7
votes
1answer
190 views

“All math is useful eventually”

We have all heard the argument : a lot of mathematics that was thought to be useless, abstract constructions with no links to the real world ended up being of use, like some arithmetic is useful in ...
5
votes
6answers
253 views

Fundamental Theorem of Trigonometry

This is a pretty open ended question and I apologize, in advance, if this is not the place for it. But what do you recommend should be given the title of the Fundamental Theorem of Trigonometry and ...
5
votes
1answer
105 views

Are there treelike representations of axioms, theorems, lemmas and corollaries?

I was watching Bill Shillito Lectures on Higher Mathematics, in the second episode he says the basic stuff about axioms and theorems - that axioms are unproved statements in which we build theorems ...
7
votes
3answers
133 views

Realizing groups as symmetry groups

We're supposed to think of (non-Abelian) groups as groups of symmetries of some object. Sometimes it isn't obvious what this object is. For example, the fundamental group of a topological space acts ...
8
votes
6answers
9k views

“Where” exactly are complex numbers used “in the real world”?

I've always enjoyed solving problems in the complex world during my undergrad. However, I've always wondered where are they used and for what? In my domain (computer science) I've rarely seen it be ...
19
votes
0answers
185 views

projective profinite groups

I'm reading the first chapter of Serre's Galois Cohomology. On p. 58, He gives two examples of projective profinite groups: the profinite completion of free (discrete) groups; the cartesian product ...
9
votes
2answers
1k views

Categories of mathematics

I am interested in understanding how mathematics is divided into many categories, such as what categories are particular cases of what, what categories do not or have little overlap with what. This is ...