Should Abelian Be Capitalized in Mathematical Texts?

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Discussion Overview

The discussion revolves around the capitalization of the term "Abelian" in mathematical texts, exploring the reasons behind different conventions and the implications of such choices. It touches on aspects of language, reverence for mathematicians, and editorial practices.

Discussion Character

  • Debate/contested
  • Conceptual clarification

Main Points Raised

  • One participant expresses a personal preference for capitalizing "Abelian" out of reverence for the mathematician Niels Henrik Abel and questions the lack of capitalization in some texts.
  • Another participant suggests that lowercasing names can be seen as an honor in certain scientific contexts, citing examples like "kelvin," "joule," and "gauss," and notes that "abelian groups" are often written in lowercase.
  • A third participant acknowledges the perspective on lowercasing names and expresses gratitude for the insight.
  • It is mentioned that the capitalization of "Abelian" is an editorial convention that has evolved over time, with a reference to an external discussion for further context.

Areas of Agreement / Disagreement

Participants do not reach a consensus on whether "Abelian" should be capitalized, with multiple viewpoints presented regarding the significance of capitalization and editorial conventions.

Contextual Notes

The discussion highlights the lack of a definitive answer regarding the capitalization of "Abelian," indicating that practices may vary and are subject to change over time.

Mandelbroth
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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?
 
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Mandelbroth said:
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.
 
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D H said:
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.
 

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