32
votes
5answers
3k views

What recent programmes to alter highly-entrenched mathematical terminology have succeeded, and under what conditions do they tend to succeed or fail?

I think we all occasionally come across terminology that we'd like to see supplanted (e.g. by something more systematic). What I'd like to know is, under what circumstances is it reasonable to believe ...
33
votes
2answers
4k views

How did “normal” come to mean “perpendicular”?

How and when did the word "normal" acquire this meaning? When I first thought of this, I couldn't really come up with any explanation that wasn't complete speculation -- pretty much all I was able to ...
9
votes
2answers
414 views

Origin of the term “generic” in set theory

In set theory, in particular the context of forcing, if $M$ is a model of $\sf ZFC$ and $P\in M$ is a partial order, we say that $G\subseteq P$ is a generic filter (or $M$-generic or generic over $M$) ...
10
votes
1answer
627 views

Why are they called Specht Modules?

I know that the simple modules of $\mathbb{C}S_n$ are called Specht Modules, and they are named after the German Mathematician Wilhelm Specht because he studied them, but I think these modules were ...
28
votes
3answers
1k views

Why aren't fields called “bodies” instead?

The discrepancy regarding the names of commutative division algebras in German and English has always startled me. In English they are called fields, whereas their original German name is Körper ...
6
votes
1answer
390 views

Origin of the term “weight” in representation theory

In representation theory, there are the related concepts of weights and roots. Since both are kinds of generalised eigenvalues, and eigenvalues are roots of e.g. the characteristic polynomial, the ...
4
votes
1answer
353 views

Where does the name “Reynolds operator” come from?

I always found it strange that, in the context of invariant and representation theory, averaging over the group is called the "Reynolds operator". As far as I know the work of Reynolds was in fluid ...
14
votes
3answers
1k views

Who introduced the terms “equivalence relation” and “equivalence class”?

Consider that the question does not concern the origin of the ideas of equivalence relation and equivalence class. It exactly concerns the origin of the terms "equivalence relation" and "equivalence ...
27
votes
3answers
2k views

What is the difference between an automorphic form and a modular form?

This is more of a question about terminology than about math. The term "automorphic form" is clearly a generalization of the term "modular form." What is not clear is exactly which generalization it ...
5
votes
1answer
221 views

constant averages along orbits

What should one say to describe the situation in which a function $T$ from some set $X$ to itself, and a function $f$ from $X$ to some characteristic-zero field $K$, have the property that the average ...
2
votes
2answers
482 views

Why limit of discrete series representation?

In what sense is the limit of discrete series representation of $SL(2, \mathbb{R})$ a limit of discrete series representations? Where does the name origin from?
6
votes
0answers
308 views

Why the $M$ for Thom spaces?

I've heard $E$ is for entire space, $B$ is for base space, so what is $M$ for?
8
votes
2answers
1k views

Why the letter “p” for genus?

Does anybody know why the genus (arithmetic or geometric) of a curve was historically denoted by $p$ ($p_a$ and $p_g$)? What does the letter "$p$" stand for? Any references would be greatly ...
7
votes
3answers
777 views

What is so “plactic” about the plactic monoid?

The plactic monoid is the monoid consisting of all words from the alphabet $\mathbb{Z}^+$ modulo certain relations. It is important mainly because its elements enumerate semistandard Young tableaux. ...
11
votes
2answers
2k views

What's tropical about tropical algebra?

Please allow me to ask a potentially dumb question (or maybe more precisely, a question floating on clouds of ignorance): Why is a max-plus algebra called a tropical algebra?
10
votes
3answers
1k views

What's so “schematic” about schemes?

Well, the title clearly follows the title of this question. Why the objects so successfully defined by Grothendieck have been called "schemes"? In my opinion the original French word (schéma) doesn't ...
17
votes
3answers
2k views

Why did Gabriel invent the term “quiver”?

A quiver in representation theory is what is called in most other areas a directed graph. Does anybody know why Gabriel felt that a new name was needed for this object? I am more interested in why he ...
7
votes
1answer
1k views

When did the term “Lie group” first appear?

Does anyone know who was the first to coin the term "Lie group"? The following thesis from 1928 suggests that the term was already in use by that time: "Systems of Two Differential Equations from the ...
30
votes
3answers
3k views

Origin of terms “flag”, “flag manifold”, “flag variety”?

These terms have become common in Lie theory and related algebraic geometry and combinatorics, as seen in many questions posted on MO, but it's unclear to me where they first came into use. Probably ...
18
votes
1answer
879 views

Why and how did preschemes become schemes?

Originally (e.g., in the first edition of EGA and in Mumford's Red Book), what are now called "schemes" were referred to as "preschemes." The word "scheme" was reserved for what are now called ...
6
votes
0answers
443 views

Historical and terminological questions about Dan Kan's Ex functor and its relation to the classical case of simplicial complexes

Recall that we may define a functor $\xi:\Delta\to \operatorname{Poset}$ sending a simplex $[n]$ to the set of monotone injections $[k]\hookrightarrow [n]$ for $k\geq 0$ (effectively, $k\leq n$ as ...
28
votes
2answers
2k views

Why are parabolic subgroups called “parabolic subgroups”?

Over the years, I have heard two different proposed answers to this question. It has something to do with parabolic elements of $SL(2,\mathbb{R})$. This sounds plausible, but I haven't heard a ...
16
votes
3answers
1k views

Origin of the term “localization” for the localization of a ring

I'm curious if the term localization in ring theory comes from algebraic geometry or not. The connection between localization and "looking locally about a point" seems like it should be the source ...
6
votes
3answers
1k views

Terminology occuring in automorphic representation and relationship between them

When one tries to read about automorphic representation few terms come up more than others namely, 1.Cuspidal 2.Square Integrable 3.Absolutely Cuspidal 4.Super Cuspidal My understanding about ...