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Results tagged with soft-question
Search options questions only
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user 4721
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.
75
votes
14
answers
6k
views
Why is Set, and not Rel, so ubiquitous in mathematics?
The concept of relation in the history of mathematics, either consciously or not, has always been important: think of order relations or equivalence relations.
Why was there the necessity of singling …
12
votes
2
answers
773
views
Where does the term "torsor" come from?
Is there a heuristic reason why principal homogeneous spaces of a group (object) $G$ (in some categories) are called $G$-torsors? Does it have anything to do with the idea of "torsion", somehow? When …
- 4,008
126
votes
15
answers
15k
views
Does Physics need non-analytic smooth functions?
Observing the behaviour of a few physicists "in nature", I had the impression that among the mathematical tools they use a lot (along with possibly much more sofisticated maths, of course), there is c …
- 34.7k
73
votes
5
answers
18k
views
Mathematics of path integral: state of the art
I was told that one of the most efficient tools (e.g. in terms of computations relevant to physics, but also in terms of guessing heuristically mathematical facts) that physicists use is the so called …
- 2,821
48
votes
12
answers
9k
views
How to explain to an engineer what algebraic geometry is?
This question is similar to this one in that I'm asking about how to introduce a mathematical research topic or activity to a non-mathematician: in this case algebraic geometry, intended as the most c …
63
votes
11
answers
8k
views
Why certain diophantine equations are interesting (and others are not) ?
It is quite clear why certain differential equations, among the jungle of possible diff equations that is possible to conceive, are studied: some come from physical problems, or from "spontaneous" mat …
- 50.6k
24
votes
8
answers
39k
views
A symbol to denote the set of prime numbers ?
It strikes me that there is no widely accepted symbol to denote the set of usual prime numbers in $\mathbb{N}$.
Look:
$$\zeta(s)=\prod_{p\in \mathrm{?}}\frac{1}{(1-p^{-s})}$$
Wouldn't it be nicer …
- 1
23
votes
6
answers
2k
views
Are rings really more fundamental objects than semi-rings?
The discovery (or invention) of negatives, which happened several centuries ago by the Chinese, Indians and Arabs, has of course be of fundamental importance to mathematics.
From then on, it seems th …
- 4,679
41
votes
1
answer
3k
views
Are there any "homotopical spaces"?
This is a somewhat vague question; I don't know how "soft" it is, and even if it makes sense.
[Edit: in the light of the comments, we can state my question in a formally precise way, that is: "Is th …
- 398
3
votes
2
answers
441
views
Heuristics for 2-morphisms of (algebraic) stacks
For topological spaces and simplicial sets one can consider each pair of parallel morphisms $f,g:X\rightrightarrows Y$ as equipped with a set of 2-morphisms given by homotopies $H:f\simeq g$ (let's ig …
- 45.7k
5
votes
2
answers
841
views
About Kodaira's book on deformations
I happened to read the following sentence in the blog by the physicist Jacques Distler:
"What makes Kodaira’s Complex Manifolds and Deformation of Complex Structures such a delight to read is that …
- 11
38
votes
3
answers
3k
views
"Softness" vs "rigidity" in Geometry
According to common wisdom, there are structures in Geometry that have a more "topological" flavor, others that are more "geometrical", and others that are halfway between. Usually, geometries${}^*$ t …
CommunityBot
- 1
13
votes
1
answer
2k
views
Convenient definition of "category of Riemannian manifolds"?
Has a notion of "category of Riemannian manifolds" been defined and used in the literature?
For which reasons is it or would it (not) be a useful notion?
I think the objects should be all (perhaps c …
- 54.6k
13
votes
3
answers
2k
views
What's so "schematic" about schemes?
Well, the title clearly follows the title of this question.
Why the objects so successfully defined by Grothendieck have been called "schemes"? In my opinion the original French word (schéma) doesn't …
CommunityBot
- 1
12
votes
2
answers
1k
views
Geometric meaning of small extensions ?
Let $(A,\mathfrak{m}_A)$ be a local Artinian $k$-algebra with residue field $k$. Then the scheme $\mathrm{Spec}(A)$ can be loosely seen as a "fat point", or an "infinitesimal neighbourhood" of a point …
- 3,918