The Basel Problem — Sum of Reciprocal Squares

In 1650, Pietro Mengoli posed what became one of the most famous unsolved problems of the era: what is the exact sum of 1 + 1/4 + 1/9 + 1/16 + … (the sum of reciprocals of all perfect squares)? It defeated the best minds for nearly a century. Euler solved it in 1734, proving the answer is π²/6 — a breathtaking appearance of π where no circle was in sight. The result shocked the mathematical world and launched the theory of infinite series.