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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 …

I am trying to prepare a "mathematics talk" for five year olds from my daughter's elementary school. I have given many mathematics talks in my life but this one feels very tough to prepare. Could the …

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 spread into many see …

I am trying to not forget my old math. I finished my PhD in real algebraic geometry a few years ago and then switched to the industry for financial reasons. Now I get the feeling that I want to do a p …

Yitang Zhang recently published a new attack on the Twin Primes Conjecture. Quoting Andre Granville : “The big experts in the field had already tried to make this approach work,” Granville sai …

Let $0 < k_1 < k_2 < k_3 < \cdots $ be all the zeros of the Riemann zeta function on the critical line: $$ \zeta(\frac{1}{2} + i k_j) = 0 $$ Let $f$ be the Fourier transform of the sum of Dirac de …

This is a atypical question for the forum. I'd like to get some advice on whether I should keep pursuing Math in the traditional route, i.e. get a PhD, do research & teach, etc. Due to financial con …

It's a commonplace to state that while other sciences (like biology) may always need the newest books, we mathematicians also use to use older books. While this is a qualitative remark, I would like t …

Just out of curiosity, I wonder whether there are non-amenable groups with arbitrarily large Tarski numbers. The Tarski number $\tau(G)$ of a discrete group $G$ is the smallest $n$ such that $G$ admit …

Most open problems, when formalized, naturally involve quantification over infinite sets, thereby obviating the possibility, even in principle, of "just putting it on a computer." Some questions (e.g …

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 difficult techniques. Even m …

For probably twenty years, category theorists have known of some objects in the Platonic universe called "(weak) $\infty$-categories", in which there are $k$-morphisms for all $k\in \mathbb N$, with s …

Perhaps the "proofs" of ABC conjecture or newly released weak version of twin prime conjecture or alike readily come to your mind. These are not the proofs I am looking for. Indeed my question was ins …

"No". That was my answer till this afternoon! "Mathematics without proofs isn't really mathematics at all" probably was my longer answer. Yet, I am a mathematics educator who was one of the panelists …

Let $p_n$ be the $n$-th prime number, as usual: $p_1 = 2$, $p_2 = 3$, $p_3 = 5$, $p_4 = 7$, etc. For $k=1,2,3,\ldots$, define $$ g_k = \liminf_{n \rightarrow \infty} (p_{n+k} - p_n). $$ Thus the twin …