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Results tagged with soft-question
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user 3709
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.
6
votes
Which mathematicians have influenced you the most?
Simon Donaldson. His proofs involve (to quote wikipedia) a creative use of analysis. I loved his proof of the theorem of Narasimhan and Seshadri.
15
votes
2
answers
4k
views
Learning Arakelov geometry
I have a complex analytic background (Griffiths and Harris, Huybrechts, Demailley etc). Also, I understand some PDE. I want to learn Arakelov geometry (atleast till the point I can "apply" computation …
- 3,383
5
votes
What's your favorite equation, formula, identity or inequality?
$(A-\lambda _1) (A-\lambda _2) \ldots = 0$, the Cayley-Hamilton theorem.
11
votes
Problems where we can't make a canonical choice, solved by looking at all choices at once
Sard's theorem provides such an example. Given a random smooth map between two manifolds (lets say compact and of the same dimension), there is no canonical way of constructing a regular value. But, S …
9
votes
2
answers
607
views
Hyperbolic PDE in mathematics
Hyperbolic PDE (like the wave equation) are roughly speaking, PDE that satisfy the “finite propagation speed of information” property. They are ubiquitous in mathematical physics (essentially, most fu …
- 3,383
6
votes
Where is number theory used in the rest of mathematics?
If Arakelov geometry counts as number theory, then, http://arxiv.org/pdf/math/0401029v1.pdf demonstrates the computation of the Analytic torsion (a purely analytic object involving the product of dete …
2
votes
How do you decide whether a question in abstract algebra is worth studying?
This paper has a very nice introduction (it is on "pointless topology"). So apparently, one may come up with very random definitions for their own sake and hope someone "applies" them to more "concret …
3
votes
Why do we need random variables?
Practically everything we measure in real life (for instance the time taken for an apple to fall on Newton's head) is "random" in the sense that if we perform the experiment again, we will not get the …
- 3,383