Apéry's Constant

The sum of the reciprocal cubes, proved irrational by Roger Apéry in 1978 to a stunned audience.

Specifications & Metrics

symbol

ζ(3)

approx

1.20205690315959…

Core Principles & Analysis

• Euler had cracked the even powers — ζ(2) is π²/6 — but the odd case resisted for centuries.
• Apéry's 1978 proof was met with disbelief until Cohen and others verified the arithmetic.
• It appears in the electron's gyromagnetic ratio corrections in quantum electrodynamics.