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The point of this question is to compile a list of theorems that don't give credit to right people in the sense that the name(s) of the mathematician(s) who first proved the theorem doesn't (do not) appear in the theorem name.

For instance the Cantor Schröder Bernstein theorem was first proved by Dedekind.

I'd also like to include situations in which someone conjectured something, didn't prove it, then someone else conjectured the same thing later, also without proving it, and was credited with having first conjectured it.

Similar unfair things which I didn't remember to include might also be considered.

Some kind of reference is appreciated.

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Maybe this should be made a community wiki? –  Shuhao Cao Jun 3 '13 at 20:06
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I learned a while back that you need a mod to make a question CW (but not an answer). –  Ataraxia Jun 3 '13 at 20:07
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This has been discussed before: here and here and here. –  vadim123 Jun 3 '13 at 20:14
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Note that you can now buy your own theorem. –  Calvin Lin Jun 3 '13 at 20:17
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Not only theorems: after being so dumb as species as not taking almost into consideration half of our members in science, there are several women who had been snubbed even very reciently. Take a peek to news.nationalgeographic.com/news/2013/13/… . This is annoying, deeply unfair and can push women further away from science. –  DonAntonio Jun 3 '13 at 21:52

20 Answers 20

Wikipedia has an article on everything: List of misnamed theorems.

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Obviously this list is incomplete without Stigler's law of eponymy, stipulating that no scientific discovery is due to the person it is named for, and which, according to Stigler, is due to Robert K. Merton.

http://en.wikipedia.org/wiki/Stigler%27s_law_of_eponymy

[I know this is not a theorem. We have "eponysterical". Has anyone coined "ironymous" or "erronymous"?]

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Counterexamples: Galois group, Noetherian ring/module, and Artin $L$-function. Those concepts are aptly named for the person who isolated their essential defining feature. –  KCd Jun 3 '13 at 23:53
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@KCd, Good points---I did say it wasn't a theorem! Laws can be difficult to enforce. That's why I prefer theorems: they enforce themselves. –  S123 Jun 4 '13 at 1:29

L'Hospital's rule was popularized by him but proved by Johann Bernoulli. Supposedly he paid off Bernoulli to keep quiet.

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And usually L'Hospital gets all the credit instead of L'Hôpital. –  WimC Jun 3 '13 at 21:09
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Which is not at all wrong since the circumflex just denotes a left-out 's' from old French spelling. –  Gregor Bruns Jun 3 '13 at 23:09
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L'Hospital spelled his name thus. L'Hôpital is due to modern(ish) spelling reform. –  wnoise Jun 3 '13 at 23:12
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The last sentence ("Supposedly he paid off Bernoulli to keep quiet") is fine if the intention is to be funny, but the truth is that L'Hospital hired Bernoulli to teach him calculus, and it was part of the contract that L'Hospital could publish what he learned in a book. And he did. And got the credit. That's all. –  ShreevatsaR Jun 4 '13 at 6:18
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L'Hôpital really did as much as you could expect in giving Bernoulli credit for the work in the textbook. The miscredit is to due to all but L'Hôpital. –  Ragib Zaman Jun 4 '13 at 13:32

A proof of the Bolzano-Weierstrass theorem was published by Bolzano about 2 years after Weierstrass was born.

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They got their math started early back in the day ;) –  Dhruv Ranganathan Jun 3 '13 at 21:29

I think the best example of this is Pell's equation, which was studied and solved by Lord Brouncker. John Pell had literally nothing to do with it, but Euler got the two of them mixed up.

There are plenty of examples of $A$ getting legitimate credit for their own work even though $B$ did it first, or European $A$ getting legitimate credit for work done earlier and independently by Asian $B$, but this is an example of an unconnected person getting entirely undeserved credit through a complete error.

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Nobody's mentioned the Pythagorean theorem yet?

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en.wikipedia.org/wiki/Baudhayana a solid 200-300 years before Pythagoras. In his defense, Pythagoras never claimed the theorem as his. –  slebetman Jun 4 '13 at 6:10
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I think in most of these cases the people didn't claim the result was their own; it's just that sloppy people named results after the first places they learned them, even if those sources explicitly mentioned the original source! –  Daniel McLaury Jun 4 '13 at 9:02
    
It may have been that both of them discovered it separately. –  Neer Jun 4 '13 at 13:13
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@Neer Most probably. Pythagoras had no possibility of contacting Baudhayana. Of course we Chinese always like to pretend to be the inventors - apparently much before Baudhayana, some Chinese math book stated without proof that the hypotenuse of a right triangle with sides 3 and 4 has hypotenuse 5 (six words: 勾三股四玄五). That person gets all the credit in our textbooks ;) –  user54609 Jun 4 '13 at 13:50
    
@EricDong Zhou Bi Suan Jing ? Yeah I've read about it using translator,in maths there is nothing without proof. :P –  Neer Jun 4 '13 at 15:38

Wilhelm Killing:

To quote Wikipedia:
" From 1888 to 1890, Killing essentially classified the complex finite dimensional simple Lie algebras, as a requisite step of classifying Lie groups, inventing the notions of a Cartan subalgebra and the Cartan matrix "

Also Coleman in the greatest mathematical paper of all time says
"By one of those miscarriages of justice which are commonplace in mathematics, most of the fundamental results about Lie algebras which were discovered by Killing are usually attributed to E.Cartan."
and
" He (Wilhelm Killing) exhibited the characteristic equation of the Weyl group when Weyl was 3 years old and listed the orders of the Coxeter transformation 19 years before Coxeter was born."

Also Killing was the one who introduced the notion of the 'characteristic polynomial' (see this).

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To make this example even more entertaining, the Killing form was popularized by Élie Cartan. (Although according to Wikipedia, Killing wrote it down first, but then didn't do anything with it). –  Matt Pressland Jun 4 '13 at 15:57
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To make this example still more entertaining, I had thought for a long time that the Killing form was not named after any mathematician at all, but rather, like, it kills nilpotent algebras ... –  Hagen von Eitzen Jun 10 '13 at 15:40
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@HagenvonEitzen: The first thing my professor said to us when he taught us about the Killing form was that it was named after a mathematician and not because it kills nilpotent algebras:) Probably he had the same misinterpretation as you, about the 'etymology' of the Killing form. –  P.. Jun 10 '13 at 18:46

Not quite an answer but maybe relevant:

Arnold's Principle: If a notion bears a personal name, then this name is not the name of the discoverer.

Berry Principle: Arnold's Principle is applicable to itself.

[source]


By the way this MO thread on Arnold's principle contains a lot of actual answers to OP question.

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Yours seems like the same answer as this. –  Git Gud Jun 3 '13 at 21:01

Fermat's last theorem was proved by Andrew Wiles and Richard Taylor. The Poincaré conjecture was proved by Grigori Perelman. Maybe the millennium problems won't change name if they are proved. By the way, I think the name of the theorem also should credit the person who came up with the conjecture since this is also an important part.

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More precisely, Andrew Wiles and Richard Taylor proved FLT. –  John Bentin Jun 3 '13 at 20:49
    
@JohnBentin Yes, thank you. –  N.U. Jun 3 '13 at 20:51
    
@JohnBentin, with important help from Ribet, Shimura, Taniyama,...! One of the nice things about modern mathematics is how many different people contribue to a given theorem. –  S123 Jun 3 '13 at 20:59
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I'm not sure if things like Poincaré's conjecture are what the OP is looking for, because no one would interpret the name as giving credit to Poincaré to the proof. –  Trevor Wilson Jun 3 '13 at 21:05
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I'd like to add something that I think may have some historical significance in the future: FLT was actually proved by both Wiles and Taylor. The latter one is many times omited, but the truth is, imo, that without his actuation the problem Wiles's proof showed back in 1993 could probably never have been solved and we'd still be trying to prove that theorem... –  DonAntonio Jun 3 '13 at 21:48

Burnside's lemma was first proved by Frobenius. Vandermonde's identity was known in China long before. Pólya's enumeration theorem is due to Redfield. And $3/4$ of calculus was proved by Euler, but credited to all sorts of other people!

The list goes on ad nauseam.

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Gaussian elimination was known in China about 2000 years earlier. Even within Europe, Newton used it long before Gauss. –  Erick Wong Jun 3 '13 at 20:24
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The Euler remark is funny. +1 –  Git Gud Jun 3 '13 at 20:45
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The following is taken from the Wikipedia article List of things named after Leonhard Euler: "Physicists and mathematicians sometimes jest that, in an effort to avoid naming everything after Euler, discoveries and theorems are named after the `first person after Euler to discover it'." –  A Walker Jun 3 '13 at 21:13
    
Burnside attributed the lemma to Frobenius, but it was known to Cauchy forty years earlier. I like to call it the Cauchy-Frobenius-Burnside-Redfeld-Pólya lemma because I think it's funny. –  MJD Jun 4 '13 at 13:18
    
Actually before Euler calculas was known in India. –  Neer Jun 4 '13 at 16:31

Stokes' Theorem was basically formulated by everyone else but Stokes.

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Edmonds-Karp's algorithm is actually Dinic's. In addition to that, Dinic found a better running time.

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Fibonacci's contributions to the study of the Fibonacci sequence are essentially zero. One of the numerous arithmetic exercises in his 1202 book Liber Abaci is to calculate the decimal expansions of the first twelve Fibonacci numbers; this is the source of the name, and his sole connection with the problem.

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How about the famous cryptosystem RSA? It was named after Ron Rivest, Adi Shamir and Leonard Adleman who invented it in 1977, but it was already invented years earlier (1973) by Clifford Cocks. Unfortunately for him his invention was classified, and only 20 years later it turned out that he was actually the one who discovered the algorithm first...

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My contribution:

$\bullet$ The Cantor Schröder Bernstein theorem was first proved by Dedekind.

$\bullet$ The Cauchy-Schwarz inequality should perhaps also be credited to Viktor Bunyakovsky and Cauchy.

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This gets very murky. Are you sure about Cauchy-Schwarz? There are so many different settings. Even your own link disagrees with your statement above. :) –  Ted Shifrin Jun 3 '13 at 20:08
    
@TedShifrin I didn't even read it. I had read something else on a different source and assumed it was the same in the wiki page. I'll edit my answer. Thanks. –  Git Gud Jun 3 '13 at 20:10
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Cauchy proved the inequality for finite dimensional real vector spaces. Bunyakovsky obtained the integral inequality from here. Later, Schwartz proved it for inner product spaces. So Cauchy-Schwartz is the right name IMO, Cauchy discovered it and Schwartz proved the most general case... –  N. S. Jun 4 '13 at 15:07
    
@N.S. I agree. I'll keep my answer because your comment is informative and clarifies everything. Thanks. –  Git Gud Jun 4 '13 at 15:11

Zorn's lemma was formulated and proved in various forms prior to Zorn, going back to the Hausdorff maximal principle. The version currently known as "Zorn's Lemma" was formulated and proved by Kuratowski in 1922. Zorn's contribution, in 1935, was an equivalent but different maximal principle.

(See Paul J. Campbell, "The Origin of ‘Zorn's Lemma’", Historia Mathematica 5 (1978), pp. 77–89.)

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The calculus (integral) is a good example, Leibnitz and Newton "invented" it indipendently, but Newton tried to discredit Leibnitz, so when i learned in college in the UK they taught it to me as Newton integral, although i later learned in Austria that the method we use nowadays is Leibnitz' and Newtons method was unpractical. Actually, the formal definitions and proofs were given by Riemann and some French and Italians of which i can't remember the Names.

Sum and mean of the rectangles under a curve as an approximation of the integral was already used by Babylonians, Egyptians and Greeks even though we are not sure if they already did infinitesimal calculus (Archimedes did, for example contained in the proof the arc length formula).

Also, i would like to mention that the Pythagorean Theorem was used for centuries before Pythagoras did. The Babylonians also devised an own method of approximation in order to calculate the square roots needed for the pythagorean theorem. Evidence has been found on clay tablets used probably by babylonian schoolboys where they had to calculate such things as exercise.

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Well, the famous Fermat's last theorem was actually first proposed by Diophantus, the father of algebra. Fermat said to have solved it, in a comment on a book, but said that it was too wordy. It was re-proved 400 years later by Andrew Wiles in 1995.

And Fermat gets all the fame. Huh.

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Didn't know about Diophantus. Nice one. –  Git Gud Jun 4 '13 at 17:28
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This doesn't ring true to me. Fermat's comment explicitly mentions that two cubes cannot sum to a cube, and likewise with fourth powers. I'm fairly certain that the relevant passage of Diophantus was only discussing Pythagorean triples. –  Erick Wong Jun 8 '13 at 10:47
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@AnonymousPi Reference, please. Everything you are claiming seems to be highly non-standard, and the same source you cite Wikipedia disagrees with your original claim about Diophantus. Or is it just a typo that you wrote $b^2$ instead of $b^n$? –  Erick Wong Jun 8 '13 at 22:36
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@AnonymousPi The standard version of the story goes as follows: Diophantus writes about finding solutions to $a^2+b^2 = c^2$ (from my rough transcription of the Latin into Google Translate, this seems to be true). In the margin beside this passage, Fermat wrote about $a^3 + b^3 = c^3$, $a^4 + b^4 = c^4$, and more generally $a^n + b^n = c^n$. I don't see how Diophantus should get credit for this at all. –  Erick Wong Jun 8 '13 at 22:51
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Fermat's remark "Cubus autem duos in cubos, et quadratoquadratem ... " (my emphasis) won't make sense if Diophantus hat mentioned the higher powers. –  Hagen von Eitzen Jun 10 '13 at 15:42

Pascal's triangle existed way before him.

The Chinese call it Yang Hui Triangle, not even the first Chinese mathematician to discover it in 11th century.

It was two Persians who first found it in 10th century.

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