computations [].

Fast algorithms

Fast algorithms is the area of computational mathematics that studies algorithms of computing a given function with a given precision using the least possible number of bit operations. Assuming that the numbers are written in the binary system, the signs 0 and 1 of which are called "bits". One "bit operation" is defined as writing down one of the signs 0, 1, plus, minus, bracket; putting together, subtracting and multiplying two bits. Andrey Kolmogorov was the first who set up problems on the bit complexity of computations. The complexity of multiplication M(n) is defined as the number of bit operations sufficient to calculate the product of two n-digit numbers by means of the given algorithm.

Multiplying two n-digit integers by the usual school method "in a column", we obtain the upper bound M(n) = O(n^2). In 1956 A.N.Kolmogorov conjectured that the lower bound for M(n) for any method of multiplication is also of the order n^2, that is, it is impossible to calculate the product of two n-digit integers faster than by n^2 operations (the so called ``Kolmogorov n^2 conjecture). The n^2 conjecture seemed realistic, because in all the previous history people multiplied numbers with the complexity of order O(n^2), and if a faster method of multiplication existed then in all probability it would have been already discovered.

In 1960, Anatolii Karatsuba found a new method of multiplication of two n-digit numbers, now known as the Karatsuba algorithm, for which the order of complexity is M(n) = O(n^{\log_23}) = O(n^{1,58496\ldots}), thus disproving the n^2 conjecture. This result was explained by Karatsuba at the Kolmogorov seminar at Moscow State University in 1960, after which that Kolmogorov's seminar came to an end. The first paper describing the method was prepared by Kolmogorov himself,[5] where he presented two different and not connected with each other results of two of his students.

Later on the basis of Karatsuba's idea[8][9] thousands of fast algorithms were constructed [], which were implemented in practically all modern computers, not only as software, but as hardware as well.

A French mathematician and philosopher fr:Jean-Paul Delahaye[12] referred to the Karatsuba method of multiplication as the «one of the most useful results of mathematics». -- All what is written above right, important and well-sourced. It's impossible to write less in Fast Algorithms shapter, the text will be not inderstandable and invokes remarks if not to define concretely what we means in fast algorithms in the complexity etc. The story of Kolmogorov statement and disproving of this statement is also very interesting. If you will insist, I can add the line where Knuth wrote in his book the Art of Computing programming that the idea of A.A. Karatsuba was quite new, there are no sources that it was ever used before. The presented text is very small if to comptare it with texts of many other mathematicians, not speaking about Steven Jobs. Mathtruth (talk) 11:03, 13 May 2013 (UTC)


 * First, this is not a "relatively small change" to the article as requested above. The problem with making big changes at once is that it is hard to discuss and provide feedback.


 * Second, even at a first glance there are some problems. For example, you wrote:


 * Up to this day (2011) this result of Karatsuba that later acquired the title "the Moore-Karatsuba theorem", remains the only precise (the only precise non-linear order of the estimate) non-linear result both in the automata theory and in the similar problems of the theory of complexity of computations.  A literature search (e.g. on google or google scholar or Web of Knowledge or Inspec) for the term "moore-karatsuba theorem" turns up zero references other than copies of this Wikipedia page and this one article by colleagues of Karatsuba.  Also, calling it the "only precise nonlinear result" in "the theory of complexity of computations" is either badly phrased or dubious, or both.  There are lots of nonlinear results in complexity theory, from bounds on sorting complexity to FFT additions to solution of max-flow problems or linear programming.

Look here: http://lib.mexmat.ru/books/3537/s2 This is a book:Logic. Avtomata. Algoritms Aйzerman MA, LA Gusev, Rozonoer LI etc.. p.412 :the Theorem of Moore-Karatsuba the authors of this book are not students or friends of A.A. Karatsuba. 91.79.207.189 (talk) 18:44, 15 May 2013 (UTC)


 * Later on the basis of Karatsuba's idea[8][9] thousands of fast algorithms were constructed [], which were implemented in practically all modern computers, not only as software, but as hardware as well. This appears to be a shortened version of your argument, above, that all divide-and-conquer algorithms are derived from Karatsuba's ideas. Since the latter is contradicted by the the literature, the shortened version does not belong either.

It's not contradicts to anything, you are not able to present any publication with any FASt "divide and conquer" method before A.A. Karatsuba method from 1960!91.79.207.189 (talk) 15:22, 15 May 2013 (UTC)


 * Fast algorithms is the area of computational mathematics that studies algorithms of computing a given function with a given precision using the least possible number of bit operations. Assuming that the numbers are written in the binary system, the signs 0 and 1 of which are called "bits". One "bit operation" is defined as writing down one of the signs 0, 1, plus, minus, bracket; putting together, subtracting and multiplying two bits.  This article is not the place to promote an idiosyncratic definition of "fast algorithm".    In computational complexity theory, many different abstract machine models are used to quantify algorithm complexity, not just counts of binary-arithmetic operations.


 * We can speak in in some articles about some models which we consider as important: we have supporting sources like Kolmorov and Knuth, you have only your tendentious opinion as always91.79.207.189 (talk) 16:10, 15 May 2013 (UTC)


 * Furthermore, biography articles are not the place to be having these discussions. If you want to argue about complexity theory, go to the computational complexity theory article.  If you want to argue about the origin of the divide-and-conquer idea, go to the divide-and-conquer algorithms article.  If you want to argue about the important theorems of Moore automata, go to the Moore machine article.   The technical material here should only be a short summary of technical material described elsewhere on Wikipedia.  If you can't convince editors in those subject areas, then a biography article is not a backdoor to insert your claims.  — Steven G. Johnson (talk) 20:27, 14 May 2013 (UTC)

We don't want to argue with anybody tendentious, but we don't prevent you to write any your tendentious and unsourced opinions about the origin of divide and coinquer and first fast algorithms, and even about Gauss who, as you believe without any grounds made the FFT before Fourier made FT --- you play UNHONEST GAME here at the Wikipedia pages --- you speak about many sources, but as your sources about Gauss authority you give: 1) two unpublished texts 2) two published texts where it's written that in one Gauss paper are certain elements of the FFT, but not the METHOD!

THis is an unhonest game! You mislead people: you are writing you have many sources supporting your point of view but you haven't. Moreover, for you a paper written by people who have no own algorithms who do nothing in computational math or in number theory has the same weight as a paper written by a classic of science like A.N. Kolmogorov or A.A. Karatsuba. You mislead people --- your sources are worse than ours. But we do not prevent to express you any your opinion on pages devoted to FFT and divide and conquer. Do not prevent us to write an article which absolutely satisfies to all Wikipedia rules: it is well-sourced, and these are sources written by specialists not by people who have no own results in the subject; it's notable and about a very notable scientist it's possible to correct certain places there (and nobody prevents it, the theorem was called by Moore-Karatsuba in 1970 in USSR, we don't know about the present situation there), but in whole in general, the text does not contain any exaggeration, that can not be corrected do not deleting the main lines of the text. 91.79.207.189 (talk) 16:10, 15 May 2013 (UTC)

First of all I ask the adniminstrators to delete from the present text this lien "Karatsuba's multiplication algorithm is an example of what is now termed a divide and conquer algorithm; it was subsequently surpassed in asymptotic performance by the Schönhage–Strassen algorithm." beacuse of the reason that this is created 1) wrong impression about the story of this problem; 2) it's a very subejctive 3) it's unsourced, but supports only the point of view of Steven J
 * About 1) There are many divide and conquer algorithms, but only FAST divide and conquer algoeirhms are valuable, the first FAST method did A.A. Karatsuba, there were no any publications before A.A. Karatsuba did his method. It's true, there are some sources (dubious) wich claim absolutely tendenciously and without any pooves that some other persons did fast Sorting etc algorithms, but anyway it's only one view there are many sources which claim A.A. Kaarstuba did it the first, not only in Russia, in the book by Knuth "The Art of Computing Algorithms" from 1969 it's written that A.A. Karatsuba idea was not known before. And this is a very notavle PUBLISHEd source.

2) This line invokes an expression that the method of A.A. Karatsuba is something not very important, one example of divide and conquer, not the first, not the main, but only "one of", and Schonhage and Strassen did independenly something better that did A.A. Karatsuba. In realty, it's absolutely wrong interpretation which prescribed the brillant result to toher persons. Schonhage and Strassen did some kind of generalization of A.A. Karatsuba method, it's a very important result. but it can be even compared with resul of A.A. Karatsuba by importance. 3) The Schonhage and Starssen algorithm is mostly theoretical result, in practice just A.A. KAratsuba method is implemented and widely used. That is ahy no one source will claim the Schonhage-Strassen method "surpassed" in any quality the A.A. Karastuba method. So this line is dubious, unsourced, expressed only subjective and very unjustice opinion of Steven J about A.A. KArastuba method. I ask to delete it. 91.79.207.189 (talk) This is just a small change --- Stuaryetes!91.79.207.189 (talk) 15:22, 15 May 2013 (UTC)
 * If you do not start assuming good faith, either using IP or using your account, your ability to edit Wikipedia will be limited. Please discuss in a civilized way as your opponents do.--Ymblanter (talk) 16:26, 15 May 2013 (UTC)


 * With regards to the points of the anon commenter (another WP:SOCK?):
 * As amply documented in the divide-and-conquer algorithm page, the consensus in reputable literature (e.g. famous textbooks and other widely cited sources) is that there are indeed many divide-and-conquer algorithms, several of which predate Karatsuba's algorithm (whether you personally feel these claims are "dubious" is irrelevant to Wikipedia policy). Your claim about Knuth is false.  Knuth (TAOCP vol. II, sec. 4.3.3), writes: A similar but slightly more complicated method for doing multiplication ... was apparently first suggested by A. Karatsuba in ... Curiously, this idea does not seem to have been discovered before 1962.  Taken in context, it is crystal clear that "this idea" refers to the algorithm for multiplication, not to divide-and-conquer algorithms in general (which are not discussed or even named as a general idea in that section of Knuth). The existence of other divide-and-conquer algorithms does not mean that Karatsuba's algorithm is not important, but it does mean that it is not the "main" or the "first" divide-and-conquer algorithm (or the first "fast algorithm" period).  Karatsuba described the first faster-than-O(N2) multiplication algorithm, which was indeed an important contribution; I don't understand why this is not enough for you.
 * It is not an insult to Karatsuba to place his work in context by pointing out that Karatsuba's algorithm was later surpassed in asymptotic complexity. (It is unambiguously and obviously true that the Schönhage–Strassen algorithm has better asymptotic complexity than Karatsuba: N log N log log N < Nlg 3, as is amply documented by sources in the Schönhage–Strassen algorithm page.  The Schönhage–Strassen algorithm page also cites several sources explaining that the algorithm is indeed used in practice by several popular libraries for > ~104 digits.  Nor is it clear that the Schönhage–Strassen algorithm is "based" on Karatsuba, since both FFT algorithms and Fourier-convolution ideas predate Karatsuba.)  I'm not wedded to the particular phrasing, but to present these ideas in proper context the presentation should include three facts: first, that Karatsuba was the first to improve upon naive multiplication (an important milestone in computer science!); second, that Karatsuba or its descendents (e.g. Toom-Cook, which is based explicitly on Karatsuba) are still in use today; third, that (rather different) asymptotically faster algorithms were eventually discovered (and are used in practice for sufficiently large sizes).
 * — Steven G. Johnson (talk) 15:19, 16 May 2013 (UTC)


 * It's wrong statement that the FFT ideas predate Karatsuba ideas --- all FFT publications have been after Karatsuba result and never before.

The statement that "thousands of fast algorithms" based on the A.A. Karatsuba is right --- to prove it, it's sufficiently to write in the Google search "Karatsuba like" and you obtain the list of references in thousands of very reputable published papers and books with algorithms based on A.A. Karatsuba idea. There is a very reputable opinion that just the name "divide and conquer" was introduced in the West to not refer to A.A. Karatsuba, because in the time of the Cold War, some people from the West very often practice plagiarism of Russian (and East Europian in general) works (sometimes was and in opposite direction --- say bomb), especially in mathematics and cybernetics. There are no publications with any divide and conquer algorithms before A.A. Karatsuba ---> A.A. Karatsuba COULD NOT use somebody else results when he did his result. After him, all Kolmogorov lectures beginning from 1960 and all publications beginning from 1962, all creators of the FFT, Sorting and other algorithms COULD use A.A. Karatsuba ideas. This is just we wrote. Your claims that some alfgorithms predate A.A. Karatsuba algorithms do not confirm by pulications ( of this algorithms). As for other later text-books and later papers --- this is not a ground, there are many plagiaristic papers and books all around the world.

As about line which must be deleted: 1) on the pages dedicated to famous mathematicians one needs to write only right, but not tendentious lines. Your line that A.A. Karatsuba is "one example" of divide and conquer --- is tendentious. You haven't publications before A.A. Karatsuba result, your opinion is based on the opinion of certain sources that can be plagiaristic and tendentious --- why in general to write it? 2)Why to write that some algorithm surpassed the A.A. Karatsuba algorithm in the text in 3 lines devoted to A.A. Karatsuba? You clearly want to diminish the importance of A.A. Karatsuba income to the science. Your intensions are not honest and clean. Moreover, Schonhage and Strassen used just A.A. Karatsuba ideas both in multiplication and using FFT, which was based on A.A. Karatsuba ideas. You haven't reputable sources (specialists in Fourier analysis) who would write that Gauss made first FT in any form, moreover all dubious sources with this claim appear only 25 years later A.A. Karatsuba result and 20 years later FFT appearing. Please, delete your tendentious, diminishing the A.A. Karatsuba results line. This is only your private opinion, based on your private relation to A.A. Karatsuba.91.79.174.10 (talk) 09:27, 17 May 2013 (UTC) I think there are many sources and many literature (reputable:))!!) which claimes that aliens visited our planet. May be, some of these sources will claim, the alieans know and did the first fast multiplication algorithm and the FFT before A.A. Karatsuba. To prove it, one needs to have publications (of aliens) before 1960 (on our planet Earth). If you haven't them, all sources AFTER --- means ZERO --- NOTHING! You haven't real grounds to claim somebody before A.A. Karatsuba did the first fast algorithm. But We HAVE GROUNDS to claim that A.A. Karatsuba did it.91.79.174.10 (talk) 09:27, 17 May 2013 (UTC)

I read some parts of the discussion above about the FFT and Gauss. I can not understand: StevenJ believes, Gauss was so stupid, he did a method, like the FFT, but didn't understand it? Other mathematicians of the Gold time for mathematics, including great French mathematicians, english great number theorists Hardy etc., they have been also so stupid that didn't notice that Gauss makes a new method like the FFT? All mathematicians including the author --- Gauss --- have been stupid and didn't notice that Gauss invented a powerful method, and must waiting 180!!! years when clever people like Heideman, Johnson and Burrus finally noticed --- Gauss made the FFT!!! Absurd, absurd, absurd! I don't believe that Heideman, Johnson and Burrus wrote that Gauss is the author of the method similar to the FFT. They wrote something else. One nneds to find this paper. Besides, nobody told to Fourier that Gauss already made a form of the FT! And Gauss himslef never told it to anybody and never wrote it!83.149.209.253 (talk) 15:55, 17 May 2013 (UTC)


 * One of the nice features of Wikipedia policy is that we don't need to have or respond to these arguments. I summarized the consensus view of reputable literature on the subject, and we have provided ample citations many times in the relevant pages.  Your personal disbelief is not relevant.  — Steven G. Johnson (talk) 20:25, 17 May 2013 (UTC)

31.23.3.34 (talk) 17:52, 9 June 2013 (UTC)