Tagged Questions

1
vote
0answers
29 views

Categorical notions involving $\ell_p$ spaces.

First of all, apologies for a somewhat vague question but let me give a try. We know what the projective objects in the category of Banach spaces are: these are precisely $\ell_1(\ …
7
votes
3answers
398 views

Importance of separability vs. second-countability

For me second-countability always felt like to be the more important and fundamental concept from general topology than separability. I wonder whether there are any points which ca …
33
votes
17answers
3k views

Modern Mathematical Achievements Accessible to Undergraduates

While there is tremendous progress happening in mathematics, most of it is just accessible to specialists. In many cases, the proofs of great results are both long and use difficul …
2
votes
1answer
222 views

Derivation of Bessel functions

I am writing a summary on a work on Fluid Dynamics that develops irrotational flow states that appear to interact amongst each other according to the equations of Electromagnetism …
3
votes
1answer
251 views

Is it true that Nature promotes products?

I hope this question is not unreasonable. We all know how to take products of numbers, this generalises to a huge amount of different types of products in mathematics. In a certa …
4
votes
6answers
839 views

Intuitionistic logic as quantization of classical logic?

A classically trained mathematician is more likely to be familiar (at least anecdotally) with an area of mathematical physics such as deformation quantization than with Intuitionis …
21
votes
10answers
846 views

Great mathematics books by pre-modern authors

Last summer, I read Euclid's Elements, and it was an eye-opening experience; I had assumed that three thousand years' difference would make the notation incomprehensible and the re …
61
votes
28answers
6k views

New grand projects in contemporary math

When I was a graduate student in math (mid-late eighties and early nineties) the arena was dominated by a few grand projects: for instance, Misha Gromov's hyperbolic groups, which …
31
votes
19answers
4k views

Mathematicians whose works were criticized by contemporaries but became widely accepted later

Gauss famously discarded Abel's proof that an algebraic equation of degree five or more cannot have a general solution (Abel himself had rejected divergent series as the work of th …
12
votes
4answers
817 views

motivating geometric representation theory

I am wondering if there is a good motivation for geometric representation theory from within the questions of classical representation theory. In other words, I'd be curious to se …
0
votes
1answer
244 views

Do you set a one or two commas when using \mapsto?

I am currently revising a paper and I am completely confused about the commas. Is it correct English to write 1) "The canonical map $X \to Y$, $x \mapsto f(x)$, is injective." or …
3
votes
0answers
125 views

Is it difficult to prove that nature is chaotic?

If we have a Markov coding or another symbolic description of a dynamical system it is usually easy to prove that the system is chaotic (in the sense of of Li-York, Devaney, positi …
34
votes
10answers
2k 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 n …
30
votes
30answers
4k views

Trichotomies in mathematics

Added. Thanks to all who participated! Let me humbly apologize to those who were annoyed (quite understandably) by this thread, deeming it nothing more than an exercise in futility …
54
votes
15answers
3k 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 …

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