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Results tagged with soft-question
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user 126667
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.
42
votes
why haven't certain well-researched classes of mathematical object been framed by category t...
Fundamentally I agree with Mike Shulman's comment and I do not really want to claim the following fancy language is at all necessary to answer this question, but you may (or may not) find it illuminat …
- 25.2k
10
votes
Accepted
Are rings really more fundamental objects than semi-rings?
Of course the real question is whether abelian groups are really more fundamental objects than commutative monoids. In a sense, the answer is obviously no: the definition of commutative monoid is sim …
29
votes
What is the definition of "canonical"?
Not a definition, exactly; I would say the situation is similar to that of forgetful functor. If I say there is a canonical isomorphism between X and Y, then what I mean is that if asked, pretty muc …
14
votes
Are there any important mathematical concepts without discrete analog?
Is there a discrete analogue of the notion of discreteness?
7
votes
Between abstract and concrete: What's the right way to think of specific categories?
There is nothing really particular to categories about this question. You may as well ask:
If one is talking about a specific group, say the group $\mathbb{Z}/3\mathbb{Z}$, should one think of it as …
- 25.2k
22
votes
Describe a topic in one sentence.
Algebraic geometry: CommRing behaves a lot like Setop.
2
votes
Algorithmic Combinatorics resources?
The method of coupling from the past can be used to sample uniformly at random from certain distributions. Here is a simple demonstration which illustrates the method, and here it is in action comput …
30
votes
How do you keep your research notes organized?
Same answer as Charles except I've tried to organize the stuff which is coherent enough to make it to my computer in a personal wiki. I use gitit for various reasons including LaTeX support, but I'm …
47
votes
Most interesting mathematics mistake?
Pontryagin made a famous mistake while computing the stable homotopy groups of spheres (specifically, π2) which led to the discovery of the Kervaire invariant. I won't spoil what the mistake was: wat …