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In one of my lectures today we paused at the term abelian and noted that it is an incredibly high honor to have an adjective with the first letter uncapitalized (apparently other countries leave the first letter capitalized) based on one's name. Other than abelian, the only other examples that were mentioned were noetherian and artinian. Are there other examples?

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closed as off-topic by YoTengoUnLCD, Jyrki Lahtonen Aug 23 '17 at 5:52

This question appears to be off-topic. The users who voted to close gave this specific reason:

  • "This question is not about mathematics, within the scope defined in the help center." – YoTengoUnLCD, Jyrki Lahtonen
If this question can be reworded to fit the rules in the help center, please edit the question.

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    $\begingroup$ You know what is funny? Abel (noun) $\to $ abelian (adjective) $\to $ abelianize (verb) $\to $ abelianization (noun). $\endgroup$ – Kenny Wong Aug 22 '17 at 21:41
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    $\begingroup$ Q: What's purple & commutes? A: An abelian grape. $\endgroup$ – PM 2Ring Aug 22 '17 at 21:43
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    $\begingroup$ Don't forget archimedean and cartesian, although they're sometimes capitalized by people who don't know the convention. $\endgroup$ – PM 2Ring Aug 22 '17 at 21:44
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    $\begingroup$ For quite a while, I thought the "Heaviside" function was "heavyside" and it made sense, because all the weight was on one side of the $y$-axis. $\endgroup$ – B. Goddard Aug 22 '17 at 21:53
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    $\begingroup$ I gotta be the mean guy here, but how is this not off-topic? $\endgroup$ – YoTengoUnLCD Aug 22 '17 at 23:20

16 Answers 16

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Killing form - here you might not even be aware that it is based on a name :)

(At the other end, I learned that some native English speakers think that eigenvalues are possibly named after some Karl-Friedrich Eigen guy)

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    $\begingroup$ When I first got to the name "Killing Field" in my differential geometry class, I audibly gasped. $\endgroup$ – Duncan Ramage Aug 22 '17 at 21:43
  • $\begingroup$ While funny this is not an answer. Let's not forget the Green Theorem ;D. $\endgroup$ – quid Aug 22 '17 at 22:28
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Sylvester named a lot.

Would "jacobian" count?

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    $\begingroup$ Jacobian is a noun. $\endgroup$ – Sean Roberson Aug 22 '17 at 21:39
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    $\begingroup$ It can be a jacobian determinant. $\endgroup$ – NickD Aug 22 '17 at 21:43
  • $\begingroup$ Sometimes, where a noun phrase of the form adjective+noun could have been used, we use only the adjective and omit the noun, so that the adjective stands in for the entire noun phrase. For example, consider "the quick and the dead," which means "the quick (living) people and the dead people." I always wondered if "the Jacobian" was an example of that grammatical construction. $\endgroup$ – David K Aug 22 '17 at 21:54
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    $\begingroup$ @SeanRoberson : Jacobian elliptic functions? $\endgroup$ – Michael Hardy Aug 22 '17 at 22:06
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Euclidean geometry; cartesian plane; pythagorean triple.

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Hermitian is an example: those matrices whose inverse is its conjugate transpose.

Of course, many objects bear mathematicians' names alone just as an adjective (see Duncan's example on topological spaces). We also have Eulerian paths and Hamiltonian circuits, as well as Lagrangian interpolating polynomials.

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    $\begingroup$ I think you're mixing Hermitian and unitary. $\endgroup$ – Jose27 Aug 23 '17 at 22:15
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When I first learned abstract algebra I wondered what ethers were that a noetherian ring had none of. (Later I was on the faculty at Bryn Mawr where a colleague used Emmy Noether's desk.)

And of course there's "algorithm":

The words 'algorithm' and 'algorism' come from the name al-Khwārizmī.[61] Al-Khwārizmī (Persian: خوارزمی‎‎, c. 780–850) was a Persian mathematician, astronomer, geographer, and scholar in the House of Wisdom in Baghdad, whose name means 'the native of Khwarezm', a region that was part of Greater Iran and is now in Uzbekistan.[62][63] About 825, he wrote a treatise in the Arabic language, which was translated into Latin in the 12th century under the title Algoritmi de numero Indorum. This title means "Algoritmi on the numbers of the Indians", where "Algoritmi" was the translator's Latinization of Al-Khwarizmi's name.[64] Al-Khwarizmi was the most widely read mathematician in Europe in the late Middle Ages, primarily through his other book, the Algebra.[65] In late medieval Latin, algorismus, English 'algorism', the corruption of his name, simply meant the "decimal number system". In the 15th century, under the influence of the Greek word ἀριθμός 'number' (cf. 'arithmetic'), the Latin word was altered to algorithmus, and the corresponding English term 'algorithm' is first attested in the 17th century; the modern sense was introduced in the 19th century.

https://en.wikipedia.org/wiki/Algorithm#Etymology

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Cartesian. Fuchsian. Boolean. Pfaffian. Hermitian.

Wrong part of speech, but I'm fond of Bezoutiant. [Maybe Bezoutian is more elegant, but the form I'm fond of has the T at the end.]

Alas, these all have capital letters. One might think a schlicht function was eponymous (there are mathematicians called Schlicht) but not so.

This is off topic, but back in the day, while dumpster diving for profs' discarded offprints, I found an offprint for a paper with a title like "On the Poynting Vector of Cosmic Love Waves". I think Haight-Ashbery was just becoming a thing then, and the title tickled my fancy.

Changing the topic to eponymous monstrosities, we have Rao-Blackwellization. (A swell concept, which might otherwise be called Jensenification, if I had any say in the matter.)

Changing topix yet again. I have just learned that there are entries for people with these surnames in the Math Genealogy database: Eigen, Star, Strong, Stronger, and Null. So they are like Schlict: non eponyms of strong topoogy, stronger topology, and null set.

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I guess riemannian and gaussian work here. In French "galoisien" stands for Galois.

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  • $\begingroup$ When is "Riemannian" not capitalized? $\endgroup$ – Jesse Madnick Aug 23 '17 at 5:04
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Topological spaces can be Tychonoff, Hausdorff, Frechet, Kolmogorov, and Urysohn, all of whom were pioneering topologists. Probably the most common one to hear is Hausdorff, in sentences like "A locally Euclidean, 2nd countable, Hausdorff space is a manifold".

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    $\begingroup$ These are not adjective forms, but persons names. And it is vulgar even if widespread to treat them merely as adjectives rather than as parts of coumpound nouns. We speak of the Obama administration, but we don't say his administration of Obama enough for us. That's a compound noun. "Euclidean" and "Archimedean" and "Gaussian" are adjective forms. $\endgroup$ – Michael Hardy Aug 22 '17 at 22:08
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Platonic solids, though usually capitalized.

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newtonian, grassmannian, minkowskian, gramian, hessian, wronskian, lipschitzian, holderian, galilean, lorentzian

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  • $\begingroup$ "lipschitzian"? "holderian"? I don't think I've ever seen either of those. Curious for a reference. $\endgroup$ – Jesse Madnick Aug 23 '17 at 5:07
  • $\begingroup$ @Jesse Madnick There are also lipschitzianity and holderianity. The web is full. See for "lipschitzian" the authoritative source by R. T. Rockafellar; Directionally Lipschitzian Functions and Subdifferential Calculus, Proceedings of the London Mathematical Society, Volume s3-39, Issue 2, 1 September 1979, Pages 331–355, doi.org/10.1112/plms/s3-39.2.331 and for "holderian" azjm.org/index.php/azjm/article/view/749/327 $\endgroup$ – trying Aug 23 '17 at 8:36
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Euclidean, diophantine, pythagorean, cevian,

...and surely Bourbaki got something named after him....?

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  • $\begingroup$ No., because Bourbaki is not a person (albeit the Nazis, during II World War, search for the famous mathematician Nicolas Bourbaki, from the Nancago university), and didn't prove a theorem. $\endgroup$ – Bernard Aug 22 '17 at 23:49
  • $\begingroup$ Well there is the Alaoglu-Bourbaki Theorem, for example. $\endgroup$ – Dirk Aug 23 '17 at 5:01
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bayesian

Thomas Bayes (/ˈbeɪz/; c. 1701 – 7 April 1761)[2][3][note a] was an English statistician, philosopher and Presbyterian minister who is known for having formulated a specific case of the theorem that bears his name

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Studentized residuals, Studentized ranges.

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archimedean (e.g., archimedean valuation or nonarchimedean valuation) -- some people capitalize and some don't (also some people hyphenate nonarchimedean and some don't). i never capitalize or hyphenate.

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    $\begingroup$ That's not saying much, you don't even capitalize the word "I" even at the beginning of a sentence... $\endgroup$ – Rahul Aug 22 '17 at 23:22
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    $\begingroup$ He said that. Your comment is redundant, props to kimball for efficiency! $\endgroup$ – mtheorylord Aug 23 '17 at 1:23
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Is it the case that the only eponymous concept among all of Erdős's myriad contributions in over $1500$ papers is the Erdős number?


PE+TT
P.E. & Terry Tao, image from Wikipedia.
Of course there is the Erdős–Rényi random graph model...

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Hilbert Space, Cantor finite, Dedekind finite, Kuratowski finite, Douglas algebra, Toeplitz operator, Leibniz's notation, Gödel's constructible universe, Pascal's triangle, Peano Axioms, Poisson Distribution, Sierpiński Space

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