This is the first video in a two part series explaining how Euler discovered that the sum of the reciprocals of the square numbers is π^2/6, leading him to define the zeta function, and how Riemann discovered the surprising connection between the zeroes of the zeta function and the distribution of the primes, leading ultimately to his statement of the Riemann Hypothesis. This video focuses on how Euler developed a method to approximate this sum to 17 decimal places, as well as how the Bernoulli numbers naturally appear as part of this problem.
This mathologer video touches on many of the same topics we do in this video, including Euler-Maclaurin and sums of powers. It is highly recommended! https://www.youtube.com/watch?v=fw1kRz83Fj0
Theme music by Keith Welker.
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