Should Abelian Be Capitalized in Mathematical Texts?

[Mandelbroth]

I've always capitalized the word Abelian. Abel has always been one of my idols, and I've just seen it as the right thing to do, both in reverence of a mathematical prodigy and in proper use of the English language. However, I've gone back to review some algebra before attempting to learn some algebraic geometry, and a lot of people do not capitalize the word.

Is there a reason for this?

 

[D H]

Is there a reason for this?

Getting your name lowercased is an extreme honor in some branches of science and mathematics. For example, look at the units for temperature (kelvin), energy (joule) and magnetic flux (gauss). Mathematicians have gaussian distributions, boolean algebras, and of course abelian groups.

 

[Mandelbroth]

Getting your name lowercased is an extreme honor in some branches of science and mathematics. For example, look at the units for temperature (kelvin), energy (joule) and magnetic flux (gauss). Mathematicians have gaussian distributions, boolean algebras, and of course abelian groups.

I'd never thought of it that way. Thank you.

 

[UltrafastPED]

It is an editorial convention. Over time, conventions have changed.

See this discussion: http://mathoverflow.net/questions/44946/why-is-abelian-infrequently-capitalized

 

[blue_raver22]

There are a few reasons why the word "Abelian" may not always be capitalized. First, it is important to note that while the mathematician Niels Henrik Abel is certainly a significant figure in the development of group theory and algebra, the term "Abelian" itself is not named after him. It is derived from the name of the mathematician Augustin-Louis Cauchy, who used the term "Abelian" to refer to mathematical structures that follow certain commutativity properties. Therefore, some mathematicians may not see the need to capitalize the term as a form of reverence to Abel.

Additionally, the convention of capitalizing mathematical terms can vary among different fields and even among different individuals. Some may choose to capitalize the term "Abelian" as a way to emphasize its importance or to distinguish it from other mathematical concepts, while others may not see the need to do so. Ultimately, whether or not to capitalize the term is a matter of personal preference and style, and as long as the meaning is clear, both capitalization and non-capitalization are acceptable.