27
votes
Accepted
Was Kolmogorov enraged after learning about the Karatsuba multiplication algorithm?
Karatsuba's own report can be found in his 1995 paper Сложность вычислений (Complexity of computations). The phrasing he uses is "сильно взволновалo", which Google does translate as "...
- 80k
12
votes
Accepted
History of Direct Sums and Direct Products
"Direct sum" and "direct product" did not use to mean what they now mean in the OP sense, and even today the old usage persists. Van der Waerden in Moderne Algebra (1930-31) (the ...
- 80k
12
votes
Accepted
How and when did the dedicated study of locally compact groups begin?
The symbolic starting date is 1933, when Haar introduced left invariant measures and proved their existence on second-countable locally compact groups, see his Der Massbegriff in der Theorie der ...
- 80k
11
votes
Accepted
History of irreducible polynomials and motivation for them
I will skip the pre-history of solving polynomial equations and factoring polynomials. Let me mention that the analogy between long division of numbers and polynomials goes back to medieval Islamic ...
- 80k
11
votes
Accepted
What was the motive for inventing Gröbner bases?
Fortunately, Buchberger himself described the context of his discovery, see Historical background to Gröbner's paper by Abramson. The method, in general outline, was known to Gröbner long before the ...
- 80k
10
votes
Accepted
(Co)Homology: From topology to the rest of mathematics?
I'd recommend Weibel’s History of homological algebra (1999)(pdf). He describes many threads, such as roots of group cohomology in Hurewicz’s observation that cohomology of an aspherical space $Y$ ...
- 7,809
9
votes
Accepted
How did the modern understanding of Galois theory come about?
The systematic modern terminology and presentation of the Galois theory is due to Artin, a part of his joint project with Emmy Noether to reformulate the "concrete" older algebra in abstract terms, ...
- 80k
8
votes
Accepted
Did Galois make use of the concept of a basis?
No, he did not. You are used to see Galois theory from the modern point of view, developed by Emmy Noether and two of her students: van der Waerden and Emil Artin. I suggest that you read B. Melvin ...
- 5,976
8
votes
Accepted
Why do we call Chinese monoid "Chinese"? Why not "American"?
I do not have the paper "Plactic-growth-like monoids" at hand at the moment but the history is correctly rendered in
[J. Cassaigne, M. Espie, F. Hivert, D. Krob, J.C. Novelli, The chinese monoid, ...
8
votes
What are the modern connections of the Pentagramma Mirificum studied by Gauss?
The Pentagramma Mirificum is a spherical figure formed by a series of five great circle arcs, each orthogonal to the next, and it probably does deserve a Wikipedia entry. However some elementary ...
- 80k
8
votes
Accepted
When did Macaulay rings become Cohen-Macaulay rings?
Actually, the name Cohen-Macaulay rings and Macaulay rings areboth due to Zariski and Samuel (Commutative Algebra, Volume 2, App. 6, p. 396, 1958):
Definition 1. Let $A$ be a local ring. The common ...
- 4,400
7
votes
Accepted
Where are Pierre Samuel's videos of Bourbaki proceedings available?
It appears to be from the following broadcast (source):
ARTE (FRANCE TÉLÉVISION - LA CINQUIÈME) Émission « Archimède » du 14 novembre 2000 consacrée à Bourbaki, réalisée avec la collaboration de ...
- 1,224
7
votes
Accepted
What was the significance of Eisenstein's discovery of invariants?
The terminology did not change that much. Algebraic forms are more often called homogeneous polynomials, but for polynomials in two variables "binary form" is still often used. Invariant of a binary ...
- 80k
7
votes
(Co)Homology: From topology to the rest of mathematics?
As a complement to the answer provided by Francois Ziegler, I would add the first three paragraphs of Homological Algebra (1956), by Henri Cartan and Samuel Eilenberg:
During the last decade the ...
- 5,976
7
votes
Accepted
History of extension problem of abelian groups
A detailed account of the early history of group extensions is given in chapter 9 of Nicholson's 1993 PhD thesis (freely available from Oxford's research archive). Later, cohomological, developments ...
- 80k
6
votes
Accepted
Where does the letter S in "$S$-units" and in localization $S^{-1} R$ come from?
As Francois Ziegler suggests in his comment, the notation $S$ and term $S$-unit might go back to Artin and Whaples in their paper about the product formula: "Axiomatic Characterization of Fields by ...
- 5,869
6
votes
Gauss's anticipation of quaternions and their relation to congruences
I asked a mathematician who is an expert to abstract algebra and he showed me that Gauss's congruence was actually correct. To prove Gauss congruence let's introduce the following notation: $$x = a+bi,...
- 4,679
6
votes
Accepted
How did the terms "center" and "centralizer" come up in group theory?
The center (originally the central) seems to have appeared between the first and second edition of Burnside’s book (1897, §53 vs. 1911, §93) and more precisely in de Séguier (1904, §51):
Ainsi l’...
- 7,809
6
votes
Accepted
Jordan called isomorphisms (iso.) and homomorphisms "iso. holoedriques" and "iso. meriedriques" respectively; translation of holoe/meried-driques?
To quote from Jordan's Traité des substitutions et des équations algébriques (1870), p. 56 (https://archive.org/stream/traitdessubstit00jordgoog#page/n79/mode/2up):
"§ 67. A group Γ is called "...
6
votes
When did mathematicians realize that theory of algebraically closed fields admits quantifier elimination?
A useful sketch of history is given in Alfred Tarski's Elimination Theory for Real Closed Fields by van den Dries. The result was known to Tarski by 1948 (when his Decision Method for Elementary ...
- 80k
5
votes
Accepted
What are the modern connections of the Pentagramma Mirificum studied by Gauss?
[I do not have enough reputation to add comments so I have to make this an answer]
FWIW, I have written a Polish Wikipedia article on pentagramma mirificum. For the time being, you can try to make ...
- 128
5
votes
Accepted
Why is the term "isotropic" used to describe a quadratic form and a vector?
This is an example of how a term migrates from the original context by broken telephone through various generalizations and transfers. It started with Poncelet introducing "imaginaries", i....
- 80k
4
votes
Accepted
Where did the notion of the product in a category first appear?
It appears in MacLane's 1950 paper Duality for Groups, published in the Bulletin of AMS. Of course, he is dealing specifically with the category of groups, but the definition is categorical. Section 3,...
- 80k
4
votes
Why was solving polynomial equations historically considered so interesting?
The conics as geometric shapes were investigated comprehensively by many ancient Greek mathematicians. After Descartes's innovation of introducing coordinates, they were seen as essential examples of ...
- 3,760
4
votes
Why is the number of elements in a group called "order"?
I will promote my comment to an answer. The theory of permutations and permutation groups was the original (abstract) setting of group theory, and so the term originated there. I believe the reason ...
- 141
4
votes
Accepted
Could a "field" have non-commutative multiplication originally?
Not quite. There was some vagueness in Dedekind's early formulations, but the tendency was to use "Körper" or "field" when the multiplication is commutative from the start. As a curiosity, in Russian ...
- 80k
4
votes
First Use of the Short Exact Sequence
To narrow down your search:
The lower bound is (probably) 1941. Dieudonne in his book "A history of Algebraic and Differential Topology" writes when discussing Gysin's exact sequence (which ...
- 1,755
4
votes
Accepted
Intuitions for Frobenius' generalization of characters to nonabelian finite group given the historical context
We can’t redo the history. It just happens to be the case that Dedekind’s questions to Frobenius about group determinants were the original inspiration. It is not intuitive. Only later did Frobenius ...
- 5,869
3
votes
Where are Pierre Samuel's videos of Bourbaki proceedings available?
These videos (some of them, maybe) were on view during an exhibition about Bourbaki and his early collaborators at Bibliothèque de l'École normale supérieure.
Presumably the Association des ...
- 131
3
votes
How did the modern understanding of Galois theory come about?
My impression is that Artin's role in the development of Galois theory is usually greatly overrated. Kiernan's article jumps from 1900 to Artin in the late 1930s. Certainly a "modern" Galois theory ...
- 31
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