This Might Be The Strangest Constant in Math

Add up the reciprocals of every perfect cube -- 1 + 1/8 + 1/27 + 1/64 + … -- and the sum doesn't blow up. It converges to 1.2020569…, a number called Apéry's constant. And after centuries of work, mathematicians still cannot tell you what it actually is. TIMESTAMPS: 0:00 Intro — summing reciprocal cubes 0:32 The sum converges: watching the digits settle 0:55 Introducing ζ(3) — Apéry's constant 1:34 The Basel problem and Euler's π²/6 2:09 Beukers' double integral approach 3:05 The logarithmic fix — why the integral converges 3:38 Rotating coordinates to reveal π 4:05 Trying the same trick for cubes — hitting the wall 5:10 Even powers have closed forms; odd powers have nothing 5:59 Apéry's 1978 announcement and the skeptical reception 6:49 Cohen verifies the proof — every step holds 7:34 ζ(3) in QED — the electron's magnetic moment 8:49 What we still don't know — transcendence, closed forms, motivic cohomology 9:43 Closing — the simplest questions take the longest Music: All music by Vincent Rubinetti Piece 1: Reflections Piece 2: Trinkets Piece 3: Resonance #aperysconstant #riemannzetafunction #numbertheory #basel problem #euleridentity #quantumelectrodynamics #irrationalnumbers #motiviccohomology