Mathematical concepts named after mathematicians that have become acceptable to spell in lowercase form (e.g. abelian)?

Question

I would like to collect a list of mathematical concepts that have been named after mathematicians, which are now used in lowercase form (such as "abelian"). This question is partly motivated by my former supervisor, who joked (something like):

You know you've made it as a mathematician when they start using your name in lowercase.

This is a community wiki, please:

1. One mathematician per answer. Please update already-existing answers if that mathematician already exists.
2. Please give a brief description of the concept and the person (ideally with links to wikipedia).
3. This is not about whether or not you agree with the capitalisation.

Expect your answer to be edited otherwise.

Answer 1

For something even more common, "boolean" (e.g. "boolean type", "boolean algebra") is increasingly not being capitalized as well. George Boole formalized the manipulation of logical statements, and thus his name crops up frequently in connection to logic.

Answer 2

Like "cartesian", "algorithm" is not only a lowercased but a derivative form of the name of a mathematician (al-Khwarizmi).

Answer 3

cartesian. Many things are described as cartesian, after René Descartes. In philosophy things attributed to Descartes tend to keep the capital when described as "Cartesian", but in mathematics, I've seen "cartesian product" lower case a few times.

What's weird is that this isn't more prevalent, given that Descartes is older than Abel by almost 200 years, and I conjecture that cartesian products, cartesian planes and the like come up at least as much as abelian groups... And since the adjectival form of "Descartes" isn't just the name+ending, it's strange how common the capitalised form has remained...

Google books reveals that lowercase "cartesian plane" was used in the following books (for example):

• Algebra Through Practice: Volume 2, Matrices and Vector Spaces, By T. S. Blyth, E. F. Robertson
• Cracking the MCAT with CD-ROM, By James L. Flowers
• Symmetry And Spectroscopy Of Molecules, By K Veera Reddy

Answer 4

Many things have been named gaussian after Carl Friedrich Gauss: gaussian distribution, gaussian integers, etc.

Answer 5

I've seen "jacobian" in lower case in a few books.

For the uninitiated: it refers to either a matrix of partial derivatives, or its determinant. This is named after Carl Gustav Jacob Jacobi.

Sources using lowercase "jacobi":

• Claus Bendtsen, Preliminary Experiences with Extrapolation Methods for Parallel Solution of Differential, in Parallel scientific computing, 1994.
• Foundations of Modern Analysis, By J. Dieudonne.

Answer 6

David Rusin compiled a list of mathematicians whose names appear in the 1991 MSC. (That's the "mathematics subject classification".)

There are 357. He claims Abel's name is the only one among these which appears noncapitalized in the MSC. The other people who have been named in this question (Noether, Descartes, Euclid, Karoubi, Gauss, Boole, Jacobi) all appear in the MSC.

Of course, the 1991 MSC is nearly twenty years old, and is likely to reflect more-formal-than-average usage.

Answer 7

Noetherian rings:

https://en.wikipedia.org/wiki/Noetherian_ring

in honor of Emmy Noether:

https://en.wikipedia.org/wiki/Emmy_Noether

Example sources:

• Lectures on modules and rings, By Tsit-Yuen Lam
• Commutative algebra, By Oscar Zariski, Pierre Samuel, Irvin Sol Cohen
• Model theory and modules, By Mike Prest

(plus many others)

Answer 8

The wronskian, named after Józef Hoene-Wroński, sometimes appears uncapitalised (though it doesn't on Wikipedia, it does in several of the first hits on Google Scholar).

The wronskian of a set of $n$ functions, as a function of $x$, is defined as the determinant of the matrix whose $(i,j)$'th entry is the $(i-1)$'th derivative of the $j$'th function, evaluated at $x$.

Answer 9

Here they talk about abelian and tauberian theorems after (Niels-Henrik Abel and Alfred Tauber), however it is also common to use Abelian theorem and Tauberian theorem. Also, in the last paper, by Lennart Carleson, we can read about "this thread" — that is about people that becomes adjectives.

Answer 10

I have found the term "karoubianization" in the literature (although google only finds for me instances where it is capitalized...). It is a synonym for "pseudo-abelianization" or "idempotent-completion", and refers to the process whereby one enlarges a category universally so that all its idempotents split. The word refers to Max Karoubi.

Answer 11

Well, both newton and gauss are units which are often written in lower case, e is Euler's number, and (of course) abelian groups is generally lowercased. However, it's very standard to keep upper-case Cartesian, Jacobian, Noetherian, Artinian, Newtonian, Gaussian, Eulerian, and other such constructions, with the occasional exception of boolean, when used as a noun rather than an adjective (as in "this number is a boolean").

Answer 12

One that hasn't been mentioned yet is "banachizable" (see e.g. Horvath, "Topological Vector Spaces and Distributions", or Dreseler, B., Schempp, W. On the Fourier transformation on spaces of $(p,q)$-multipliers.) It refers to a topological vector space that can be made into a Banach space by giving it a suitable norm.

Answer 13

Euclid's name has been attached to euclidean space and the euclidean algorithm.

Answer 14

The algebraic structure formed by a set with a commutative binary operation is described as abelian. If $G$ is a group, then the quotient group $G/[G,G]$ (where $[G,G]$ is the commutator subgroup) is the abelianization of $G$.

The Niels Henrik Abel wikipedia page suggests that he pretty much invented group theory. [[citation needed]]