22 votes

Why are étale morphisms called "étale"?

From Milne's site: There are two different words in French, "étaler", which means spread out or displayed and is used in "éspace étalé", and "étale", which is rare ...
anon's user avatar
  • 221
16 votes
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How did Grothendieck encounter and adopt the categorical language?

Grothendieck's familiarity with the categories predates Kansas. In 1948-1949 he attended Séminaire Cartan at École Normale Supérieure, where he "took the liberty of speaking to Cartan, as if to ...
Conifold's user avatar
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11 votes
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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 ...
Conifold's user avatar
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10 votes

Origins and history of branched covering

The theory of branched (or ramified) coverings has its origins in continuation of analytic functions and the attempts to find maximal analytic continuations of a given function. However, certain ...
Margaret Friedland's user avatar
10 votes
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(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 $Y$ ...
Francois Ziegler's user avatar
10 votes
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When was the first time/s that sheaves entered algebra and algebraic geometry?

Here is what Dieudonné has to say on contributions other than Serre's in History of Algebraic Geometry (VIII.1.6 and VIII.1.11): "As early as 1909, Severi, while defining the arithmetic genus of ...
Conifold's user avatar
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9 votes
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Why are étale morphisms called "étale"?

The use of étale predates SGA, and "spread out" fits Grothendieck’s idea of all-encompassing topos, "vast" and "slack", better than usual, as these things go. The name of étale morphisms derives from ...
Conifold's user avatar
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9 votes
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When did mathematician start to draw figures from equation?

The coordinate method may be traced to antiquity, specifically to the works of Apollonius of Perga (c. 262 – c. 190 BC) The following quotation from Carl B. Boyer,"Apollonius of Perga" (1991). A ...
Margaret Friedland's user avatar
8 votes

What is the history behind the concept of "schemes" in algebraic geometry?

“A story says that in a Paris café around 1955 Grothendieck asked his friends “what is a scheme?” The very first time the word “schéma” was uttered, in Paris, at an official seminar talk, was during ...
tttbase's user avatar
  • 602
8 votes

Origins of Zariski topology

Zariski introduced his topology in this paper: The compactness of the Riemann manifold of an abstract field of algebraic functions, Bull. Amer. Math. Soc., 50 (1944), 683-691. You can read it online ...
KCd's user avatar
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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 ...
José Carlos Santos's user avatar
6 votes
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Who first had the idea to study surfaces via rings of functions, as in algebraic geometry?

A canonical reference on this is Dieudonne's History of Algebraic Geometry. An abridged version Historical Development of Algebraic Geometry is freely available, see also Easton's slides. Let me make ...
Conifold's user avatar
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6 votes
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Where was the word "pencil" first used in (projective) geometry and what is the reason behind this curious name?

From the Earliest Known Uses of Some of the Words of Mathematics site : PENCIL OF LINES. Desargues coined the term ordonnance de lignes, which is translated an order of lines or a pencil of lines [...
nwr's user avatar
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5 votes

Grothendieck's approach to solving problems

"The way to understand a mathematical problem is to express it in the mathematical world natural to it -that is, in the topos natural to it. Each topos has a natural cohomology, simply taking the ...
Ascenso's user avatar
  • 53
5 votes

Who first described the fundamental group as the group of deck transformations?

The answer to the title question is Poincaré, in the very note Sur l’Analysis situs (1892) where he first introduced the fundamental group. Cf. the description by “Saint-Gervais”: Now Poincaré ...
Francois Ziegler's user avatar
5 votes
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Who first described the fundamental group as the group of deck transformations?

The idea of a relation between fundamental groups and permutations of the universal cover long predates Grothendieck and SGA. It appears implicitly already in Riemann's work on complex surfaces in ...
Conifold's user avatar
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5 votes

Why are étale morphisms called "étale"?

The mathematical terminology "étalé" [spread out] was used by Grothendieck in his 1957 Tohoku paper, and was preexisting at that time. Grothendieck, A. (1959). Technique de descente et théorèmes d'...
Colin's user avatar
  • 151
4 votes

Omar Khayyam is well known as a mystical poet (Quatrains). He is also known as a mathematician. Are these the same?

According to the wiki page, he is a mathematician and a famous poet.Many of the books and magazines we read when we were students stated that Omar Khayyam (we say Ömer Hayyam) was a mathematician and ...
scarface's user avatar
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4 votes

Grothendieck and Fields medal 1962

There is a very interesting [resource], let me sum up my conclusions. The beginnings of the Fields medal were not about honoring the best mathematicians, but "The committees used the medal as a ...
user234212323's user avatar
4 votes
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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....
Conifold's user avatar
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4 votes

Who first had the idea to study surfaces via rings of functions, as in algebraic geometry?

The idea is usually attributed to Dedekind and Weber in Theorie der algebraischen Functionen einer Veränderlichen (1882): [1, 2, 3, 4, 5,...].
Francois Ziegler's user avatar
4 votes

What is the history behind the concept of "schemes" in algebraic geometry?

"The term itself was coined by Chevalley, although accepted in a more restrictive sense than the term as used by Grothendieck. In Foundations of Algebraic Geometry, André Weil had introduced into ...
tttbase's user avatar
  • 602
4 votes

When was the first time/s that sheaves entered algebra and algebraic geometry?

Jean Pierre Serre was awarded the Field medal in 1954. I recommend you his talk for the occasion. Cohomologie et géométrie algébrique. Congrès int. d’Amsterdam, 1954, vol. III, pp. 515-520 He starts ...
user234212323's user avatar
4 votes
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The reason why sheaf theory emerged

Sheaves were created by Leray to avoid doing anything resembling applied mathematics while he was in a prisoner of war camp during World War II, as he was an expert on PDEs and did not want this to ...
KCd's user avatar
  • 5,607
4 votes

What is the history of vector bundles and their characteristic classes?

There are brief historical notes on the history of vector bundles and characteristic classes in section 6.5.4 of Luke-Mishchenko, Vector Bundles and Their Applications. A more detailed account is ...
Conifold's user avatar
  • 76k
3 votes

How did Grothendieck encounter and adopt the categorical language?

In the "Esquisse Thématique des Principaux Travaux Mathématique 4.a Algèbre catégorique", Grothendieck says: En fait, de facon continuelle depuis 1953, je me suis senti dans l'obligation, ...
user234212323's user avatar
3 votes

Where was the word "pencil" first used in (projective) geometry and what is the reason behind this curious name?

This is a question about English terminology. As others on here have pointed out, the French terminology is different. The original meaning of the English word “pencil” is a fine brush; this is also ...
fdb's user avatar
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3 votes

Material models of Riemann surfaces

Kharkiv University (Ukraine) subscribed to all models made M. Schilling, who probably was a student of Klein, and who run a company making and selling these models. Currently they photograph them and ...
Alexandre Eremenko's user avatar
3 votes

Complete list of publications of Rebecca Barlow

Math Sci Net lists 6 publications, dating from 1984-1999.
kimchi lover's user avatar
  • 2,555
3 votes

History of cohomology theory

Cohomology theories were introduced independently by A. Kolmogorov, Ueber die Dualitat im Aufbau der kombinatorischen Topologie, Mat. Sbornik, vol. 1, 1936, 97-102, and by J. W. Alexander, On the ...
Alexandre Eremenko's user avatar

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