Puzzles
Add up the reciprocal of every square number, forever. What do you get?
Take 1 + 1/4 + 1/9 + 1/16 + 1/25 and so on, adding the reciprocal of every perfect square out to infinity. The sum obviously keeps growing more slowly and seems to approach some fixed number, but which one? Mathematicians across Europe tried and failed to find it for decades before a young Leonhard Euler cracked it in 1734.
Reveal the answer
The sum equals pi-squared over 6, approximately 1.6449. Euler's solution, comparing the series to the infinite factorization of the sine function, was so unexpected it made his reputation overnight, and was later generalized into the Riemann zeta function at the heart of modern number theory.
— Leonhard Euler, De Summis Serierum Reciprocarum — 1734 (the Basel Problem)