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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.

Joey Eremondi
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Git Gud
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    Maybe this should be made a community wiki? – Shuhao Cao Jun 03 '13 at 20:06
  • @Cao Sure. I'm trying to find how to do it. – Git Gud Jun 03 '13 at 20:07
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    I learned a while back that you need a mod to make a question CW (but not an answer). – rurouniwallace Jun 03 '13 at 20:07
  • I've placed the request; although I have "moderator tools" access I can't do it. – vadim123 Jun 03 '13 at 20:08
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    This has been discussed before: here and here and here. – vadim123 Jun 03 '13 at 20:14
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    Note that you can now buy your own theorem. – Calvin Lin Jun 03 '13 at 20:17
  • You are asking for erronymous theorems? – Stephen Jun 03 '13 at 20:23
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    Maybe the most famous one is Fermat's Last Theorem. – Hu Zhengtang Jun 03 '13 at 20:23
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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 http://news.nationalgeographic.com/news/2013/13/130519-women-scientists-overlooked-dna-history-science/ . This is annoying, deeply unfair and can push women further away from science. – DonAntonio Jun 03 '13 at 21:52
  • Pythagoras's theorem was known and used a looooooooong time before Pythagoras himself, by the Babylonians and the Egyptians. – Fixed Point Jun 03 '13 at 22:51
  • @FixedPoint This doesn't mean that pythagoras didn't discover and proved it independently. Discoveries that happen independently should probably mention all the authors, even though one of them discovered the result centuries after. – Bakuriu Jun 04 '13 at 07:29
  • That sounds kind of unsustainable @Bakuriu. – jwg Jun 04 '13 at 11:12
  • @jwg What is unsustainable? What I wanted to say is that: ($X_1$ proved $Y$ in year $A$ $\wedge$ $X_2$ proved $Y$ in year $B > A$) $\not\rightarrow$ $X_2$ didn't discover $Y$(where with "to discover" I mean to prove a fact that didn't know before) History shows that there are tons of theorems discovered independently. – Bakuriu Jun 04 '13 at 14:21
  • @Bakuriu, probably hundreds of people have independently discovered Cauchy-Schwarz, Pythagoras, Fermat's little theorem, the Euler characteristic of convex polyhedra, etc. Should all of their names be added to the names of the theorems, and these be updated every year to reflect the new independent discoveries? – jwg Jun 04 '13 at 14:37

24 Answers24

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

Zen
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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"?]

Stephen
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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 03 '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. – Stephen Jun 04 '13 at 01:29
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A proof of the Bolzano–Weierstrass theorem was published by Bolzano about 2 years after Weierstrass was born.

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

vadim123
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  • This was the first thing I was going to post. :) – Henry T. Horton Jun 03 '13 at 20:10
  • In Portugal this is also (and perhaps better) known as Cauchy's rule. – Git Gud Jun 03 '13 at 20:14
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    And usually L'Hospital gets all the credit instead of L'Hôpital. – WimC Jun 03 '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 Botero Jun 03 '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 03 '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 04 '13 at 06:18
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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 04 '13 at 13:32
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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.

MJD
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Nobody's mentioned the Pythagorean theorem yet?

Daniel McLaury
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    http://en.wikipedia.org/wiki/Baudhayana a solid 200-300 years before Pythagoras. In his defense, Pythagoras never claimed the theorem as his. – slebetman Jun 04 '13 at 06:10
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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 04 '13 at 09:02
  • It may have been that both of them discovered it separately. – Neer Jun 04 '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 ;) – ithisa Jun 04 '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 04 '13 at 15:38
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    I imagine the Pythagorean theorem is folk mathematics and goes back extremely far, and that 3-4-5 triangles might even be prehistoric. – Daniel McLaury Jun 04 '13 at 20:16
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    Pythagororean Theorem was known before Pythagoras, but it was proved after his death, and the first proof was using Thales Theorem. – Yiorgos S. Smyrlis Jan 12 '14 at 16:19
  • @YiorgosS.Smyrlis It is perhaps inadvertently appropriate then that we call it the Pythagorean Theorem instead of Pythagoras' Theorem. Can we concretely trace a written proof back to a member of the Pythagorean school (maybe Hippasus)? – David H Jan 12 '14 at 17:31
  • So far as I know, it can't even be established that a real person named Pythagoras ever lived. – Daniel McLaury Apr 25 '16 at 18:58
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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).

P..
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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). – mdp Jun 04 '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
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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.

Anonymous Pi
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vonbrand
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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 03 '13 at 20:24
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    The Euler remark is funny. +1 – Git Gud Jun 03 '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'." – awwalker Jun 03 '13 at 21:13
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    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 04 '13 at 13:18
  • Actually before Euler calculas was known in India. – Neer Jun 04 '13 at 16:31
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Stokes' Theorem was basically formulated by everyone else but Stokes.

Kofi
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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.

MJD
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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...

TMM
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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.)

MJD
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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.

Git Gud
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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 03 '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 03 '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, Schwarz proved it for inner product spaces. So Cauchy-Schwarz is the right name IMO, Cauchy discovered it and Schwarz proved the most general case... – N. S. Jun 04 '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 04 '13 at 15:11
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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.

Community
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Start wearing purple
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The calculus (integral) is a good example, Leibnitz and Newton "invented" it independently, 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 whose names I can't remember.

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.

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

ipavlic
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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 (i.e. Karaji and Khayyam).

msm
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Wilson's Theorem may be an example.

2

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.

N.U.
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  • More precisely, Andrew Wiles and Richard Taylor proved FLT. – John Bentin Jun 03 '13 at 20:49
  • @JohnBentin Yes, thank you. – N.U. Jun 03 '13 at 20:51
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    @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. – Stephen Jun 03 '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 03 '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 03 '13 at 21:48
  • @TrevorWilson Yes, you are probably right. I should have thought about that. – N.U. Jun 04 '13 at 06:52
  • @DonAntonio If you're going to do that, then you have to start including Frey-Serre-Ribet as well, since that was really the critical connection that allows the Wiles-Taylor results to be applied to FLT in the first place. – Steven Stadnicki Jan 31 '14 at 17:39
  • @StevenStadnicki, and Faltings....? Anyway, I meant the last kick in 1993-1994, not all the huge contributions towards the solution before that. – DonAntonio Jan 31 '14 at 17:42
  • I once went to a talk by Serre where he used "Wile's Theorem", so I strongly suspect that those doing research in this area do not use the term "Fermat's Last Theorem"! Similarly, the Poincaré conjecture is just a special case of Geometrisation so it would be odd to call it "Perelman's Theorem", as "Perelman's Theorem" is a much bigger beast. It would be like saying "Fermat's Last Theorem is that $a^{257}+b^{257}\neq c^{257}$ for all values of $a$, $b$ and $c$": it is merely a special case, not the whole picture. – user1729 Nov 04 '14 at 12:32
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When I first heard that some people are calling the standard trick from calculus books the Feynman's trick my first impression was WTF?! Are you kidding me?!

Then I saw that more and more people calling the trick known to Leibnitz as the Feynman trick. I knew where it came from, I have read Surely you are joking Mr Feynman?! This might be one of the most preposterious cases illustrating the Stigler's law of eponymy.

The other similar situation is with Glasser's Master Theorem that dates back to Boole, 1857. There isn't yet a Wikipedia or Wolfram article for Feynman's trick, but there is for Glasser's Master Theorem. Boole is not even mentioned in these articles.

Kuga
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In his paper Robert Granger argues that the Lucas-Lehmer test could in principle have been discovered by the ancient Greeks. The Miller–Rabin primality test was first discovered by Russian mathematician M. M. Artjuhov in 1967. See: Artjuhov, M. M. (1966–1967), "Certain criteria for primality of numbers connected with the little Fermat theorem", Acta Arithmetica, 12: 355–364.

Pedja
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An interesting "inappropriate" credit is for the Diffie-Hellman key exchange, not mentioning Ralph Merkle.

Hellman himself suggested the algorithm be called Diffie–Hellman–Merkle key exchange and has quoted that:

"The system...has since become known as Diffie–Hellman key exchange. While that system was first described in a paper by Diffie and me, it is a public key distribution system, a concept developed by Merkle, and hence should be called 'Diffie–Hellman–Merkle key exchange' if names are to be associated with it. I hope this small pulpit might help in that endeavor to recognize Merkle's equal contribution to the invention of public key cryptography."

I find it very interesting that one of the names of the key exchange actually would like to add another name for credit.

Alex Them
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  • The Wiener process, also called Brownian motion, was already known to Louis Bachelier (11 March 1870 – 28 April 1946) who worked on an option pricing theory five years before Einstein published his Brownian motion paper (1905). Norbert Wiener showed among other things the non-differentiability of the Brownian paths in the early 1920-ies.

  • An early version of Ito's lemma (1944) was known to Wolfgang Doeblin (17 March 1915 – 21 June 1940).

Kurt G.
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Newton's relations are two classical identities in the study of symmetric functions. They were derived by Albert Girard in 1629 before Newton was even born.

BatsOnASwing
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