What are examples of mathematical concepts named after the wrong people? (Stigler's law)

Question

It's a common observation in Lie theory that Cartan matrices and the Killing form are named after the wrong people; they were discovered by Killing and Cartan, respectively. I remember learning about many other examples of this phenomenon, but can't think of too many at the moment. Wikipedia has some examples here and here, but I'm curious about more obscure examples.

Bonus points for an interesting story behind why the concept was incorrectly named. Concepts that were deliberately named in honor of another mathematician don't count.

Answer 1

According to Wikipedia, Markov's inequality is due to Chebyshev, and Chebyshev's inequality is due to Bienaymé.

On top of that, Hölder's inequality was first proved by Rogers, and Jensen's inequality by Hölder. What a mess!

Answer 2

Q: Who proved the Cayley-Hamilton Theorem?

A: Frobenius!

We now have the interesting question: Is this a maximal example of Stigler's law? That is, can we find distinct persons A, B, and C who are given credit for a result proven by D? Or A and B who are given credit for a result proven by C and D?

Answer 3

Stokes's theorem was stated by William Thomson (Lord Kelvin) in a letter to Stokes. The letter is reproduced on the cover of Spivak's Calculus on Manifolds. I believe the theorem was named after Stokes because he frequently put it on the Tripos exam in Cambridge.

Answer 4

Zorn's lemma is neither due to Zorn, nor is it a lemma. It is a theorem due to Kuratowski.

Answer 5

The Cantor-Schroeder-Bernstein theorem was proved by Dedekind; this link is to Dedekind's collected works and there is an informative note at the end.

Answer 6

The Pell equation was named so because Euler thought that John Pell was responsible for some key results involving this equation. While Pell was a notable mathematician, he had essentially no connection to the equation. The common belief is that Euler mistook Pell for Lord Brouncker who indeed had a number of results related to the "Pell" equation.

Answer 7

The Frobenius automorphism associated to a prime ideal in a Galois extension of number fields was actually developed by Dedekind, who wrote about it (and the associated ramification groups, later found by Hilbert) in a letter to Frobenius on June 8, 1882. Frobenius published this construction in a paper in 1896. Some citations:

1. Frobenius, Collected Works, Vol. 2, pp. 719--733.

2. van der Waerden, Modern Algebra, Vol. 1 (Spring 1966), p. 203.

3. Zassenhaus, Canadian Math. Bulletin 18 (1975), p. 448.

Answer 8

The most amazing example I know is the Cayley formula which was discovered by Carl Borchardt nearly 30 years earlier. Not only Cayley knew about this, in his paper he specifically wrote that this formula is due to Borchardt, and all he wants to do is give a new simple proof (without determinants as in the matrix tree theorem).

Answer 9

Bézout's theorem

This result was discovered first by Newton in 1665. Even though MacLaurin (1720) and Leonhard Euler gave proofs, the theorem is usually attributed to Etienne Bézout who much later (1776) gave an incorrect proof of the result.

Answer 10

Our linear algebra professor had a joke he told every year at the same spot in the lectures, for some 30 or 40 years. He'd say in an absolutely dry voice and facing the blackboard: "And this is the Cauchy–Bunyakovsky–Schwarz inequality, named like this because it was first proved by Lebesgue". Apparently, Cauchy just did it just as an inequality for sums (ie findim spaces), and Bunyakovsky and Schwarz independently as an inequality for integrals (ie for L2).

Answer 11

The number of plane trees with no vertex of degree one and with $n$ endpoints is known as a Schröder number, from a 1870 paper by Ernst Schröder. In 1994 David Hough discovered that these numbers were known to Hipparchus (c. 190 - after 127 B.C.)! For a popular account, see https://math.mit.edu/~rstan/papers/hip.pdf. For a more scholarly treatment, see http://stl.recherche.univ-lille3.fr/sitespersonnels/acerbi/acerbipub5.pdf (Wayback Machine).

As an irrelevant aside, how do you make accent marks in MathOverflow? Schroder is supposed to have an umlaut over the o.

Answer 12

In my first algebra book the Eisenstein criterion for irreducibility of a polynomial is named Schönemann criterion and is left as an exercise. This is confusing when all others are talking about the Eisenstein criterion ;-). In fact, here is a quote from Wikipedia:

The criterion is named after Ferdinand Eisenstein. It was published by T. Schönemann in Crelle's Journal 32 (1846), p. 100, and was popularized by Eisenstein in Crelle's Journal 39 (1850), pp. 166-169. Eisenstein's application of this theorem was to polynomials with coefficients in Z[i], not Z.

Answer 13

In reference to exactly this phenomenon (and in particular to the case of Pell's equation), Andre Weil once observed that "This has happened many times in mathematics. For example, I live on 'von Neumann Circle'. I live there. Yet still it is called 'von Neumann Circle' ".

Answer 14

Currying should, I believe, be referred to as Schönfinkeling.

Answer 15

Quoting from Alan Sokal's 2005 paper on the multivariate Tutte polynomial:

"The Potts model was invented in the early 1950s by Potts’ thesis advisor Domb. The $q = 2$ case, known as the Ising model, was invented in 1920 by Ising’s thesis advisor Lenz. (I hasten to add that these are the only two cases I know of where the thesis advisor’s invention was named after the graduate student, rather than the other way around.)"

Answer 16

Chow varieties were invented by Van der Waerden (Chow was his student). And Hilbert schemes were invented by Grothendieck (who called them Hilbert schemes himself, however).

Answer 17

If you search for almost any eponymous topic in Wikipedia, you'll find that it was first studied by someone else. For example, the Gaussian distribution (according to Wikipedia) was first studied by de Moivre. It seems that in many cases, naming the body of work was given to the person who first applied its study to some other field (using the earlier example, Gauss used the distribution in astronomy).

The common story goes that L'Hôpital bought "the rights" to L'Hôpital's rule, as he was a nobleman and not a mathematician by trade, although I am not sure about the veracity of that story.

Although I am no expert on the history of Mathematics, it seems as though ideas or formulae assumed their names from certain mathematicians due either to a.) the more notable application or publication of the theory or b.) attribution by mathematicians of a later generation to pay tribute to (or garner attention from) the work of their predecessors.

Answer 18

An article in the current issue of American Mathematical MONTHLY (G. Folland, "A tale of topology," Am. Math. Monthly 117 (8) pp.663-672, Oct. 2010) quotes Walter Rudin as follows:

Thus it appears that Čech proved the Tychonoff theorem, whereas Tychonoff found the Čech compactification -- a good illustration of the historical reliability of mathematical nomenclature.

Folland's article suggests the truth is more complicated, as it usually is.

Answer 19

The Banach-Steinhaus theorem was first proved by Hahn, the Hahn-Banach theorem was first proved by Helly.

Answer 20

The Vandermonde Determinant/Matrix. Apparently Vandermonde never explicitly discussed his eponymous determinant. According to Lebesgue in his survey of Vandermonde work, it was probably due to somebody misinterpreting Vandermonde's notation.

Answer 21

Burnside's Lemma, which asserts that the number of orbits of a group action is the average number of fixed points, was known to Cauchy. Burnside himself even attributed it to Frobenius in his book.

Answer 22

There was a paper published in 2006 entitled "Simpson's Paradox in the Farey Sequence". The paradox is not Simpson's nor is the sequence Farey's. Bonus points.

Answer 23

Jones' Conjecture. Jones does not even exist; it's a Western pseudonym of Chuan-Min Lee.

Answer 24

Expanding on the example given in the original post, here's an excerpt from Borel's "Essays in the History of Lie Groups and Algebraic Groups" (p. 5):

It has been remarked that, as far as terminology is concerned, posterity has not been kind to [Killing]: Cartan subalgebras, Weyl groups, fundamental reflections, roots, and the Coxeter transformation first appeared in his papers in some form. On the other hand, what now goes by his name, the "Killing form" seems to be a misnomer, and it may well be that I am the culprit. Cartan, Chevalley and Weyl never used this terminology. Once, J.J. Duistermaat and J.A.C. Kolk pointed out to me that, to their knowledge, its first occurence is in a paper of mine (Sém. Bourbaki, Exp. 33, May 1951). I do not remember why I chose it, though I probably felt I was innovating, since it is between quotation marks. It is rather likely that discussions with some members of Bourbaki had influenced me, but I cannot blame it directly on Bourbaki, since "Killing form" appears in Bourbaki drafts only from 1952 on. It is true that Killing was the first to remark that the coefficients of the characteristic equation (of a regular semisimple element), i.e. the elementary symmetric functions of the roots, are invariant under the adjoint group, but he did not make much use of the remark and did not single out the sum of the squares of the roots, of which Élie Cartan made such fundamental use in his thesis (1894). It would be more correct to speak of the Cartan form.

Answer 25

The Cayley numbers (also known as the Octonions) were discovered earlier by John T. Graves. The story is nicely explained in John C. Baez's paper, The Octonions, Bull. Amer. Math. Soc. 39 (2002), 145-205.

Answer 26

In honour of the recently departed Benoit Mandelbrot, perhaps it is appropriate to offer up the example of the Mandelbrot set, the first pictures of which were drawn in 1978 by Robert Brooks and Peter Matelski (according to Wikipedia).

Answer 27

I was once told that Riemann's integral is due to Darboux, while Lebesgue integral is due to Borel. Riemann invented the Cauchy integral instead.

Answer 28

Banach algebras should probably be called Gelfand Algebras, or something similar. I'm not sure of the history here, but presumably the "Banach" is attached because this is the study of "complete" normed algebras. I don't believe that Banach actually did much work on algebras (as opposed to Banach spaces).

Answer 29

1. Cauchy–Riemann equations were known to d'Alembert and Euler.

2. Two-dimensional Voronoi diagrams were used by Descartes, three-dimensional - by Dirichlet. Also should be noted, that this construction has several other names in physics: Wigner–Seitz cells, Thiessen polygons.

Answer 30

In logic:

• Tarski's undefinability theorem was obtained by Gödel before Tarski, who obtained it independently. Gödel did not publish the theorem. See Roman Murawski (1998), "Undefinability of truth. The problem of priority: Tarski vs Gödel", History and Philosophy of Logic, v. 19 n. 3. pp. 153-160

• The result sometimes known as Gödel's diagonal lemma was first stated by Carnap. Gödel (1934) explicitly attributed the result to Carnap (see Kurt Gödel, Collected Works, v. 1, p. 363).