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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.

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    $\begingroup$ By the way, in the mathematical community "Stiegler's law" is often referred to as "Arnol'd's law", inclusive of the corollary "Arnol'd's law applies to Arnol'd's law as well". $\endgroup$ May 10, 2010 at 20:24
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    $\begingroup$ To further complicate things, there is also Whitehead's law: "Everything of importance has been said before by someone who did not discover it." $\endgroup$
    – bhwang
    May 10, 2010 at 21:38
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    $\begingroup$ Oh gosh, I could not imagine that there are SO many wrong names. Perhaps some day there will be a big important Brandenburg theorem, of course just because another one has proven it. ;-) $\endgroup$ May 10, 2010 at 23:09
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    $\begingroup$ Not that I have a problem with the question per se, but "the wrong people" is pretty ambiguous. The first person to study something might not be the most deserving -- often a crucial application or popularizations trumps the actual innovation. Nor is it necessarily the case that the intent of the naming was to honor the inventor -- frequently the naming is done for reasons of analogy ("Euler systems" come to mind). $\endgroup$ May 11, 2010 at 1:10
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    $\begingroup$ Stigler's law is called Boyer's Law by H.C. Kennedy in "Who Discovered Boyer's Law?" (Amer. Math. Monthly vol. 79 1972, 66--67). It says that "Mathematical formulas and theorems are usually not named after their original discoverers." The label Boyer's law was chosen because Boyer gave many examples of this phenomenon in his book A History of Mathematics. $\endgroup$
    – KConrad
    Sep 8, 2010 at 17:12

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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

Link, doi: 10.1215/S0012-7094-79-04642-8

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):

enter image description here

enter image description here


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.

Link, doi: 10.1215/S0012-7094-79-04605-2


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

GDZ, eudml


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.

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  • $\begingroup$ I never heard that! (Although the names of Goresky and MacPherson are sometimes mentioned). What is the source? $\endgroup$ Jun 28, 2010 at 15:24
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    $\begingroup$ The answer is incorrect, since the KL 1979 paper (Invent. Math.) was the first to state the KL Conjecture based on Hecke algebras and KL polynomials. Kazhdan and Lusztig were motivated by questions about singularities of Schubert varieties, Springer's representations of Weyl groups, Jantzen's work on Verma modules, etc. Vogan was approaching similar machinery from the direction of real Lie group representations, which led him after the KL paper to complete parts of his own program using "KLV polynomials". See Steven Kleiman's history of intersection homology (arXiv) for the role of GM. $\endgroup$ Aug 7, 2010 at 16:00
  • $\begingroup$ Dear Victor, I've just discovered your comment! Usually I get an automated alert whenever somebody comments in one of my answers. I could almost swear I didn't get any for your comment. Next time, don't hesitate to email me! (My address is very easy to find, for instance on my MO page.) $\endgroup$ Aug 7, 2010 at 18:10
  • $\begingroup$ Dear Victor, dear Jim: Thank you very much for your comments. I'll try to explain how I view things in an edit (soon to come) to my answer, and you'll tell me why I'm wrong. In a nutshell, I'm referring to what Vogan did before, and not after, the Inventiones KL paper. Things are very clearly explained in the very first two paragraphs of projecteuclid.org/… Also I made this claim several times in presence of David Vogan, and he never objected. (I'm sure you know his honesty and modesty.) $\endgroup$ Aug 7, 2010 at 19:49
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    $\begingroup$ The link iecn.u-nancy.fr/~gaillard/vogan_ref.pdf seems to be dead - and I found it neither on the new site nor in the Wayback Machine. (But since the bibliographic data and the link to the journal version are given, this probably doesn't really matter.) $\endgroup$ Aug 14, 2022 at 7:52
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Marden’s theorem was proved by Siebeck.

What rankles is that Marden himself cited Siebeck but it is now called Marden’s theorem. Dan Kalman was the one who brought this to people's attention and his defense is

I call this Marden’s Theorem because I first read it in M. Marden’s wonderful book.

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De Bruijn sequences are so named because Nicolaas Govert de Bruijn enumerated them in 1946, but he later acknowledged the priority of C. Flye Sainte-Marie, who enumerated them already in 1894.

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Cayley numbers, best known nowadays as the octonions, were first discovered by John Graves in 1843 (https://en.wikipedia.org/wiki/Octonion).

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  • $\begingroup$ Aargh — despite attempting to scan the previous answers before posting, I missed this one. $\endgroup$ Nov 23, 2023 at 17:01
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Cartan discovered the Killing form, and Killing discovered the Cartan matrix.

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    $\begingroup$ That's the example I used in the original post :) $\endgroup$ May 13, 2010 at 1:44
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    $\begingroup$ Aw, nuts, that's what I get for not reading things carefully. :) $\endgroup$ May 13, 2010 at 2:08
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The notion of Frobenius manifold is due to Dubrovin

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    $\begingroup$ Why -2 votes??? $\endgroup$
    – Yougeeaw
    Aug 31, 2011 at 10:17
  • $\begingroup$ This seems to be a concept that was deliberately named in honor of Frobenius, and as such, was explicitly excluded by the OP. $\endgroup$ Nov 23, 2023 at 5:15
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