Interestingly, there's not only theorems but also conjectures in this list. Interesting bit: > ITEM 125 (Polya): > CONJECTURE: If a function has a power seri

Interestingly, there's not only theorems but also conjectures in this list. Interesting bit: > ITEM 125 (Polya): > CONJECTURE: If a function has a power series with integer coefficients and radius of convergence 1, then either the function is rational or the unit circle is a natural boundary. > Reference: Polya, Mathematics and Plausible Reasoning, volume 2, page 46. Has this conjecture been proved or disproved by now?