What are examples of mathematical concepts named after the wrong people? (Stigler's law) - MathOverflow [closed]

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

2010-05-10T19:08:55Z

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

2010-05-10T19:18:31Z

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

2010-05-10T19:42:02Z

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

2010-05-10T19:52:00Z

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

2010-05-10T20:06:56Z

Pythagoras' Theorem apparently predates Pythagoras.

Answer by Harrison Brown for What are examples of mathematical concepts named after the wrong people? (Stigler's law)

2010-05-10T20:08:31Z

I don't know if this is a real example, but it led to a nice gem in a recent abstract on the arXiv: "Glaisher's correspondence goes back to Euler."

(As far as I know Glaisher generalized Euler's bijection, which is why he gets the eponym -- in addition some people say "Euler-Glaisher" instead.)

Answer by Nate Eldredge for What are examples of mathematical concepts named after the wrong people? (Stigler's law)

2010-05-10T20:11:13Z

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

2010-05-10T20:14:11Z

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

2010-05-10T20:29:07Z

Euler's nine point circle was never discussed by Euler. This is an error of the "argument by authority" type: Catalan propagated that incorrect attribution made by another scholar, the "learned Terquem", without checking it himself.

Answer by Jonathan Sparling for What are examples of mathematical concepts named after the wrong people? (Stigler's law)

2010-05-10T20:43:14Z

And the Bianchi identities are due to Ricci (according to Levi-Civita).

Answer by Nurdin Takenov for What are examples of mathematical concepts named after the wrong people? (Stigler's law)

2010-05-10T21:01:51Z

Cauchy–Riemann equations were known to d'Alembert and Euler.
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 by Matthew Daws for What are examples of mathematical concepts named after the wrong people? (Stigler's law)

2010-05-10T21:03:22Z

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

2010-05-10T21:16:51Z

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

2010-05-10T21:27:29Z

The "Lichnerowicz formula" relating the square of the Dirac operator to the Laplacian has been proved more than 30 years earlier by Schrödinger.

See: E. Schrödinger, Dirac'sches Elektron im Schwerefeld, Sitzungsber. Preuß. Akad. Wiss., Phys.-Math. Kl. 1932, 105-128 (1932).

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

2010-05-10T21:29:39Z

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

2010-05-10T21:31:23Z

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:

Frobenius, Collected Works, Vol. 2, pp. 719--733.
van der Waerden, Modern Algebra, Vol. 1 (Spring 1966), p. 203.
Zassenhaus, Canadian Math. Bulletin 18 (1975), p. 448.

Answer by J.C. Ottem for What are examples of mathematical concepts named after the wrong people? (Stigler's law)

2010-05-10T21:31:38Z

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 attributted to Etienne Bézout who much later (1776) gave an incorrect proof of the result.

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

2010-05-10T21:52:10Z

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

2010-05-10T22:19:40Z

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

2010-05-10T23:00:55Z

In my first algebra book the Eisenstein criterion for irreducibilty 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 by Martina Balagovic for What are examples of mathematical concepts named after the wrong people? (Stigler's law)

2010-05-11T01:16:16Z

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

2010-05-11T02:02:03Z

To expand on Pasquale's comment, here's a quote from Arnold's article:

Similarly to the fact that America does not carry Columbus's name, mathematical results are almost never called by the names of their discoverers.

In order to avoid being misquoted, I have to note that my own achievements were for some unknown reason never expropriated in this way, although it always happened to both my teachers (Kolmogorov, Petrovskii, Pontryagin, Rokhlin) and my pupils. Prof. M. Berry once formulated the following two principles:

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

The Berry Principle. The Arnold Principle is applicable to itself.

Perhaps somebody knows which results by Kolmogorov et. al. he is thinking of.

Answer by Michael Thaddeus for What are examples of mathematical concepts named after the wrong people? (Stigler's law)

2010-05-11T04:14:02Z

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

2010-05-11T09:55:49Z

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

2010-05-11T10:25:46Z

Nakayama's lemma was first proved by Krull in a special case, and by Goro Azumaya in the general case.

Answer by Kevin O'Bryant for What are examples of mathematical concepts named after the wrong people? (Stigler's law)

2010-05-11T22:00:34Z

Farey fractions were introduced by C. Haros. John Farey asked a question about them that reached Cauchy, and Caucy then attributed the question and result to Farey, and the rest is history.

Answer by J. H. S. for What are examples of mathematical concepts named after the wrong people? (Stigler's law)

2010-05-12T21:01:15Z

It seems to me that Lagrange's theorem may well be one of the most prominent examples of the phenomenon under discussion.

According to J. J. Rotman,

the theorem was inspired by work of Lagrange (1770), but it was probably first proved by Galois.

Curiously enough, the Wikipedia article adscribes the first complete proof of the theorem to Pietro Abbati Marescotti.

Answer by David Hansen for What are examples of mathematical concepts named after the wrong people? (Stigler's law)

2010-05-13T01:43:23Z

Cartan discovered the Killing form, and Killing discovered the Cartan matrix.

Answer by To be cont'd for What are examples of mathematical concepts named after the wrong people? (Stigler's law)

2010-05-15T14:58:52Z

Pell's equation

By a mistake of Euler, the Diophantine equation y^2 - Ax^2 = 1 has been erroneously known as "Pell's equation"; but, in fact, the English mathematician John Pell (1611-1685) did no more than copy it down in his papers, from Fermat's letters of 1657 and 1658.

For an extensive historical account on "Pell's equation", see Sir Thomas L. Heath, Diophantus of Alexandria : A Study in the History of Greek Algebra (Dover Pub., New York, 1931-1963, 552 pages), Supplement, Section II: "Equation y^2 - Ax^2 = 1, pp. 277-292. Particularly in page 285, after a presentation of the history of the equation up to Fermat's time (including citations to Pythagoreans, Archimedes, Diaphanous, and the Indian solution), one can read that:

" ... Fermat rediscovered the problem and was the first to assert that the equation x^2 - Ay^2 = 1, where A is any integer not a square, always has an unlimited number of solutions in integers. His statement was made in a letter to Frénicle of February, 1657 (cf. Oeuvres de Fermat, II, pp.333-4). Fermat asks Frénicle for a general rule for finding, when any number not a square is given, squares which, when they are respectively multiplied by the given number and unity is added to the product, give squares. If, says Fermat, Frénicle cannot give a general rule, will he give the smallest value of y which will satisfy the equations 61y^2 + 1 = x^2 and 109y^2 + 1 = x^2 ? (Footnote 3: Fermat evidently chose these cases for their difficulty; the smallest values satisfying the first equation are y=226153980, x=1766319049, and the smallest values satisfying the second are y=15140424455100, x=158070671986249)." And, after a extensive quotation of Fermat's letter, in page 286, one can read that: "The challenge was taken up in England by William, Viscount Brouncker, first President of the Royal Society, and Wallis (Footnote 1: An excellent summary of the whole story is given in Wertheim's paper "Pierre Fermat's Streit mit John Wallis" in Abhandlungen zur Gesch. der Math., IX. Heft (Cantor-Festschrit), 1899, pp.557-576). See also H. Konen, Geschichte der Gleichung t^2-Du^2=1, Leipzig (S. Hirzel), 1901). At first, owing apparently to some misunderstanding, they thought that only rational, and not necessarily integral solutions were wanted, and found of course no difficulty in solving this easy problem. Fermat was, naturally, not satisfied with this solution, and Brouncker, attacking the problem again, finally succeeded in solving it. The method is set out in letters of Wallis (Footnote 2: Oeuvres de Fermat, III, pp.457-480, 490-503) of 17th December, 1657, and 30th January, 1658, and in chapter XCVIII of Wallis' Algebra; Euler also explains it fully in his Algebra (Footnote 3: Part II, chap. VII), wrongly attributing it to Pell (Footnote 4: This was the origin of the erroneous description of our equation as the "Pellian" equation. Hankel (in Zur Geschichte der Math. im Alterthum und Mittlelalter, p.203) supposed that the equation was so called because the solution was reproduced by Pell in an English translation (1668) by Thomas Brancker of Rahn's Algebra; but this is a misapprehension, as the so-called "Pellian" equation is not so much as mentioned in Pell's additions (Wertheim in Bibliotheca Mathematica, III, 1902, pp.124-6); Konen, pp.33-4 note). The attribution of the solution to Pell as a pure mistake of Euler's, probably due to a cursory reading by him of the second volume of Wallis' Opera where the solution of the equation ax^2 + 1 = y^2 is given as well as information as to Pell's work in indeterminate analysis. But Pell is not mentioned in connexion with the equation at all (Eneström in Bibliotheca Mathematica, III, 1902, p.206)."

For more information about "Pell's equation", see Harold M. Edwards, The Fermat's Last Theorem: A Genetic Introduction to Algebraic Number Theory (Springer-Verlag, New York, 1977, 410 pages), pp. 25-33. Particularly in page 33 one can read that

"This problem of Fermat is now known as "Pell's equation" as a result of a mistake on the part of Euler. In some way, perhaps from a confused recollection of Wallis's Algebra, Euler gained the mistaken impression that Wallis attributed the method of solving the problem not to Brouncker but to Pell, a contemporary of Wallis who is frequently mentioned in Wallis's works but who appears to have had nothing to do with the solution of Fermat's problem. Euler mentions this mistaken impression as early as 1730, when he was only 23 years old, and it is included in his definitive Introduction to Algebra written around 1770. Euler was the most widely read mathematical writer of his time, and the method from that time on has been associated with the name of Pell and the problem that it solved --- that of finding all integer solutions of y^2 - Ax^2 = 1 when A is a given number not a square --- has been known ever since as "Pell's equation", despite the fact that it was Fermat who first indicated the importance of the problem and despite the fact that Pell had nothing whatever to do with it."

See also André Weil, Number Theory : An approach through history - From Hammurapi to Legendre (Birkhäuser, Boston, 1984, xv+375 pages), in many different pages. In particular, at page 174, one can read that:

"Pell's name occurs frequently in Wallis's Algebra, but never in connection with the equation x^2 - Ny^2 = 1 to which his name, because of Euler's mistaken attribution, has remained attached; since its traditional designation as "Pell's equation" is unambiguous and convenient, we will go on using it, even though it is historically wrong."

Raul Nunes ( raul_nunes@uol.com.br ) NEST Nunes' Exposition of Scientific Truths ( http://www.geocities.com/raulnunes )

Answer by Scott Guthery for What are examples of mathematical concepts named after the wrong people? (Stigler's law)

2010-05-16T18:53:19Z

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 by Pierre-Yves Gaillard for What are examples of mathematical concepts named after the wrong people? (Stigler's law)

2010-05-21T04:42:10Z

I think the Kazhdan-Lusztig Conjectures are due to Vogan.

EDIT.

True or false, the claim is mainly based on the very first two paragraphs of

[II] Irreducible characters of semisimple Lie groups II. The Kazhdan-Lusztig conjectures. David A. Vogan, Jr. Duke Math. J. Volume 46, Number 4 (1979), 805-859. --- The link

http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.dmj/1077313724

gives a universal access to the first page, which contains the two paragraphs in question. In case you don't have access to the full paper, here is a scan of the references (to completely understand the two paragraphs):

http://www.iecn.u-nancy.fr/~gaillard/vogan_ref.pdf

Here are two more references:

[I] Irreducible characters of semisimple Lie groups I, David A. Vogan, Jr., Duke Math. J. Volume 46, Number 1 (1979), 61-108.

http://projecteuclid.org/DPubS?service=UI&version=1.0&verb=Display&handle=euclid.dmj/1077313255

[KL] David Kazhdan and George Lusztig, Representations of Coxeter groups and Hecke algebras, Inventiones Mathematicae, Volume 53, Number 2, 165-184.

http://gdz.sub.uni-goettingen.de/en/dms/load/img/?PPN=PPN356556735_0053&DMDID=dmdlog14

I would summarize things as follows.

Step 1. In [I] Vogan made a certain conjecture.

Step 2. [II] and [KL] were written simultaneously. Each paper cites the other. In [KL] Kazhdan and Lusztig also made a certain conjecture. When he learned this, Vogan immediately (or at least very fast) proved that the "Step 1 conjecture" implies that of Kazhdan and Lusztig. (He even showed that the "Step 1 conjecture" generalizes that of Kazhdan and Lusztig.)

But, again, the best is to read carefully the first two paragraphs of [II]. Vogan explains this much more clearly than I, and it's always better to hear things from the horse's mouth.

Answer by Scott Guthery for What are examples of mathematical concepts named after the wrong people? (Stigler's law)

2010-05-23T17:53:05Z

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

Answer by Péter Komjáth for What are examples of mathematical concepts named after the wrong people? (Stigler's law)

2010-06-28T14:52:14Z

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

Answer by David Nacin for What are examples of mathematical concepts named after the wrong people? (Stigler's law)

2010-06-29T01:19:57Z

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

2010-06-29T02:25:58Z

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

2010-08-07T13:40:43Z

Morse theory is named after Marston Morse; it was widely used at least 50 years earlier. Wikipedia mentions Cayley and Maxwell, in the context of topography. Maxwell also used it in his work on electromagnetism, as detailed (complete with extensive passages from Maxwell's treatise) in the appendix of Mystery of point charges (A. Gabrielov, D. Novikov and B. Shapiro) available here (subscription)

Answer by Jim Humphreys for What are examples of mathematical concepts named after the wrong people? (Stigler's law)

2010-08-07T14:29:12Z

Many of the examples mentioned go back to earlier centuries, when insulated national traditions and slow communications promoted mistaken labelling of results and concepts. A much more recent example from the 1950s involves the notion of Bruhat ordering on a general Coxeter group, motivated at first by the example of finite crystallographic reflection groups in Lie theory. The name seems to have been suggested by D.N. Verma in the late 1960s. For some reason the ordering itself fails to appear (even in the exercises) in Bourbaki's influential 1968 Chapters IV-VI dealing with Coxeter groups, root systems, Weyl groups and affine Weyl groups. Deodhar and others propagated the term "Bruhat ordering" in their papers, and as late as 1990 I routinely used this term in my book Reflection Groups and Coxeter Groups. But by then Borel, who had gotten more deeply involved in sorting out the history of Lie theory, objected that the ordering was not at all found in Bruhat's development of the Bruhat decomposition but had occurred for Weyl groups in Chevalley's treatment of the partial ordering of closures of Bruhat cells (Schubert varieties) in the flag variety.

As a result many of us now try in principle to start with something like Chevalley-Bruhat ordering (shortened to Bruhat ordering) or even Chevalley ordering. But this runs counter to a large body of literature including the 1979 Kazhdan-Lusztig paper.

Side remark: While Coxeter was the first to recognize the special presentation of a finite real reflection group that led to the term Coxeter group in Bourbaki, the general definition owes at least as much to people like Iwahori and Tits. Coxeter was interested in traditional (often intricate) combinatorial geometry and not in Lie theory or its generalizations. But short labels are easier to invent and tend to stick.

Answer by Carl Mummert for What are examples of mathematical concepts named after the wrong people? (Stigler's law)

2010-08-07T14:45:14Z

In logic:

Tarski's undefinability theorem was obtained by Gödel before Tarski, who obtained it independently. Gödel did not publish the theorem. See Roman Murawskia (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).

Answer by Nate Eldredge for What are examples of mathematical concepts named after the wrong people? (Stigler's law)

2010-10-13T20:05:25Z

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 by Andrew D. King for What are examples of mathematical concepts named after the wrong people? (Stigler's law)

2010-10-13T20:35:39Z

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

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

2010-10-13T20:54:35Z

Some people have tried to give examples with as high a multiplicity as possible. I want to try to break the record for the smallest non-zero example: Martin's axiom was introduced by Martin and Solovay. (I judge that to have multiplicity 1/2.)

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

2010-10-14T15:49:54Z

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

2010-10-14T16:18:43Z

Liouville talked about the Legendre function when he studied the so-called Euler Gamma function. It made me doubt about who defined the Gamma function first.

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

2010-10-14T18:14:51Z

The algebraic numbers that are now commonly called "Gauss sums" were studied in more general form than that introduced in Gauss's Disquisitiones by Lagrange [1]. In that same work, Lagrange shows how to generate an abelian extension of degree n by adjoining an nth root after, if necessary, adjoining the nth roots of unity. These generators were later called "Kummer generators". Jacobi sums, which are closely related to Gauss sums, were studied earlier than Jacobi by Gauss and Cauchy.

Finally, a story best recounted by Weil [2]: "For reference, we recall that the Gauss sums appear among the local constant factors in the functional equations of the $L$ functions; these factors are also called "nombres radiciels" ("root-numbers", "Wurzelzahlen"), undoubtedly because of Hilbert, who a had a sort of genius for bad terminology, where it would have been sensible to name "Wurzelzahl" that which before him had been named a "Lagrange resolvent" , and "Lagrangian Wurzelzahl" that which here has been called a Gauss sum".

[1] Lagrange, Reflexions sur la resolution algebrique des equations, Nouveaux Mem. de l'Acad. R. des Sc. et B.-L. de Berlin, 1770-1771 = Oeuvres, vol. III, p. 332;

[2] Weil, La Cyclotomie Jadis et Naguere.

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

2010-10-14T21:57:54Z

If the Russians are to believed, Kuratowski's theorem in graph theory was proved earlier by Pontryagin, but he hadn't published his notes.

Answer by Jeff Norden for What are examples of mathematical concepts named after the wrong people? (Stigler's law)

2010-10-15T00:33:31Z

Perhaps counterexamples to Stigler's/Arnol'ds law are actually the rare items. The most significant one that I know is the Cartesian coordinate system which, strangely, seems to have actually been invented by Descartes!

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

2010-10-18T21:43:12Z

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

2010-10-18T23:09:37Z

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

Answer by Richard Stanley for What are examples of mathematical concepts named after the wrong people? (Stigler's law)

2010-10-19T00:24:02Z

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 http://math.mit.edu/~rstan/papers/hip.pdf. For a more scholarly treatment, see http://stl.recherche.univ-lille3.fr/sitespersonnels/acerbi/acerbipub5.pdf.

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

Answer by Jeffrey Shallit for What are examples of mathematical concepts named after the wrong people? (Stigler's law)

2010-11-08T01:57:28Z

Farey series, attributed to Farey, were actually first studied by Haros.

Answer by Steven Landsburg for What are examples of mathematical concepts named after the wrong people? (Stigler's law)

2010-11-08T02:19:35Z

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

2011-01-18T20:06:50Z

I had a companion observation that almost noone attributes the well-known sum-of-roots, product-of-roots etc. polynomial formulas as Vieta's formulas as I posted on Yahoo!Answers.

Because as user absird pointed out, it makes that sort of topic Google-proof; at least a bad name is better than no name for purposes of searching or discussion.

('Yes it's very hard to refer to something when noone knows it by its proper name or uses that name. I tried many Google searches on "sum-of-roots product-of-roots" and it was almost impossible to get a coherent lead.')

MathWorld notes: The theorem was proved by Viète (also known as Vieta, 1579) for positive roots only, and the general theorem was proved by Girard.

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

2011-01-18T21:36:53Z

Apparently the Robin boundary condition was never studied by Robin. (Gustafson, K. and T. Abe, (1998b). The third boundary condition – was it Robin's?, The Mathematical Intelligencer, 20, 63–71.)

Answer by Mark Bennet for What are examples of mathematical concepts named after the wrong people? (Stigler's law)

2011-01-18T22:35:47Z

According to this link Steiner Systems were mentioned by by W Woolhouse in 1844 before the famous Kirkman Schoolgirl problem (P Kirkman 1847) - Steiner's work was more systematic and did advance the theory, but it came in 1853.

Answer by T.B. for What are examples of mathematical concepts named after the wrong people? (Stigler's law)

2011-01-19T07:04:24Z

The Shimura-Taniyama conjecture was originally known as the Weil conjecture see http://www.ams.org/notices/199511/forum.pdf, also see the comment of Weil on page 7 (with other examples) in his response to Lang on the same issue as in the question posed here.

Additionally, the Frey curve was actually first considered by Yves Hellegouarch.

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

2011-07-08T21:08:57Z

The notion of Frobenius manifold is due to Dubrovin

Answer by Adam Azzam for What are examples of mathematical concepts named after the wrong people? (Stigler's law)

2011-07-09T02:21:06Z

A favorite of mine is l'Hôpital's rule. l'Hôpital paid Johann Bernoulli a retainer to keep him updated on developments in calculus and to solve problems he had. Correspondence shows that Bernoulli stated and proved the rule, which l'Hôpital then published.

Heine-Borel was first published by Borel, not Heine. In fact, Heine's name was attached because he was using similar methods to solve related problems. Too bad for both of them that it was actually Dirichlet who was the first recorded to have proved it, but his notes were published posthumously and after Borel's proof.

Cramer's Rule was published first by MacLaurin, and some believe MacLaurin knew the proof some 20 years before Cramer's publication.