23 votes
Accepted

Emmy Noether's announcement in 1932 ICM

All past ICM proceedings are available online in one place: https://www.mathunion.org/icm/proceedings. Scroll down to the year 1932, where pp. 189-194 in volume 1 is Noether's paper, which starts on p....
KCd's user avatar
  • 5,597
13 votes
Accepted

The First Published book on Algebraic Topology

"The first" is either Listing (1847), or Veblen (1922), or Lefschetz (1942), depending on what counts. Here's Dieudonné's book list from his History of Algebraic and Differential Topology: &...
Conifold's user avatar
  • 76k
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 ...
Conifold's user avatar
  • 76k
11 votes
Accepted

A knot cannot be tied in 4-dimensions, but when was this conjectured and proven?

A nice account is found in a note to R. Steiner's Die vierte Dimension (1995; translation): Felix Klein (1845–1925) seems to have been the first mathematician to draw attention to this phenomenon ...
Francois Ziegler's user avatar
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
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 $Y$ ...
Francois Ziegler's user avatar
10 votes

History of various definitions of topology

By the time these definitions were introduced as definitions there was a body of previous work, where they were convenient side notions for stating theorems in special cases for subsets of real line, ...
Conifold's user avatar
  • 76k
9 votes
Accepted

What topological ideas did Gauss introduce to his student Möbius?

While you already accepted an answer, it seems not superfluous to add another one, in particular since you are implicitly asking for a better translation/understanding of the passage you quoted. ...
Peter Heinig's user avatar
9 votes

What is the source of Hermann Weyl's remark about "near-sighted policemen" with respect to compact spaces?

The closest match I could find is in H. Weyl, "Harmonics on homogeneous manifolds." Annals of Mathematics, Second Series, Vol. 35, No. 3, July 1934, pp. 486-499, as reproduced in K. ...
njuffa's user avatar
  • 6,516
8 votes
Accepted

Who discovered the singular cup product?

The history of the cup product is described on pages 135–136 of Never a Dull Moment: Hassler Whitney, Mathematics Pioneer by Keith Kendig. A key event was the 1934 International Conference in Topology,...
Timothy Chow's user avatar
  • 1,506
8 votes
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On the history of Haar measure

Cohn himself recommends historical notes at the end of sections 15, 16 of Abstract Harmonic Analysis by Hewitt and Ross, volume 1. Here is an excerpt: "Invariant integration on one or another ...
Conifold's user avatar
  • 76k
8 votes
Accepted

Who proved Banach fixed point theorem in abstract metric spaces for the first time?

Pages 97-107 of the book Mathematical Lives: Protagonists of the Twentieth Century From Hilbert to Wiles is an article by Guerraggio about Caccioppoli. On p. 100, Guerraggio says the contraction ...
KCd's user avatar
  • 5,597
8 votes
Accepted

Who is or was Stephen Barr, author of Experiments in Topology?

The cross references to other titles by the same author in Stephen Barr's books quickly revealed that he is also the author of the following: Stephen Barr, A Miscellany of Puzzles: Mathematical and ...
njuffa's user avatar
  • 6,516
8 votes

The First Published book on Algebraic Topology

I searched MathSciNet for books with "Algebraic Topology" in the title... Lefschetz, Solomon Algebraic Topology. American Mathematical Society Colloquium Publications, Vol. 27 American ...
Gerald Edgar's user avatar
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8 votes
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Continuity, Hausdorff

Roughly it goes like this. Hausdorff (and others at the time) considered "manifolds" $M$, where for each point $p \in M$ there are "coordinate neighborhoods" which are in 1-1 ...
Gerald Edgar's user avatar
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7 votes
Accepted

Who first proved the "Cantor-Heine theorem" on uniform continuity?

An explicit definition of uniform continuity was first published by Heine in Über Trigonometrische Reihen (On Trigonometric Series), Journal für die Reine und Angewandte Mathematik, 71 (1870), pp. 353–...
Conifold's user avatar
  • 76k
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
7 votes

Which book covers topology historically?

J. Dieudonne, A History of Algebraic and Differential Topology, 1900 - 1960.
Alexandre Eremenko's user avatar
7 votes
Accepted

Origin of Compactness

See Wiki's entry on Compact space : Alexandrov, Pavel and Urysohn, Pavel (1929), "Mémoire sur les espaces topologiques compacts", Koninklijke Nederlandse Akademie van Wetenschappen te Amsterdam, ...
Mauro ALLEGRANZA's user avatar
7 votes

Which book covers topology historically?

I don't entirely understand the question, but this book is probably relevant: J. H. Manheim, The Genesis of Point Set Topology (1964). I must have borrowed it from a library a long time ago. It is ...
Calum Gilhooley's user avatar
6 votes

Which book covers topology historically?

I. M. James, History of Topology. This is a collection of 40 essays by different authors, on topics related mostly to manifolds and algebraic topology. Perhaps the page https://mathshistory.st-andrews....
KCd's user avatar
  • 5,597
6 votes
Accepted

Normed vector space : when and who?

A good source for these types of questions is Miller's site Earliest Known Uses of Some of the Words of Mathematics. On the norms in vector spaces we find the following: "On page 57 of his 1908 ...
Conifold's user avatar
  • 76k
6 votes
Accepted

Historical ways of *presenting* or axiomatizing the notion of a topological space

An early definition of topology is given in the book Kuratowski, Topology I (first edition, 1933). It is defined in terms of a "closure operator", $X\mapsto\overline{X}$ acting on the set of ...
Alexandre Eremenko's user avatar
6 votes
Accepted

Topologies without the axiom that finite intersection of open sets is open

There was no early discussion of topology without closure under finite intersections. The open set definition first given by Bourbaki (1940) includes this condition, and its predecessors in terms of ...
Conifold's user avatar
  • 76k
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
Accepted

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
  • 76k
5 votes

Motivation of Continuous Functions

Isolation of the modern concept is generally attributed to Bolzano (1817; translation) and/or Cauchy (1821), with some controversy on their independence: see Grattan-Guinness (1970), Freudenthal (1971)...
Francois Ziegler's user avatar
5 votes
Accepted

What exactly did Poincaré mean by 'simply connected'?

In the setting of the conjecture (closed manifolds) he certainly meant “homeomorphic to the $n$-sphere” — see second page of that fifth complement: simplement connexe au sens propre du mot, c'est-à-...
Francois Ziegler's user avatar
5 votes

On the history of Haar measure

Try these references: Section 7.5 of History of Topology, edited by I. M. James. Section 2.2 of the chapter "Topological Features of Topological Groups" in Handbook of the History of General Topology,...
lhf's user avatar
  • 331
5 votes

Who is the John Thomas of "Thomas's Plank" and "Thomas's Corkscrew"?

I can't speak to whether my father (John David Thomas II) is the author of Thomas' Plank and Thomas'Corkscrew, but he DEFINITELY is the John Thomas you reference that taught at NMSU. I am grateful to ...
David Thomas's user avatar

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