Adding up the reciprocals of every square number gives a surprising answer
Add 1/1² + 1/2² + 1/3² + 1/4² and so on, forever. The sum clearly settles on some finite number — but what number? Mathematicians across Europe failed to find it for nearly a century before a 28-year-old solved it in 1735.
Reveal the answer
π²/6, or about 1.6449. Leonhard Euler's solution stunned mathematicians because pi — normally tied to circles — turned up in a sum that had nothing obviously to do with geometry. The problem, first posed by Pietro Mengoli in 1644, is named the Basel problem after Euler's hometown.
— Leonhard Euler, De Summis Serierum Reciprocarum — Presented 1735