The Simple Math Problem Nobody Could Solve

Video Description

Thanks to Brilliant for sponsoring this video! Try everything Brilliant has to offer at https://brilliant.org/PhysicsExplained — and get 20% off an annual premium subscription. You can also support this channel via Patreon: https://www.patreon.com/physicsexplained For over half a century, the world’s greatest mathematicians — including Leibniz and the Bernoulli brothers — tried and failed to solve the Basel Problem, a question about the sum of the reciprocals of the square numbers. Along the way, they explored the harmonic series, triangular numbers, and other famous infinite series, but no one could find the exact value. Then, a young Leonhard Euler stepped in… and changed mathematics forever. His astonishingly bold solution not only cracked the Basel Problem, but also revealed deep connections to π, the Riemann zeta function, and the future of number theory. In this video, we explore the history, the failed attempts, the breakthroughs in understanding series convergence and divergence, and Euler’s breathtakingly elegant solution that stunned the mathematical world. Sources & Further Reading Dunham, W. (1990). Journey Through Genius: The Great Theorems of Mathematics. Wiley. ISBN: 978-0140147391. Derbyshire, J. (2003). Prime Obsession: Bernhard Riemann and the Greatest Unsolved Problem in Mathematics. Joseph Henry Press. ISBN: 978-0309085496. Hassler, U., & Hosseinkouchack, M. (2022). Basel problem: Historical perspective and further proofs from stochastic processes. Euleriana, 2(2), 120–130. https://doi.org/10.56031/2693-9908.1032 scholarlycommons.pacific.edu ResearchGate The Euler Archive (MAA). https://eulerarchive.maa.org/ scholarlycommons.pacific.edu Benko, D. (2012). The Basel problem as a telescoping series. The College Mathematics Journal, 43(3), 244–250. https://doi.org/10.4169/college.math.j.43.3.244 Taylor & Francis Online Cezar Lupu O’Connor, J. J., & Robertson, E. F. (2006). Leonhard Euler. MacTutor History of Mathematics Archive, University of St Andrews. https://mathshistory.st-andrews.ac.uk/Biographies/Euler/ Maths History Emmell, A. (2013). Leonhard Euler and the Basel Problem. Saint Michael’s College (PDF hosted by Williams College). https://web.williams.edu/Mathematics/sjmiller/public_html/hudson/Emmell%2C%20Amber_Euler%20%26%20The%20Basel%20Problem.pdf web.williams.edu Follow me on Instagram: https://www.instagram.com/physics_explained_ig Follow me on X (Twitter): https://twitter.com/PhysicsExplain1