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teil
  • Member for 14 years, 2 months
61 votes
7 answers
9k views

Why is the Hahn-Banach theorem so important?

47 votes
9 answers
11k views

What are the reasons for considering rings without identity?

30 votes
11 answers
3k views

Are there situations when regarding isomorphic objects as identical leads to mistakes?

29 votes
4 answers
5k views

Why is it so difficult to write complete (computer verifiable) proofs?

29 votes
21 answers
9k views

What are some mathematical concepts that were (pretty much) created from scratch and do not owe a debt to previous work?

25 votes
4 answers
6k views

What was Galois theory like before Emil Artin?

21 votes
5 answers
4k views

Why are noetherian rings such natural objects in algebraic geometry?

21 votes
8 answers
4k views

What are the advantages of phrasing results in terms of exact sequences and commutative diagrams?

18 votes
4 answers
4k views

Why are modular forms (usually) defined only for congruence subgroups?

18 votes
2 answers
4k views

Why were Abelian functions so important in the 19th century?

18 votes
4 answers
4k views

Why are topological ideas so important in arithmetic?

17 votes
3 answers
4k views

Dwork's use of p-adic analysis in algebraic geometry

15 votes
4 answers
1k views

Reference request for type theory

14 votes
4 answers
3k views

Is there much difference between Kronecker's and Dedekind's methods in algebraic number theory and commutative algebra?

14 votes
1 answer
2k views

On the non-rigorous calculations of the trajectories in the moon landings

13 votes
7 answers
2k views

Is there a reason why integrals are so much easier to evaluate than sums?

12 votes
15 answers
28k views

What does it mean for a mathematical statement to be true?

10 votes
2 answers
1k views

What would be the ramifications of homotopy theory being as easy as homology theory?

10 votes
4 answers
1k views

Reference request for conceptual numerical analysis

9 votes
1 answer
2k views

Reference request for a proof of Ramanujan's tau conjecture

9 votes
2 answers
1k views

Did Joseph Doob prove that random sequences don't exist?

8 votes
1 answer
1k views

Did Apollonius invent co-ordinate geometry?

6 votes
0 answers
2k views

Fourier transforms via Kurzweil-Henstock integral on locally compact commutative groups

6 votes
1 answer
624 views

Can algebraic number fields be generalized in a similar way to function fields in 1 variable over a finite field?

6 votes
1 answer
1k views

How are mathematical objects defined from an ultrafinitist perspective?

5 votes
3 answers
1k views

Is the ability to define Haar measure the main (or only) reason to consider locally compact topological groups? [closed]

4 votes
4 answers
2k views

Why are principal ideal domains and Dedekind domains prominent, but I always seem to see Noetherian rings rather than Noetherian domains?

3 votes
2 answers
684 views

What goes wrong in a ring that does not have unique factorization?

3 votes
4 answers
3k views

Reference request for category theory works which quickly prove the theorem which generalises the 1st isomorphism theorem for groups/rings/...

2 votes
5 answers
1k views

Is it true that the only interesting topologies are metric topologies and weak topologies?