Talk:Leonhard Euler/Archive 1

Pronunciation
I think it might be handy to add that his name is pronounced OILer, since most non-mathematicians I've met (in Canada) pronounce his name YOUler. (I expect the phonetic spelling makes this clear, but this would help people (like me!) that don't know phonetics.) 65.93.74.130Jordan
 * The IPA spelling makes it sound like someone with a British accent is saying it, Oilah.207.189.230.42 04:58, 11 November 2006 (UTC)
 * I looked it up, and the IPA key appears to be correct given that the last syllable is a reduced vowel. -- Omicronpersei8 (talk) 05:02, 11 November 2006 (UTC)

I've heard some Russian professors pronouncing it as AYELER. I'm not sure if thats a pronunciation error, or if it's correct. Can someone please varify the correct pronunciation (whether it is AYEler or OYEler)? --75.28.154.105 01:46, 15 March 2007 (UTC)

Do you guys have any sources on the pronunciation? The guy was Swiss, and in France they pronounce it the way it looks You-ler. I'm told by German speakers that it's pronounced the same way. --Ruparela 19:11, 5 September 2007 (UTC)

I'm a Swiss German native speaker and I can confirm that the pronounciation stated in the article is correct. --130.82.221.44 (talk) 13:24, 28 December 2007 (UTC)

I have changed the IPA from (which makes no sense) to. The latter represents a pronunciation which is close to what the pronunciation would be in Standard German (roughly like English "oiler"). But it must be said that Euler was from Basel, and in Basel German the initial Vowel would be unrounded, and the final "r" would be a uvular fricative so a pronunciatian like might be more accurate. But then he lived in the 18th century, so who knows what Basel German sounded like then. ph_spaelti (talk) 13:01, 1 March 2008 (UTC)

IPA Pronouncer
In Electrical Engineering school, the professor wrote Euler on the blackboard, yet he pronounced it Oiler. I thought, "Surely he's got it wrong." Nope. It is Oiler. Anyhow, wouldn't it be cool if you could point and click IPA anywhere it occurs in Wikipedia and software would pronounce it correctly? --151.200.238.201 04:34, 11 November 2006 (UTC)

Bad corrections
He is considered (together with Gauss) to be the greatest mathematician ever.

Changed to

He is considered (together with Gauss) to be one of the two greatest mathematicians.

Jerryseinfeld 18:38, 18 Nov 2004 (UTC)

Extending the biography
I've put up a copy of the 1911 Britannica biography for Euler at Leonhard Euler/EB1911 biography. Feel free to wikify and merge into this article... - Fredrik | talk 23:07, 10 Mar 2005 (UTC)

invitation to st petersburg. it said before that catherine the great invited him to st petersburg in 1727, but she hadn't been born then. I have read that she invited him BACK to st petersburg, in 1766. I changed the sentance to read that he had been invited by catherine I, (EB1911 says that as well) but maybe the original author meant to talk about 1766....

Can someone check
Hey, guys, so it is late and I am reading the biographies of the greats... Anyhow, here is a remark that I did not dare inster but if true have place in the article: I have heard Euler had 13 kids (well, they did not have TV at the time) and had to feed them through the production of math papers. As a direct result he is the most prolific mathematician in history to this day. Second is Paul Erdos, who by the way, also has a place on the list of the greatest mathematicians. And Euclid, too. Generally, the whole greatest mathematician deal is a bit dumb. Anyhow. Goof night - and do not forget - CONJECTURE AND PROVE.

Nicky


 * The fact he had a lot of kids wasn't the reason he was so productive, he loved sharing his work with others so they could build on his ideas. He also had a love of teaching.  This is in contrast with another great mathematician, Guass, who was excatly the opposite.  Also, Erdos was more productive than Euler ONLY because he collabed with a buttload of mathematicians ,pretty much all he did was collab, which IMO doesnt really count.  And yes Euler being "one of the greatest" is just an opinion, but its an opinion shared by basically the entire math community.--Hypergeometric2F1&#91;a,b,c,x] 07:03, 20 December 2005 (UTC)

Sudoku?
What? No mention that the man invented Sudoku puzzles? (The Wikipedia entry for Sudoku does not yet mention this alleged fact either).
 * See Talk:Sudoku. &mdash; Matt Crypto 18:33, 29 November 2005 (UTC)

Calculus of variations
Euler also the inventor of Calculus of variations. This should be mentioned.--Nixer 01:10, 13 December 2005 (UTC)

Hollow Earth
The hollow earth article leads to this one, saying this man was a supporter of the idea. However, it makes no mention of it in this article. I suggest it be researched and added.
 * In hollow earth article, no reference is given for the claim that Euler supported the idea and it is even written that the belief in such a support could result from a misunderstanding of his writtings. Thus no sufficient evidences are present to make a mention of an hypothetic support of Euler to hollow erath theory necessary in Euler article. pom 11:00, 30 November 2006 (UTC)

Partition of numbers
EB 1911 has an article on Partition of numbers which relates to Euler. If anyone knows where to put this information please do so.--nixie 05:29, 6 January 2006 (UTC)

"Sir, (a+bn)/n = x, hence God exists; reply!" is false.
Care to give reference?--Sahodaran 05:38, 15 January 2006 (UTC)


 * Perhaps it is a case of lack of reference. The only souce I have seen that quote in is E.T.Bell's biography, and he was known for exaggerating myths and hearsay.  I wasn't the one who put that in the article though...--Hypergeometric2F1(a,b,c,x) 13:19, 19 February 2006 (UTC)


 * It is false- Diderot was an able mathematician- he even wrote a few mathematics papers. Borisblue 02:54, 19 April 2006 (UTC)

Königsberg Bridges
The solution to the seven bridges problem reduced the land masses to points and the bridges to lines (or edges) connecting those points (or vertices). Each point was assigned a "degree" equal to the number of lines that touched it (a point with three lines touching it has a degree of three). An Euler circuit has only points of even degree. This means it is possible to travel each line exactly once without retracing your steps and end at the same point in which you started. An Euler path has exactly two odd vertices. This means that it is possible to travel each line exactly once without retracing your steps, but you will not end where you began. The seven bridges problem is neither an Euler circuit nor an Euler path. Hence, you cannot visit each of the bridges of Königsberg without retracing your steps. I hate to delete other's work. You are welcome to reinsert the above paragraph, but in my opinion it somewhat detract from the ending of the article and clearly belongs to the Königsberg Bridges entry. David Cruise 02:43, 1 February 2006 (UTC)

"greatest"
what's wrong with the statement "He is considered to be one of the greatest mathematicians of all time."? He is, not by some author or other, but universally. "Euler was ranked number 17 on Michael H. Hart's list of the most influential figures in history." That's 17th most influential person, all considered, so he should be ranking rather higher among mathematicians, one would think, in terms of influence. dab (&#5839;) 19:52, 19 February 2006 (UTC)
 * I agree with the statement, I just think anything like that should not be included without an explicit citation (like the one you've provided here, but preferably including the opinions of more than one person, and more authoritative individuals.). Unless explicit, authoritative citations are there, it's better to let the accomplishments speak for themselves.  When stuff like that is in articles without any citation, it encourages the spread of such statements to many other articles (see recent edit warring on Nikola Tesla, for example).--ragesoss 20:02, 19 February 2006 (UTC)
 * It's undisputed. Every math teacher will say it, so what's the use of citing one particular author? Euler ranks in the league of Newton, Einstein, Euclid, Aristotle, or in terms of mathematicians, let's say Al-Khwarizmi, Fibonacci, Gauss, Galois, Goedel. Let's just say any short writeup of the History of mathematics will contain Euler's name. I see your point, though, and I suppose you might refer to Hart's list (and random other authors) in a footnote to this statement rather than under "trivia". dab (&#5839;) 20:07, 19 February 2006 (UTC)


 * Agreed. The whole "argument" is ridiculous: its a non-argument.  No debate needed.  But the real question is, "why Euler"?  Why do people start this with Euler and not Gauss, who has on his wikipedia article such statements as "profound genious"?  I think the answer is that Euler is not as well known outside mathematical circles as the other all-time greats (mainly because of his contribution style and his normal and uninteresting demeanor), and therefore laypeople who come to this article would readily notice such as statement, whereas if they visited Archimedes' article they wouldn't even notice statements of this sort, because they are so used to it being said in the lay-literature and pop-science culture.  Anyway, thats my take.--Hypergeometric2F1(a,b,c,x) 04:27, 20 February 2006 (UTC)


 * Just a side-note, he's actually ranked #77 on the list, not 17. Brutannica 21:03, 26 February 2006 (UTC)
 * doh, sorry, I thought I had half remembered a higher number. Someone must have vandalized the article at some point. We should have the full list at The 100. dab (&#5839;) 21:41, 26 February 2006 (UTC)


 * I've got him as 'most prolific', though I can't remember which book said that. DuctapeDaredevil 21:26, 16 March 2006 (UTC)

Russian
I'm sorry Ghirla, but Euler is not a "Russian mathematician". He lived and worked in Russia, true enough, but he is not an "alumnus of St Petersburg University". He is an alumnus of the University of Basel who received tenure at the University of St Petersburg. He could arguably be described as "Russian" if he was in some way naturalized during his lifetime ("Russian passport"). Do you have any evidence for that? Would he have had to give up his Swiss citizenship for that? (I don't know) dab (&#5839;) 13:47, 26 February 2006 (UTC)
 * I believe you are retrojecting modern concepts into the eighteenth century. Russia was an absolute monarchy; you were subject to the Empress Catherine if you were within the reach of her armies. I don't see why holding an appointment from her should have required that Euler give up his citizenship (which would have been of Basel); John Paul Jones didn't. Septentrionalis 05:36, 19 April 2006 (UTC)
 * I believe you are projecting obsolete language into the 21st century. If for example "presently" meant "immediately" in Shakespeare's day and "soon" today (or similar example), you would not expect the reader to assign "presently" in a statement about Shakespeare its Shakespearean interpretation.  Readers are going to give "Russian mathematician" its modern meaning unless you explain that you're using the term with its 18th century meaning.  --Vaughan Pratt (talk) 10:47, 13 February 2008 (UTC)
 * Euler lived in Russia much longer than he lived in Switzerland. It's illogical to describe him as "Swiss mathematician". At best he's "Swiss-born Russian mathematician". Compare with Isaac Asimov and George Gamow.
 * I don't think that the concept of "citizenship" or "naturalization" existed back in 18th century. We should look at his primary country of residence to decide his "affiliation". --Itinerant1 03:47, 11 November 2006 (UTC)
 * What language did he speak (I do not know myself) out of his preference? I think a better guide to nationality, is what language and culture they practiced, as opposed to where they were born or where they are residing living.  For example:  a person might have spent their lives in multiple countries, like be born in Cradlia, do a tonne of inventions in Universitia, and live out majority of their days in retirement in Paradisia … so what is their nationality?  I think the best idea is to see what culture and language they were most comfortable with throughout their entire life as a whole.  Nonprof. Frinkus 04:02, 11 November 2006 (UTC)
 * This is a good question, I don't know the answer. It seems that his wife was a daughter of a Swiss emigrant, but it's not clear how old she was when she came to Russia. His articles are mostly in Latin. --Itinerant1 04:27, 11 November 2006 (UTC)

e
I can't find annything about e (mathematical constant). 64.198.112.210 17:05, 16 March 2006 (UTC)

Had the same problem. instead of redirecting from Euler, perhaps a disambiguation page would be more in place.

HELP NEEDED
''I have merged Leonhard Euler with Leonhard Euler/EB1911 biography as requested. This merger shows contradictions beetween the versions. The format {xxxx//yyyy} marks such a contradiction. Someone please correct the text. The version after the // is the Leonhard Euler/EB1911 biography version. Anthony Appleyard 09:27, 1 April 2006 (UTC)''

Why Euler's Tomb Date?
Does anyone know why Euler's tomb has MDCCCXXXVII (1837) on it? His dates of life were 1707-1783. Dennis Runde


 * 1837 - is the year when the tomb itself was finished. It was customary back then and many other tombs have similar "discrepancies". --Alextalk 18:45, 4 May 2006 (UTC)

Celebrity?
Someone removed Celebrity template surrounding Euler's portrait, claiming Euler is not a "Celebrity". I pesrsonaly consider him a celebrity among mathematicians and I do find a template very nice and convenient. However, I checked other mathematicians (even Einstein) - those I checked indeed do not have Celebrity template. Except for Gauss. So, for consistency we either What do you think? --Alextalk 18:43, 4 May 2006 (UTC)
 * should remove Celebrity from Gauss or
 * insert Celebrity template for everyone (some don't have pictures) or
 * decide who deserved celebrity status (very complicated task).


 * How about deleting the Celebrity template? How inane.  Isn't anyone deserving of a Wikipedia article a celebrity in some circles?  Tempshill 04:07, 5 August 2006 (UTC)

Most prolific mathematician?
the page for Paul Erdos claims he's the second most prolific mathematician, after Euler. But Euler's page doesn't confirm this distinction, relegating him to "one of the most prolific".

would it be fair for me to change this page to "most prolific" and make the pages consistent, until someone shows otherwise? --Steverapaport


 * it's been 3 months since I suggested this change, and nobody has objected here. I'll make the change now.  --Steve Rapaport 13:19, 3 September 2006 (UTC)


 * Ok now someone has objected.  My best sources are that Euler "wrote 866 books and papers" (no separate count) from Men of Mathematics by E.T. Bell (1937, Simon and Schuster), and An Introduction to the History of Mathematics, 4th ed., by Howard Eves (1976, Holt, Rinehart and Winston).  Extracted here, and that his works will occupy over 75 quarto volumes (not 60) when all finally published (Guinness Book of World Records.


 * Erdos, with 1,475 papers co-authored The Man Who Loved Numbers, might be considered more prolific if you count only papers, but then there's the question of how many of those he actually helped write, versus contributing insight to. There's also the question of whether all those papers (with no books) added together would fill more volumes than the "866 books and papers" Euler wrote.  Euler's own books listed on his Wikipedia page alone cover more than 29 quarto volumes (I counted).


 * I think the "Erdos wrote more papers but Euler more total pages" would be a good guess. Steve Rapaport 07:18, 4 September 2006 (UTC)


 * How many pages precisely? I think we skip the mention of the papers/pages (unless we find a source) and say that by the Guiness book of records he is the most prolific mathematician.Borisblue 20:29, 4 September 2006 (UTC)


 * According to Dunham, the Opera Omnia consists of "over 25,000 pages in all". Fredrik Johansson 21:13, 4 September 2006 (UTC)


 * Hmm - Is this a really serious concern (one way or the other)? 'Prolific' is not a terribly well defined term, I think, and I don't believe it is really a good measure of the value of a mathematicians contribution. I can think of several mathematicians who have published much more than say Riemann, but whose contribution is much less significant. Were all the pages that Euler wrote about 'mathematics' as we understand it now? (Or were some about optics, fluid dynamics and astronomy?) Shall we just say that Euler and Erdos were probably the most prolific mathematicians (so far) and move on? Madmath789 21:36, 4 September 2006 (UTC)


 * My preference is a vague "Euler is one of history's most prolific mathematicians" or, alternatively a cited source: "Guinness book of records lists Euler as the most prolific mathematician". Borisblue 00:39, 5 September 2006 (UTC)


 * If the statement that he is the most prolific is well supported, and it is, there is no reason to weaken it. Fredrik Johansson 05:33, 5 September 2006 (UTC)


 * If Guinness is willing to put themselves on the line, why shouldn't Wikipedia with source from Guinness? I say with a reference to Guinness, "most prolific" is fine.  This also agrees with the long-standing Erdos page which says Erdos is second most prolific following Euler.  --Steve Rapaport 15:52, 5 September 2006 (UTC)


 * Yes, I think the developing consensus is that to declare Euler the most prolific, with a source from Guinness (any objections to that?). I'd prefer to see a better citation that says that Erdos is second though- it doesn't really matter how long that statement has been lying in the erdos page, it still needs to be verified. I'm sure there is a tally of both men's output somewhere. Sorry for being so fussy about the referencing- Euler is being nominated for FA right now, and I wanted to make sure all the major claims in the article were backed up. Borisblue 23:10, 5 September 2006 (UTC)

Pronunciation
The article leads off by saying it's pronounced "ˈɔʏlɐ". I'm sure this is useful for the linguistics majors who read Wikipedia, but for the rest of us, can someone use layman's English to fix this? Tempshill 04:01, 5 August 2006 (UTC)

Merger
The purpose of List of discoveries by Leonhard Euler is to comply with Summary Style. Simply put, discussion of all of Euler's contributions could fill an entire WikiProject, nevermind a Wikipedia article. I intend List of discoveries by Leonhard Euler to be a very complete list of Euler's contributions, and this article should discuss his most important and significant contributions.Borisblue 13:27, 31 August 2006 (UTC)

What a guy!
"Euler had to overcome several tragedies in his second stay" - a fire, the death of his wife, and a fatal brain hemorrhage. What?! How did he "overcome" that last one? I split off his death into a separate paragraph, as I'm pretty sure he didn't. (But if he had, I'd have voted for him as the greatest mathematician of all time.) Clarityfiend 12:45, 3 September 2006 (UTC)

Laplace quote
The translation I've seen most, almost everywhere except in Dunham's book, is "Read Euler, read Euler, he is our master in everything." I think this sounds more accurate. In any case, I'm not sure whether the quote really belongs in the lead section. Certainly, the assertion that it is the "best" way to express Euler's influence is POV. Fredrik Johansson 15:46, 4 September 2006 (UTC)
 * I've removed the "best way" phrasing. Change it if you think your version right- (personally, I think the "master in everything" sounds cooler).Borisblue 02:15, 5 September 2006 (UTC)

Euler Characteristic
It might be of interest to note that the Topology is actually born from the study of the generalization of Euler formula relating the number of vertices, edges and faces of a polyhedron (particularly by Cauchy [A.L. Cauchy, Recherche sur les polyèdres - premier mémoire, Journal de l'Ecole Polytechnique 9 (1813) Cahier 16, 66-86] and Lhuillier [S.-A.-J. Lhuillier, Mémoire sur la polyèdrométrie, Annales de Mathématiques 3 (1861), 169-189]). This generalization defines the so-called Euler characteristic of a surface, of a CW-complex or more generally of a topological space. This is central to topological graph theory and naturally arises from homology. See Euler characteristic for more details. pom 17:09, 7 September 2006 (UTC)
 * Yeah, I think this stuff deserves to be in the article. Put it in. Borisblue 14:14, 9 September 2006 (UTC)
 * Done, but it has to be polished. pom 16:24, 9 September 2006 (UTC)
 * I took some time to write it down after you gave a positive opinion; I do not understand why you simply removed everything afterwards! pom 19:48, 20 September 2006 (UTC)
 * Ok I shrinked to a single human readable sentence. Feel free to change it if necessary. pom 15:32, 23 September 2006 (UTC)

Did Euler actually introduce the Euler Characteristic, or merely the formula $$V-E+F = 2$$ for polyhedra? As it stands, the article seems to me deceptive. Radagast3 (talk) 04:24, 26 April 2008 (UTC)
 * Judging from George Pólya's expository article Guessing and Proving from 1978, it was the latter. It does not appear that Euler considered applying the characteristic to non-convex polyhedra or chain complexes.  Euler may have intended for the formula to apply only to convex polyhedra, but according to Pólya, he did not provide a suitable statement of the theorem and did not supply a valid proof.  &mdash; Myasuda (talk) 05:11, 26 April 2008 (UTC)
 * I'll take that as encouragement to edit the article. Radagast3 (talk) 06:48, 26 April 2008 (UTC)
 * Thanks for your addition to the article. Please provide a citation of the source in a footnote, and then remove the {fact} tag. Especially because this is a WP:Featured Article, it is important to keep the article fully sourced. Thanks again. Finell (Talk) 07:33, 26 April 2008 (UTC)
 * All I did was take out uncited material and added a reference to the genus article. Both theEuler characteristic and genus articles describe the relationship -- I don't think a citation is needed here. Feel free to cut the cross-link, though. Radagast3 (talk) 08:07, 26 April 2008 (UTC)
 * However, in general I think that discussion of Euler's mathematical contribution needs to be handled by careful references to more technical articles elsewhere in Wikipedia. Anything else would make the Euler article either incomplete or HUGE. Radagast3 (talk) 10:49, 26 April 2008 (UTC)

FAC
I'm not sure if the FAC template above is getting obscured- but while there have been a flurry of improvements the past few days nobody has commented on the FAC page. Comments please?Borisblue 14:14, 9 September 2006 (UTC)


 * Well... I'm not ready to support the article yet. I think it should probably have gone through peer review first. - Fredrik Johansson 19:09, 9 September 2006 (UTC)

Feynman reference
Which volume, page and chapter does the Feynman quote come from? (Euler's formula being the most beautiful formula in mathematics) The article says (I-22-10), which I would assume means volume I, page 22, chapter 10; but that chapter is apparently about conservation of momentum? Borisblue 17:51, 16 September 2006 (UTC)


 * It means page 10 of chapter 22. Fredrik Johansson 19:00, 16 September 2006 (UTC)
 * Oh, OK that makes more sense. Borisblue 19:10, 16 September 2006 (UTC)

Referencing
Should we include page numbers with the references? I'd prefer to add them since they make research easier when searching for that little tidbit of information, but I must admit it does make the references section look neater when they're not there. See this vertion for the case when the page number information is removed and the references are merged. Borisblue 03:01, 18 September 2006 (UTC)
 * Good idea to ask others' opinion. As I guess I made clear, I prefer the one-shot reference, especially for references which are not books of hundreds of pages. But I don't know if there is a default solution on Wikipedia. Isaac Newton, Ghandi and Theodore Roosevelt have option "duplicate", Pink Floyd only uses multiple for short articles. In any case, I will go and put the page number for the reference I added a couple of hours ago. Pascal.Tesson 03:54, 18 September 2006 (UTC)

Infobox
I know that some people aren't too thrilled about infoboxes and in general I am one of them. But I just added one nonetheless without completing all fields (like children, name of spouse and whatnot). That makes the infobox tolerably short and in the end I sort of like it. But I won't oppose a consensus to remove it. Pascal.Tesson 18:02, 23 September 2006 (UTC)
 * It's OK. There has been some consensus to remove some fields anyway, as you'll find at Template_talk:Infobox_Scientist. Michael Kinyon 13:05, 24 September 2006 (UTC)
 * I'm not thrilled with it to be honest- mainly because it's a cruft magnet, a lot of users are seeing the infobox as an excuse to include really non-notable and unverified (sometimes outright false) information. Borisblue 15:18, 26 September 2006 (UTC)
 * I'm not thrilled with the cruft either. But the basic idea I find ok. Maybe we could add a comment on the article's source saying "no cruft please". Whoever designed the infobox for scientists is a cruft lover for sure since it includes fields for children, spouse, societies, prizes... I even removed an earlier addition to the Euler infobox which said "Prizes: none". Sigh... Pascal.Tesson 15:25, 26 September 2006 (UTC)
 * Prizes:none? Did they even read the article? Euler won the paris academy prize twelve times! Borisblue 15:33, 26 September 2006 (UTC)

Letter from Ronald Calinger!
I emailed Ronald Calinger, leading Euler historian to review the article and he has this to say:

''Dear Borisblue, ''You have a fine short life. I urge you to include more than mathematics in the beginning comments. You should note his vital work in rational mechanics, astronomy, and optics. He was a mathemaical scientist. There is also the wrong caption under his picture. That is not the 1737 portrait. I would drop the word "arguably" about Euler being the most famous Swiss mathematician. That seems to be beyond argument. I also think it is incorrect to say that Euler's Introductio is the keystone to modern analysis. It is a precalculus text. Finally, Euler was not immediately promoted in Russia in 1727. He was moved from the medical to the mathematical section of the academy.'' Best wishes, R. Calinger

Pascal Tesson's concerns about comprehensieness were valid- I guess there isn't enough material about his non mathematical discoveriesBorisblue 15:30, 26 September 2006 (UTC)

After these various issues get fixed, you might also consider writing to Rüdiger Thiele to get his view. Another useful source of feedback would be the folks who run the Euler Archive. Michael Kinyon 15:50, 26 September 2006 (UTC)

Borisblue, I think it's great that you were able to get his input. Good job. (even though that means more work now!) Pascal.Tesson 20:16, 26 September 2006 (UTC)


 * OK, this looks like a good source on Euler's fluid mechanics- I'm not sure if my university can let me view the full article or not- but I'll try to dig it up. Borisblue 20:35, 26 September 2006 (UTC)


 * There is an entire (contemporary) book devoted to Euler's work on optics Borisblue 20:46, 26 September 2006 (UTC)

Bravo
Hey I just want to thank everyone for making this page so much better over the past year! I am a huge Euler fan and this page looks 10 times better than it did a year ago...its even featured now! Bravo...--Hypergeometric2F1(a,b,c,x) 11:37, 14 October 2006 (UTC)
 * Yeah, awesome job everyone! --Wafulz 17:03, 11 November 2006 (UTC)

Cultural depictions of Leonhard Euler
I've started an approach that may apply to Wikipedia's Core Biography articles: creating a branching list page based on in popular culture information. I started that last year while I raised Joan of Arc to featured article when I created Cultural depictions of Joan of Arc, which has become a featured list. Recently I also created Cultural depictions of Alexander the Great out of material that had been deleted from the biography article. Since cultural references sometimes get deleted without discussion, I'd like to suggest this approach as a model for the editors here. Regards,  Durova  15:58, 18 October 2006 (UTC)
 * Hmm.. now that I think of it, there really aren't many cultural depictions of Euler. As opposed to the Isaac Newton article I had been working on, where people kept on adding info about his portrayals in anime, movies etc. As brilliant as Euler is, I guess he's just a really boring guy. Borisblue 16:02, 18 October 2006 (UTC)


 * Any cultural references belong in this article. They do not warrant a separate article in this case. Finell (Talk) 16:26, 18 October 2006 (UTC)

Euler sums/summation formula
There are no mentions of either the concept of an Euler sum (e.g. 1/(1-x) for 1+x+x^2 ...), or of his wonderful summation formula (for sums with alternating signs). Why not? They are hardly insignificant.

Hair Commodore 19:22, 31 October 2006 (UTC)
 * Those two formulas were actually discovered by Isaac Newton (special cases of his generalized binomial theorem). I think this is what is meant by Euler sum: - and that formula doesn't even have its own Wikipedia article yet. Borisblue 21:13, 31 October 2006 (UTC)


 * No - what I meant, and should have said more clearly, relates to Euler's summation method (for series with alternating signs), and its ability to give "correct" answers even when the sum in question is not (strictly) convergent. There are other relations to it too - "Borel convergence" comes to mind - but my ideas are slightly too hazy at this moment to be more specific. Hair Commodore 20:04, 8 November 2006 (UTC)

As of now, there exist articles on Euler summation and Borel summation. Melchoir 07:30, 17 March 2007 (UTC)

Euler's thesis advisor
Not sure if this constitutes a WP:RS but the Mathematical Genealogy page seems to think that Bernoulli was Euler's advisor. . JoshuaZ 07:32, 3 November 2006 (UTC)
 * Given that everything else in the article is vouched for by peer-reviewed academic sources and books by academic publishers (okay, plus one guiness book of records entry), I am reluctant to admit a website. I've done a lot of research on this topic in the process of writing the biography material, and I didn't come across any academic source that says that Johann Bernoulli was any more than a tutor. Borisblue 07:39, 3 November 2006 (UTC)
 * Being a website doesn't make it necessarily less reliable. But I agree that it isn't clear that they are using the term in the same way nor is it clear where the project got it as a source. JoshuaZ 07:43, 3 November 2006 (UTC)
 * The thing is, given how prominent a mathematician Euler is, and how thoroughly researched his life story, I would think there would be some mention of Johann Bernoulli as Euler's doctoral advisor if that was true. This is the main reason I am skeptical. I realize that this is an argument by lack of evidence, but I would be reluctant to put it in the article just given the math genealogy page source. Also, given the depth and quality of sourcing that is available for Leonhard Euler, I don't think it is unreasonable to demand rigorous academic sources for every claim on this article. Borisblue 07:50, 3 November 2006 (UTC)
 * Good point. So we should leave it out unless better sourcing can be found. JoshuaZ 07:52, 3 November 2006 (UTC)
 * It don't think the math genealogy web actually checks the validity of the informations sent to him. pom 17:09, 9 November 2006 (UTC)
 * Isn't the field the scientist's "Academic Advisor", not necessarily "Ph.D. (Dissertation) Advisor"? Also, shouldn't there be symmetry, insomuch as Johann Bernoulli has Euler listed as a "Notable Student"?  (Similarly, shouldn't Joseph Lagrange be listed as a "Notable Student" of Euler's, as Lagrange has Euler listed as his "Academic Advisor" (albeit with a caveat).) Alan smithee 01:02, 25 May 2007 (UTC)
 * The sourcing standards for a featured article are more rigorous than normal. Unless the math genealogy website provides a source for where their claims come from I don't think their information should be accepted. Borisblue 02:59, 15 October 2007 (UTC)

I think I can help here. Notice the infobox field is called "Academic Advisor" (not PhD advisor). The idea is to insert PhD advisor in preference. However, the nature of an Academic genealogy is slightly flexible because PhDs historically were not the same as they are today. So in the absence of a formal PhD advisor, the idea is to substitute it with the person who closely tutored or mentored the student. In the case of Euler it is clearly Johann Bernoulli who played the mentoring role. QueenAdelaide (talk) 22:36, 21 December 2007 (UTC)

Image caption
The caption under one image includes the following: "Note the problems of the right eyelid and that Euler is clearly suffering from strabismus." I've seen over a 1,000 patients with strabismus, but I can't tell for a certainty from this painting that Euler had it. Other images seem to confirm that he had ptosis of the right eyelid, which can give the false appearance of a strabismus (i.e. pseudostrabismus). Euhler may very well have had strabismus due to amblyopia in his right eye, but I can't find any reference to confirm this. -AED 02:10, 11 November 2006 (UTC)
 * The citation is in the footnote. Historia Mathematica is certainly a reliable source, so i reverted the original wording. Borisblue 05:28, 11 November 2006 (UTC)
 * The citation refers to the fact that a cataract destroyed the vision in his left eye; not that he had strabismus. -AED 16:59, 11 November 2006 (UTC)
 * The citation refers to this particular portrait and says that it portrays Euler with strabismus. Borisblue 17:23, 11 November 2006 (UTC)
 * The portrait is discussed on pages 154 to 155 of "Leonhard Euler: The First St. Petersburg Years (1727-1741)"? -AED 19:12, 11 November 2006 (UTC)
 * Yes it is. Calinger talks about Euler's deteriorating eyesight condition, and then, on a tangent refers to various portrait depictions of Euler and says that this particular one demonstrates strabismus in the right eye. Borisblue 19:17, 11 November 2006 (UTC)
 * I don't have access to the publication. Are you able to directly quote what he states regarding strabismus and the eyelid problem? I may be able to help with the wording in the article. I have similar concerns with: "The left eye looks healthy, as it was a later cataract that destroyed it rather than gradual deterioration." This implies that eyes that experience "gradual deterioration" look unhealthy, which is not generally true. -AED 21:28, 11 November 2006 (UTC)
 * I'll make a trip to the library in a few hours with the quote. 21:59, 11 November 2006 (UTC)
 * Two portraits of Euler provide fundamental information on his medical history. His first known portrait, by a cousin named Johann George Brucker which dates from 1737, shows no detectable eye malady. Brucker paints a bright, confident and seemingly playful man. A portait from 1753 by Euler's Basel colleague Emmanuel Handmann gives close attention to the eyes. Handmann details problems with the upper lid and a condition of strabismus in the right eye. The right eye is not yet totally blind, which suggests some partial remission in its condition. The left eye has a strong dark pupil and no special deterioration. A later cataract, not constant deterioration dating from 1738, probably most harmed Euler's left eye.  Borisblue 22:18, 11 November 2006 (UTC)
 * Thanks for your efforts. I didn't mean for you to go terribly out of your way, but I appreciate it. One would conclude from reading the Wiki article that Euler definitively had strabismus; however, the only evidence for that finding is what Calinger believes Handmann was "detailing" in the 1753 portrait. It might be a bit clumsy to state "Calinger states...", but it should be reworded to reflect that this is not a commonly reported view of his ocular status. Maybe something like... "Euler is portrayed with problems of his upper lid and it has been suggested that he had strabismus." Or... "This portrayal of Euler indicates problems of the upper eyelid and strabismus in the right eye." Even if he had strabismus, whether or not he was "suffering" from it is not clear. -AED 23:46, 12 November 2006 (UTC)
 * Well you're the optometrist, and I do think the "This potrayal of Euler..." wording is better. But one thing I have to note is that these aren't Calinger's own opinions, but rather he is endorsing the position of an optometrist named René Bernoulli (not sure if he's related to the mathematician). So Rene Bernoulli said... is better than Calinger said... should we decide to go that route. Borisblue 05:28, 13 November 2006 (UTC)
 * Thanks for the info. FYI: Here is a link in which another ophthalmologist comments on Bernoulli's work (which he describes as a "comprehensive review of all the existing medical reports, documents, and portraits" of Euler). The ophthalmologist doesn't mention strabismus, but suggests that Euler's right eye was probably shruken (i.e. phthisis bulbi) which would account for the lid changes. This does seem more likely to me, but I've never seen the portrait close-up nor have I read Bernoulli's "Leonhard Eulers Augenkrankheiten" in Leonhard Euler 1707–1783. Given that Wikipedia is to reflect what is verifiable and not necessarily what is true, perhaps some mention of Bernoulli is in order. What do you think? -AED 22:46, 13 November 2006 (UTC)
 * Hmm, that's a good source, thanks for digging it up. The letter seems to have been in response to an article on blind mathematicians, which might be worth looking into. I think you can word the changes better than I can. Borisblue 23:05, 13 November 2006 (UTC)

Re: "article on blind mathematicians". I don't think I would be able to read it even if I had access to it! Regarding the right eye, I just noticed that you have already changed the wording of the caption. It looks good to me. I don't know if it's appropriate to add the speculation of phthisis bulbi on the strength of one letter to the editor. Regarding the left eye, I think I would suggest: "The left eye, not yet affected by a cataract, appears normal." I think this is consistent with the Calinger cite and takes into account comments from the aforementioned link that it may not have been entirely healthy in 1753. Should the article state that he had cataract surgery in 1771? -AED 23:24, 13 November 2006 (UTC)

Vandalism or Fact - "child molester"?
This could be a large embarrassment for Wikipedia, in how a featured article might accidentally been vandalized with this "Leonhard Euler is a child molester (pronounced [ˈɔʏlɐ], that is, Oiler)", or is it indeed a fact that should be displayed so centrally? Acts like that against children is unnatural, awful and quite a shame, though many celebrities have quite possibly molested children, from author Lewis Carroll to Islamic Prophet Muhammad. Will we be bringing everyone's potential skeleton out of the closest in bold like this with no references ... or is this a mistake (oops).
 * It was IP 71.6.30.178 that originally did the edit I speak of above, in my question. Nonprof. Frinkus 02:55, 11 November 2006 (UTC)

Vandalism
I'm pretty sure that Euler didn't write a paper about Fig Newton.

Gregbard

What is factorial zero?
In the first power series it begins...

$$e = \sum_{n=0}^\infty {1 \over n!} = \lim_{n \to \infty}\left(\frac{1}{0!} + \cdots + \frac{1}{n!}\right)$$

Can anyone direct me to what $$0!$$ is and what value $$\frac{1}{0!}$$ has?

--81.151.13.200 14:27, 11 November 2006 (UTC)


 * See the article factorial. Fredrik Johansson 14:28, 11 November 2006 (UTC)
 * That value is 1, if you're too lazy to click the link :) Borisblue 17:25, 11 November 2006 (UTC)
 * Uhh no 1/0 is infinite since 0! = 0....get your math right Penfish 01:14, 20 November 2006 (UTC)
 * Actually 0! is equal to 1. By the way, "get your math right" is not exactly a civil comment, especially when you're wrong. Pascal.Tesson 02:50, 20 November 2006 (UTC)
 * Second that; 0!=1 and the rest. Ehusman 03:02, 20 November 2006 (UTC)
 * Nor is 1/0 infinite. 71.52.4.237 05:38, 12 January 2007 (UTC)

Here's a derivation of 0!.

For any n, n! = (n+1)!/(n+1), e.g. 5! = 6!/6 and 12! = 13!/13. Therefore 1! = 2!/2 = 1, and 0! = 1!/1 = 1. Meltingpot (talk) 17:15, 13 January 2008 (UTC)
 * Simpler is just to think of n! as the product of the list of numbers from 1 to n, having n numbers in the list. 0! is the product of the list of length 0, or empty list, which is 1 for the same reason as the sum of the empty list is 0; in both cases it is the unit associated with the respective operation, namely what you would initialize the accumulator to before accumulating the members of the list, whether multiplicatively or additively.  --Vaughan Pratt (talk) 11:00, 13 February 2008 (UTC)

Red Link!
There is a red link, namely Princess of Anhalt-Dessau, in todays featured article. Does that reflect badly on wikipedia or what. TommyStardust 15:45, 11 November 2006 (UTC)
 * No. If anything, it'll encourage people to create articles on the topic. The Supreme Court of the United States article had several red links, particularly for court cases. --Wafulz 17:03, 11 November 2006 (UTC)

Contributions to Mathematics, Analysis
The current version has Euler's summation for π^2/6 twice. This is unnecessary, and I have removed the first one, as the second summation also includes an explanation of where the problem comes from.

Lifthrasir1 20:20, 11 November 2006 (UTC)
 * good, thanks. Borisblue 20:55, 11 November 2006 (UTC)

That thing on his head
I've seen the Emanuel Handmann portrait many times, and I'd like it, if it could be done, for a little note to be put on the caption of what the hell is on his head?! I wonder every time I see that picture! X_X.
 * Lol, yeah, I have no clue what that is. Thoughts? Borisblue 01:58, 12 November 2006 (UTC)


 * I think its just traditional European academic garb. This is similar to the funny hats that Gauss is pictured wearing.  This is just a guess.  Regardless, Euler is the man.  Do not question the Euler.  He could wear women's panties on his mighty head and it would be awesome, and all of the other lesser mathematicians would copy him and wear panties on their heads.--Hypergeometric2F1(a,b,c,x) 07:51, 12 November 2006 (UTC)

It's his laundry. —Centrx→talk &bull; 02:41, 12 November 2006 (UTC)

Very Limited training in philosopy
This article says that he had very limited training in philosophy (which is why Fredrick had disdain for him), and yet the same article says that he received a masters in philosophy, by camparing the (admittedly mathematical) philosophy of descartes and newton. While he may not have been profoundly talented, a masters degree is generally considered ample "training".
 * Hmm... good point. That's the problem with wiki articles that are constructed in fragments. Borisblue 19:27, 12 November 2006 (UTC)


 * To my knowledge, Fredrick wasn't chummy with Euler because Euler was a staunch Calvinist and not a Deist or Atheist as were most of the court intellectuals in his salons, such as Voltaire. Moreover, Euler was aloof and disdained much of the "court politics" and maneuvering (this follows from his religious leanings and his personality).


 * Euler had a doctorate, was extremely well educated in every subject of his day, and could probably be considered a polymath. His knowledge of philosophy wasn't the issue here, it was more of a personal and political issue.--Hypergeometric2F1(a,b,c,x) 10:50, 6 December 2006 (UTC)


 * That actually sounds right, though a lot of the sources brush it off by saying Euler was too "unsophisticated". I think the "limited training in philosophy" line came from Men of Mathematics, not exactly a paragon of rel:iability. Borisblue 03:30, 7 December 2006 (UTC)