The Basel Problem... How Euler Solved It ?

In 1650, Pietro Mengoli posed a question that would stump the greatest mathematicians for nearly a century. What is the exact value of the infinite sum of one over n squared? The Bernoulli brothers attacked it relentlessly but failed. Stirling, De Moivre, and many others tried and failed too. Then in 1734, a 28-year-old Leonhard Euler cracked it wide open using a brilliant connection between the sine function and infinite products. The answer? Pi squared over six. A sum of simple fractions with no apparent connection to circles turned out to be deeply tied to pi. This discovery opened the door to zeta functions and eventually the Riemann Hypothesis, one of the greatest unsolved problems in math today. Watch the video to see how Euler pulled it off. Sources: Euler, L. (1734). Introductio in Analysin Infinitorum – The original work where Euler presented his solution. Mengoli, P. (1650). Novum organum mathematicum – Where the problem was first posed. Dunham, W. (1999). Euler: The Master of Us All – A detailed biography covering Euler's major works including the Basel Problem. Stillwell, J. (2002). The Euler-Lucas Discoveries – Covers the historical context of Euler's breakthroughs. Wikipedia – Basel Problem Basel Problem, Euler, Leonhard Euler, Pietro Mengoli, Jakob Bernoulli, infinite series, pi, mathematics, math history, Riemann zeta function, Riemann hypothesis, mind-blowing math, math explained, number theory