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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....
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...
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/...
web.williams.edu

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