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(\ …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …

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 …