Hilbert’s 13th problem is about equations of the form x7 + ax3 + bx2 + cx + 1 = 0. He asked whether solutions to these functions can be written as the composition of finitely many two-variable functions. (Hilbert believed they could not be.) In 1957, Andrey Kolmogorov and Vladimir Arnold proved that each continuous function of n variables — including the case in which n = 7 — can be written as a composition of continuous functions of two variables. However, if stricter conditions than mere continuity are imposed on the functions, the question is still open.
The Formula to Get 42 Billion Digits of π
While writing "7 Utterly Well-written Math Books About Pi," I found a very interesting math formula that will give you 42 consecutive digits of π accurately but is still wrong.