The Basel Problem Part 2: Euler's Proof and the Riemann Hypothesis скачать в хорошем качестве

The Basel Problem Part 2: Euler's Proof and the Riemann Hypothesis

In this video, I present Euler's proof that the solution to the Basel problem is pi^2/6. I discuss a surprising connection Euler discovered between a generalization of the Basel problem and the Bernoulli numbers, as well as his invention of the zeta function. I explain Euler's discovery of the connection between the zeta function and the prime numbers, and I discuss how Riemann's continuation of Euler's work led him to state the Riemann hypothesis, one of the most important conjectures in the entire history of mathematics. If you would like to support the production of our content, we have a Patreon! Sign up at   / zetamath   Sections of this video: 00:00 Intro 01:24 Euler's Basel proof 23:20 The zeta function and the Bernoulli numbers 32:01 Zeta and the primes 48:15 The Riemann hypothesis -- Further viewing from 3Blue1Brown: Why is pi here? And why is it squared? A geometric answer to the Basel Problem    • Why is pi here?  And why is it square...   Taylor series    • Taylor series | Chapter 11, Essence o...   -- Further viewing from Mathologer: Euler's real identity NOT e to the i pi = -1 https:/   • Euler's real identity NOT e to the i ...   Euler's Pi Prime Product and Riemann's Zeta Function    • Euler’s Pi Prime Product  and Riemann...   Ramanujan: Making sense of 1+2+3+... = -1/12 and Co.    • Ramanujan: Making sense of 1+2+3+... ...   -- Thanks go to Keith Welker for our theme music. https://www.lunarchariot.com Some of the animations in this video were created with Manim Community. More information can be found at https://manim.community