The Simplest Unsolved Problem in Maths

Video source code (manim): https://quantiayt.gumroad.com/ We know e is irrational. We know π is irrational. Both are transcendental. But add them together — e + π — and suddenly, nobody can prove anything. Not a single mathematician, living or dead, can say whether this number is rational or irrational. This is one of the most embarrassing open problems in all of mathematics. In this video, we trace why irrationality proofs work for e and π individually, why every known technique shatters the moment you combine them, and what strange partial results we do have — including a proof that at least one of e + π and eπ must be irrational, without telling us which. 00:00 — Two numbers you know well 00:43 — The simple question 00:49 — We have no idea 01:14 — It gets worse 01:46 — How is this possible? 02:09 — Why e is irrational (Euler's proof) 03:21 — Why π is irrational (Lambert's proof) 03:54 — You lose both structures 04:36 — The fundamental difficulty 05:11 — At least one is irrational (the polynomial trick) 06:06 — Non-constructive existence 06:45 — Nesterenko's theorem (1996) 07:48 — Irrationality measure 08:43 — A blind spot in mathematical knowledge 09:18 — Schanuel's conjecture 10:15 — Gelfond-Schneider theorem 11:01 — Every theorem fails 11:38 — Too simple for our tools 12:09 — Where this leaves us #mathematics #numbertheory #irrational #pi #eulersnumber #openproblems #transcendentalnumbers #proof