0
votes
1answer
57 views

History of five lemma

I am interested in the history of five lemma. Who was first to prove it and What was the purpose of proving it ? http://en.wikipedia.org/wiki/Five_lemma
7
votes
0answers
102 views

Why is the Mazur swindle named so?

Often results or techniques in mathematics are called 'theorems'. Sometimes they are called 'tricks'. In no other context have I seen a result called a 'swindle'. Is there a historical reason for this ...
4
votes
0answers
33 views

Original proof of the Invariance of Domain Theorem (in English)?

Does anyone know where I can find a translation of the original proof of the Invariance of Domain Theorem in English? Wikipedia cites the original proof to be in: Beweis der Invarianz des ...
13
votes
2answers
226 views

Motivation for introducing algebraic topology?

What kind of topological questions does algebraic topology answer where point set topology is not enough? Phrased differently: Where is the line (or maybe intersection) between point set topology ...
5
votes
2answers
193 views

Who proved that existence of a retraction $r:X\times\mathbb{I}\rightarrow X\times\left\{ 0\right\} \cup A\times\mathbb{I}$ was sufficient for HEP?

It is well known that the existence of a retraction $r:X\times\mathbb{I}\rightarrow X\times\left\{ 0\right\} \cup A\times\mathbb{I}$ is necessary to make $\left(X,A\right)$ a pair having the homotopy ...
27
votes
3answers
542 views

How did we know to invent homological algebra?

Update: Qiaochu Yuan points out in the comments that the title of the question is misleading, as homological algebra did not begin with long exact sequences as I'd thought. (Original question ...
18
votes
2answers
233 views

Curious remark of D. Ravenel

In his beautiful (but difficult) book "Complex cobordism and stable homotopy groups of spheres", concerned mostly with methods of computing homotopy groups of spheres, D. Ravenel describes a general ...
8
votes
1answer
220 views

Who first discovered that the torus supports a flat structure?

Who first recognized that there exists a homogenous metric on the closed genus 1 orientable surface?
14
votes
0answers
316 views

Who was Hermann Künneth?

Question as in the title: Who was Hermann Künneth? Where can I find some biographical information beyond what is available on Wikipedia? The well-known Künneth formula, for example in the form of ...
5
votes
1answer
246 views

Historical Development of CW Complexes

I recently started learning about CW complexes. Although my understanding of them is somewhat nascent, I see that one can deduce a number of useful properties of a space if one can show it is a CW ...
4
votes
1answer
253 views

Poincare conjecture for n=2

Wolfram states "The n=1 case of the generalized conjecture is trivial, the n=2 case is classical (and was known to 19th century mathematicians)" How is it proved that every simply connected closed ...
7
votes
3answers
217 views

The Hopfian property for groups

Let $G$ be a group, which for my purposes would be abelian. To say that $G$ has the Hopf property is to say that every epimorphism of $G$ is an automorphism. Does anyone happen to recall the context ...
8
votes
2answers
247 views

Etymology of the name “deck transformation”

What does the word "deck" mean in "deck transformation"? What's the idea behind this name?