'Ten Martini' Proof Uses Number Theory to Explain Quantum Fractals
But in some ways, the proof was a bit unsatisfying. Jitomirskaya and Avila had used a method that only applied to certain irrational values of alpha. By combining it with an intermediate proof that came before it, they could say the problem was solved. But this combined proof wasn’t elegant. It was a patchwork quilt, each square stitched out of distinct arguments. Moreover, the proofs only settled the conjecture as it was originally stated, which involved making simplifying assumptions about th