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Results tagged with soft-question
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user 4692
Questions that are about research in mathematics, or about the job of a research mathematician, without being mathematical problems or statements in the strictest sense. Do not use this tag for easy or supposedly easy mathematical questions.
30
votes
11
answers
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Are there situations when regarding isomorphic objects as identical leads to mistakes?
If there are not, then would it be easier to say that 2 objects are identical as ordered fields as opposed to being isomorphic as ordered fields? Or is the word isomorphism used to emphasise the fact …
- 4,351
29
votes
4
answers
5k
views
Why is it so difficult to write complete (computer verifiable) proofs?
For example I have read that is agony to give a complete proof of the Jordan curve theorem. Since all statements are meant to be justified by the postulates, where does the difficulty lie?
- 4,351
22
votes
5
answers
4k
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Why are noetherian rings such natural objects in algebraic geometry?
I assume it is partially because they are good generalizations of polynomial rings, but what makes this generalization better than graded algebras or other generalizations of polynomial rings?
- 4,351
9
votes
2
answers
1k
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Did Joseph Doob prove that random sequences don't exist?
In the book "The Mathematical Experience" it says:
"An infinite [binary] sequence $x_1, x_2, \ldots$ is called random in the sense of von Mises if every infinite sequence $x_{n_1}, x_{n_2}, \ldot …
- 4,351
7
votes
Mathematics as a hobby
I do it as a hobby, but then again that is due to my woeful academic record putting academia out of reach.
You don't need to do anything funky to improve your mathematics, you just need time. Look at …
6
votes
1
answer
631
views
Can algebraic number fields be generalized in a similar way to function fields in 1 variable...
Global fields consist of finite extensions of $\mathbb{Q}$ (algebraic number fields) and finite extensions of $\mathbb{F}_q(x)$ (function fields in 1 variable over a finite field). The latter are isom …
- 4,351
3
votes
Quick proofs of hard theorems
The fundamental theorem of calculus; all the long and difficult proofs of Eudoxus and Archimedes became clear and simple. Similarly with co-ordinate geometry.
2
votes
Quick proofs of hard theorems
Power series. Both conceptually and computationally, in the 17th century they replaced a multitude of ad-hoc methods that had been used for millennia.