Alex Kontorovich, Discover and Read the Best of Twitter Threads by @AlexKontorovich

Alex Kontorovich

AlexKontorovich

Thread: What is the Music of the Primes? (From last night's @MoMath1 lecture on the Riemann Hypothesis. TL;DR: watch this @QuantaMagazine video https://youtu.be/zlm1aajH6gY )The tricky thing about prime numbers is that

Triple product L-functions arise naturally in (at least) the following two ways:1) (Arithmetic) Quantum Unique Ergodicity (AQUE)2) Langlands functoriality for GL(2)xGL(2)Let's first talk about AQUE (for which Lindenstrauss won a

Brief lecture 1 overview: (thread on the progression of our understanding of "Number")Imagine some birds in a dense forest. They see 1 hunter go in, so they fly up high

The concept of conditional expectation is (surprisingly?) difficult for students, until they do the following exercise:Let X and Y be iid 6-sided dice rolls, and let Z=X+Y be the sum.

Hey everybody! Gather round; I just discovered this incredible ancient way for multiplying! It's so simple; here's what you do: Say you want 3x4. So you make 3 horizontal lines,

Ok, take the quadratic polynomialf(n) = n^2-n+41,and notice that f(1)=41, f(2)=43, ... f(40)=1601 are *all* prime. There's a rather deep reason for this. (Thread)The discriminant of the quadratic isD =

Yeah, this is one of the craziest stories in the history of math, and deserves to be better known!In the mid-1500s, Cardano (building on del Ferro and Tartaglia, not entirely