User teil

66 votes

7 answers

10k views

Why is the Hahn-Banach theorem so important?

asked May 31, 2010 at 12:43

47 votes

9 answers

11k views

What are the reasons for considering rings without identity?

asked Apr 26, 2010 at 10:25

30 votes

11 answers

3k views

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

asked May 12, 2010 at 2:00

29 votes

4 answers

5k views

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

asked May 11, 2010 at 9:10

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?

asked Apr 16, 2010 at 12:46

26 votes

4 answers

6k views

What was Galois theory like before Emil Artin?

asked May 31, 2010 at 10:59

22 votes

5 answers

4k views

Why are noetherian rings such natural objects in algebraic geometry?

asked Jul 2, 2011 at 1:59

22 votes

8 answers

4k views

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

asked Apr 18, 2010 at 1:08

18 votes

4 answers

4k views

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

asked Apr 16, 2010 at 11:56

18 votes

2 answers

4k views

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

asked May 31, 2010 at 9:56

18 votes

4 answers

4k views

Why are topological ideas so important in arithmetic?

asked May 27, 2010 at 0:14

17 votes

3 answers

4k views

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

asked Mar 21, 2010 at 23:50

15 votes

4 answers

1k views

Reference request for type theory

asked Mar 22, 2010 at 22:15

15 votes

4 answers

3k views

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

asked May 31, 2010 at 9:48

14 votes

1 answer

2k views

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

asked Jan 19, 2011 at 8:37

14 votes

15 answers

28k views

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

asked May 12, 2010 at 8:58

13 votes

7 answers

2k views

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

asked Feb 18, 2011 at 0:19

10 votes

2 answers

1k views

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

asked Apr 18, 2010 at 0:10

10 votes

4 answers

2k views

Reference request for conceptual numerical analysis

asked May 11, 2010 at 9:17

9 votes

1 answer

2k views

Reference request for a proof of Ramanujan's tau conjecture

asked Mar 24, 2010 at 1:40

9 votes

2 answers

1k views

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

asked Jul 8, 2011 at 5:49

8 votes

1 answer

1k views

Did Apollonius invent co-ordinate geometry?

asked Mar 22, 2010 at 1:15

6 votes

0 answers

2k views

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

asked Mar 22, 2010 at 8:27

6 votes

1 answer

633 views

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

asked Mar 21, 2010 at 8:54

6 votes

1 answer

1k views

How are mathematical objects defined from an ultrafinitist perspective?

asked Jul 18, 2011 at 2:15

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]

asked May 31, 2010 at 9:51

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?

asked Dec 19, 2010 at 4:53

3 votes

2 answers

707 views

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

asked Jun 1, 2010 at 3:56

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/...

asked May 15, 2010 at 14:20

2 votes

5 answers

1k views

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

asked Apr 16, 2010 at 13:16

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35 Questions

Why is the Hahn-Banach theorem so important?

What are the reasons for considering rings without identity?

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

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

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

What was Galois theory like before Emil Artin?

Why are noetherian rings such natural objects in algebraic geometry?

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

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

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

Why are topological ideas so important in arithmetic?

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

Reference request for type theory

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

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

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

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

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

Reference request for conceptual numerical analysis

Reference request for a proof of Ramanujan's tau conjecture

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

Did Apollonius invent co-ordinate geometry?

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

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

How are mathematical objects defined from an ultrafinitist perspective?

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

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

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

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

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