Talk:Bernhard Riemann/Archive 1

extraordinary to ordinary
"He was promoted an extraordinary professor at the University of Göttingen in 1857 and became an ordinary professor in 1859." I would like an explanation of why he went from extraordinary to ordinary. This sentence makes it seem like that's a promotion! -- Michael Currie, 29 Aug 2004
 * I don't know what the case was but I interpret this sentence that from a temporary job he deserved a regular one. I don't see a reason to change it. helix84 00:31, 5 October 2005 (UTC)


 * "Ordentlicher Professor" (ordinary professor) is/was a more senior grade of university professor than "Außerordentlicher Professor" (extraordinary professor) in German-speaking countries (these titles are defunct in Germany now but AFAIK are still used in Austria) Tschild 11:12, 21 December 2005 (UTC)

Mystery Finally Solved

 * "All of the forces were just effects caused by the crumpling or warping of hyperspace." This is the final answer. The world must be satisfied with this metaphor and is thereby excused from further thinking about the nature of physical dynamics. Of Course! It's merely wrinkled hyperspace!
 * "The metric tensor held the secret to the unification of physics." Now, at last, we know that all natural dynamics are described by Riemann's metric tensor. That wasn't so difficult after all, now was it?. One wonders why it took so long for humanity to arrive at this simple and easy result.Lestrade 03:07, 18 February 2006 (UTC)Lestrade

Removal of spirited language
In two same session edits Lestrade has edited out some text that I personally had found very stimulating, being new to the topic of Riemannian geometry. Since I was disheartened to see these edits and because I feel that the deleted text would have an inspirational value (if they are in fact accurate) on others who are easily discouraged by mathematics I wish to suggest that the following passages be reinstated.

In connection with a lecture Riemann delivered in 1854 this sentence was deleted: "It was, without any doubt, one of the most important public lectures in the history of mathematics."

Then Lestrade, citing POV infraction. deleted this: "Like many of the most beautiful and fundamental theories of physics and mathematics, such as $$E = m c^2 $$, Riemann's great lecture is very easy to understand." and "this theorem is very easy to analyse".

While NPOV is important, it ought not get in the way of allowing encouraging language relating to the assimilation of advanced technical material when (and if) the statements in question are in fact accurate. From Lestrade's user page I cannot ascertain whether he/she might seem to have any mathematical skills making him/her suited to determine that the statements are factually incorrect. If the ubject had been of a not so technical nature I would be much more inclined to go along with the rigorous policy interpretation wielded in this case.

I feel the deletions were unwarranted and would like to see one, two or all three reverted unless some information that they are inaccurate appears. meco 20:09, 22 February 2006 (UTC)


 * Meco, it seemed to me that calling a lecture, "without any doubt, one of the most important lectures in the history of mathematics" was the result of a subjective, personal judgment. Also, to call lectures and theorems "easy to understand" and "easy to analyze" is likewise one man's opinion. It is my subjective opinion that encyclopedia articles should express views that are agreed upon by general convention and are close to being objective. Your judgments may be correct, but they seem to be your own valuations. If you think that they are not mere enthusiasm, then you can put them back, or I will do it for you.Lestrade 20:28, 22 February 2006 (UTC)Lestrade


 * I'm not competent to evaluate their degree of unbias. All I know is they triggered within me an eagerness to go deeper into the matter. That is undisputably good. In a way acting as a heuristic. We can await other opinions on this. Perhaps a rewrite of said excerpts would help. meco 09:40, 23 February 2006 (UTC)


 * I'm a huge fan of Riemann, and I vote to leave them out. Such comments can have the opposite effect as well.  If you browse through Wikipedia and read over and over that this and that is "without any doubt, one of the most important" something or others, you tend to shirk away from it as an overly obvious ploy for attention.  These statements are biased opinions and add no value to the article.

Metric tensor illustration
I like the picture, but I'm not sure it's 100% clear when taken together with the text accompanying it, which states that you need ten numbers to describe the space. The diagram has 16 separate gij components. Those in the know understand the symmetry involved but it's not immediately apparent as it currently stands. (I don't know whether it's easiest to fix it in the diagram at the loss of precision about the ordering of indices, or in the text with a bit of extra explanation.) --Bth 14:44, 31 March 2006 (UTC)

Page rendering problem in Firefox 1.5.0.7 browser
I don't know if this is the proper place to say this, but I'm being bold ;-)

At full screen width, the last two lines under the paragraph "Higher dimensions" are displayed on my browser as:

" ... the properties of a manifold, no matter how distorted it is. This is the famous metric

tensor."

The last word "metric" is covered by the diagram on the right titled "Riemann metric tensor." If I narrow the window width of the browser, one line still goes behind the diagram at its top, but the following lines 'wrap' properly and end just to the left of the diagram. I have no idea offhand if it's a problem with this article only (and thus fixable with some sort of editing), with Firefox (I'm running the latest, 1.5.0.7), or what. I just noticed it and can't offhand think of how to figure out whose problem it is.

I've made a couple of .jpg screen shots of this if anyone wants/needs to see them. --benb 04:21, 24 September 2006 (UTC)

Image caption
The image caption below Riemann's picture says "Bernhard Riemann, 1868", yet according to the text, he died in 1866. Any explanations? Oekaki 20:24, 5 July 2007 (UTC)


 * Hi Oekaki, I added the caption to the image (already on page) when putting the infobox together.


 * My research behind the image was not particularly in depth at the time. Basically the image was (is) stored in Wikimedia Commons with a link to a fuller version. I followed this link here: Wiki Riemann Full Image. Zooming in on the image the date at the bottom appears to be 1868, which I put into the caption.


 * Following your query I have looked further to try and identify the original source for this image. I've not found the original but there are images, with the wider caption, present on these sites: Lueneburg University and Schiller Institute. Both of these show, by my reading, a 1863 date for the image. I'll amend this article caption to show that date.


 * Of side note may be that there is a defaced version of Riemann's image, which can be seen here: Math Planet (Google Cache).


 * A similar image to that used here is in an Encyclopaedia Britannica article. This also references a 1863 date - it is similar but not quite the same as the image used here. See in particular the downward angle of Riemann's glasses and bow tie.


 * Further comment welcomed --- Asperal 22:11, 5 July 2007 (UTC)


 * Thanks for the explanation and the correction! --- Oekaki 19:47, 6 July 2007 (UTC)

Date of death
I have seen sources conflict on the date of Riemann's death. One group (including St. Andrews, Britannica) give a date of July 20th.

However the New Catholic Dictionary and a Dedekind transcribed document quotes June 20th. The latter document includes, on the very last page, a claimed copy of the text on his gravestone - stating (my trans. to English) died in Selasca 20 June 1866. - assuming I have interpreted the German correctly. Please correct me if I have misunderstood either text or context.

Is anyone able to confirm the correct date? --- Asperal 22:39, 5 July 2007 (UTC)


 * I think July 20th is the most probable. The text on the grave in the document by Dedekind may have been transcribed wrongly, because it says in the same document (last page, line 6) that Riemann was still alive on June 28th. Perhaps it's worthwhile to see the original. -- Jitse Niesen (talk) 21:14, 6 July 2007 (UTC)


 * Just beat me to it. I've located an image of the stone on the, aptly named, findagrave.com website. A link to Riemann's stone is here. The date is shown clearly as July so no changes to be made to the article. --- Asperal 21:33, 6 July 2007 (UTC)

WikiProject class rating
This article was automatically assessed because at least one WikiProject had rated the article as start, and the rating on other projects was brought up to start class. BetacommandBot 03:49, 10 November 2007 (UTC)

Multiple Grammar Changes
Hi all. I just wanted you to know that I'm not a troll. I just saw some grammar that could be better. Sorry for the multiple edits in a row. Monkeypox37 (talk) 06:09, 23 November 2007 (UTC)

Middle life
I have no biographical material on hand, so I would like to ask those who know it better: In the following:

"In high school, Riemann studied the Bible intensively, but his mind often drifted back to mathematics. He even tried to prove mathematically the correctness of the book of Genesis."

1. What do we mean by "high school"? Do we mean "Gymnasium"?

2. "To prove mathematically the correctness" - What exactly does that mean? What does "correctness" mean? Should it read "consistency"? (I.e. what exactly was he doing?)

Thanks. Hillgentleman (talk) 23:38, 7 December 2007 (UTC)

Riemann Hypothesis Proof
I saw the following line in the section "Later Years."

''This haste for a sick man may have hastened his end. When she heard of his death, his housekeeper at Göttingen started to throw out the papers in his study thus possibly destroying a proof of the Riemann hypothesis. No one else has yet proved it and another paper suggests that he had at least the bones of a proof''

I understand Riemann is a genius, but this seems to be pretty far fetched. Right now, only special cases of the RH have been proved, and with considerable work. Furthermore, the only proposed "correct" approach is the one recently outlined by Connes. Even then, it's only seen as the correct direction one should head, not a proof itself.

The source of the original comment isn't particularly credible in my opinion. Popular science books tend to sensationalize and distort facts beyond measure. I think it's best that it is removed from the Riemann article. —Preceding unsigned comment added by 99.189.253.18 (talk) 02:21, 28 March 2009 (UTC)

I accept that I may have gone too far the first time but I think Du Sautoy is a better mathematician than this comment suggests. So I have toned down the entry a bit and hope that this will be acceptable. I really do think the destruction of these papers is a bit like going into Leonardo's workshop after his death and burning some of the partly completed paintings. Innocently done but a tragedy all the same and notable enough to be worthy of inclusion. Budhen (talk) 14:46, 11 September 2009 (UTC)

Trigonometric series
The article references trigonometric series that are not Fourier series, but trigonometric series directly refers to Fourier series. Is there a reason? As a note, I have not entirely read the Fourier series page, but still...it seems a little suspect. JustPlainUncool
 * Agree. The trigonometric series article is not very informative regarding this. Also, the rest of that particular sentence seems rather fuzzy. This article certainly needs more references.5.151.82.6 (talk) 04:34, 10 November 2012 (UTC)

Speculation
Speculation about any lost insights of Riemann's is a waste of time. — Preceding unsigned comment added by 86.148.22.3 (talk) 16:39, 30 June 2012 (UTC)

This article seems clearly to satisfy the criteria for a C-class quality mathematics article. I'm adjusting the rating for mathematics; I suspect the others are outdated, as well, and should be reconsidered. -Bryanrutherford0 (talk) 03:17, 18 July 2013 (UTC)

Riemann's inaugural lecture
The following statement in the article should be supported by some evidence. When he finally delivered his lecture at Göttingen in 1854, the mathematical public received it with enthusiasm My recollection is that the lecture was kept private by Gauss and only became public after the deaths of Gauss and Riemann when it was published by Dedekind, 14 years after the lecture, along with other manuscripts of Riemann. Even then it was slow to become well known. Beltrami immediately took it up in its non-Euclidean geometry interpretation but his work went unnoticed too.JFB80 (talk) 17:02, 27 November 2010 (UTC).
 * LATER: The text has been changed to say Riemann's lecture was received with enthusiasm when finally published in 1868 (following the remark of Kline, Mathematical Thought vol.III p.896). My recollection though it that it was only slowly recognized.JFB80 (talk) 21:27, 10 September 2011 (UTC) JFB80 (talk) 20:06, 18 July 2013 (UTC)

Mental Calculator ?
Is he a verified mental calculator from verified sources?--Iamnofool6 (talk) 00:30, 12 February 2014 (UTC)
 * The subject is too fatuous to be worth studying or mentioning. — Preceding unsigned comment added by Smith9smith9smith9 (talk • contribs) 11:19, 14 September 2014 (UTC)

Is it similarly important that he was a Christian as that he was a mathematician?
I think he is notable because he was a mathematician rather than because he was a Christian. So why the article empathises the both in the lead as equally important?--2A02:2168:83F:8280:0:0:0:2 (talk) 00:15, 14 October 2014 (UTC)
 * I would agree that the edits by place disproportionate emphasis on Riemann's religious faith.  It does not need to be mentioned in the article lede. &mdash; Myasuda (talk) 01:51, 16 October 2014 (UTC)

After Laugwitz
The page says: "After Laugwitz, automorphic functions pop up for the first time in an essay about the Laplace equation on electrically charged cylinders." One might get the impression that Laugwitz came before this essay. However, the "after" should apparently be changed to "according to", and the sentence apparently refers to Laugwitz's biography of Riemann, which is not listed on the page. Odd. Tkuvho (talk) 13:58, 13 November 2014 (UTC)


 * Fixed! Please let me know of any other errors. Thank you.Brirush (talk) 17:47, 13 November 2014 (UTC)

Metric tensor
I've reverted a minor edit made in good faith by another user. Subsequent to this however it occurred to me that maybe this was an erroneous revert, as it is only when one considers the metric tensor together with the Levi-Civita connection that one truly fully describes a Riemmanian geometry. Perhaps a better way of handling this might be to point people to the axioms of what it means for a differentiable structure to be endowed with a Riemannian Geometry (in a similar vein to Manfredo do Carmo's excellent book on the matter). Though as this is a biographical article this is probably best handled by a link to another wikipedia article instead.RogueTeddy (talk) 06:07, 11 July 2015 (UTC)

the translation of his epitaph seems unnecessarily muddled and cryptic: Those, who love God, all things must serve to its best manner.[5] "English Revised Version romans 28:8 And we know that [to them that love God all things work together for good], even to them that are called according to his purpose." evanherk 2001:982:7A85:1:D84E:2792:2900:8CAF (talk) —Preceding undated comment added 07:56, 30 April 2016 (UTC)

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Speculation
Remarks about the possible loss of deep insights are speculation. Readers of Wikipedia can speculate for themselves, without any help from us. — Preceding unsigned comment added by 86.157.230.86 (talk) 13:09, 11 December 2016 (UTC)

Riemann has done much more
The article barely touches on Riemann's mathematical contributions! Riemann's most important contributions are in the following areas: complex analysis/geometry (holomorphic functions of one variable and complex manifold (Riemann surface)), algebraic geometry (his work on abelian integrals and birational geometry), riemannian geometry, number theory (modular forms and Dirichlet series), analytic number theory (zeta function), topology (definition of manifold and Riemannnian manifold; as a forerunner, along with Betti, to Poincaré), PDE (equations of evolution), harmonic analysis (Fourier series; btw, Riemann integral is really a (unimportant) byproduct and Riemann himself consider this "Riemann integral" as long wellknown to others (e.g. Cauchy already defined definite integral that way, not essentially different from that given by Riemann) and he just spare a short section on it for review). I shall work on this article when I have time. NOt recently though. Riemann is just so great that he deserve a better article; a better one even than the entry in DSB! — Preceding unsigned comment added by 42.244.62.237 (talk) 07:29, 11 March 2017 (UTC)
 * If you haven't read them already, there are some capsule summaries (I wrote most of them) of Riemann's primary publications at List of important publications in mathematics. They can serve as a starting point for a more detailed look at Riemann's accomplishments in this article. &mdash; Myasuda (talk) 13:23, 29 March 2017 (UTC)

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