The Riemann Zeta Function at s = 2 – ζ(2) = π²/6

The Basel problem (solved by Euler in 1734) asks for the sum 1 + 1/4 + 1/9 + 1/16 + … = π²/6. Euler’s proof used the infinite product for sin x/x and compared coefficients. This result is the first non‑trivial value of the Riemann zeta function ζ(s). ζ(2) = π²/6 appears in physics (the black‑body radiation spectrum, the Casimir effect). The fact that a sum of rational numbers equals π² (transcendental) is a deep mystery linking number theory and geometry. This is one of the most beautiful results in analysis.