MathOverflow

Let $P(n)$ be the largest prime factor of $n$. One can check that $11$ is the smallest prime that does not appear as the largest prime factor of a Mersenne number, $P(2^k-1)$. But note that $11=2^2×3-1$. What happens If we ask for the possible values...

I came across the following paper of Gaitsgory a couple of days ago
https://arxiv.org/pdf/1606.09608.
I was wondering whether there exists a proof of the Langlands program over function field using the above? The techniques used by Vincent Lafforgue are disjoint from this as far as I know. Does it shades any light on the Langlands conjecture over global...

This question was first asked here, and Qiaochu Yuan gave a partial answer, but there is a gap in his answer, and thus requires more work.
We use the definition of elementary functions given in Spivak's calculus (with some changes so this is not exactly the same). An elementary function isone which can be obtained by a finite number of operations of addition, multiplication, division, and...

EDIT: I believe that interactions between physics and mathematics are widely appreciated today. However, my impression is that many mathematicians still find it difficult to understand the physicists’ style of thinking, particularly the relative lack...