Uploads from Physics Explained

Currently Playing: The Pattern Nobody Can Prove (But Everyone Believes)

Go to https://sintra.ai/physics or use code PHYSICS to get an exclusive 72% off on all plans. 14-day money-back guarantee. In this video, we explore one of the most beautiful and mysterious ideas in all of mathematics: the Riemann Hypothesis. Beginning with the harmonic series, the Basel problem, and Euler’s zeta function, we build step by step toward Riemann’s extraordinary conjecture about the hidden pattern of the non-trivial zeros of the zeta function. Along the way, we look at convergence, analytic continuation, the functional equation, and why this unproven idea has fascinated mathematicians for more than 150 years. 🤝 Support the channel Patreon → https://www.patreon.com/physicsexplained 🔗 Follow me Instagram → https://www.instagram.com/physics_explained_ig X (Twitter) → https://twitter.com/PhysicsExplain1 Sources and Further Info Prime Obsession — John Derbyshire https://www.penguinrandomhouse.com/books/293510/prime-obsession-by-john-derbyshire/ The Music of the Primes — Marcus du Sautoy https://harpercollins.co.uk/products/the-music-of-the-primes-why-an-unsolved-problem-in-mathematics-matters-marcus-du-sautoy Euler: The Master of Us All — William Dunham https://bookstore.ams.org/dol-22/ The Riemann Hypothesis, explained — Jørgen Veisdal / Privatdozent https://www.privatdozent.co/p/the-riemann-hypothesis-explained-478 The music of the primes — Plus Maths https://plus.maths.org/music-primes Visualising The Riemann Zeta Function — Make Your Own Algorithmic Art The Riemann Hypothesis: The Story of a Millennium Problem — Gleam Math https://www.gleammath.com/post/the-riemann-hypothesis Extending the Riemann Zeta Function with Fractional Sums — Lines That Connect https://www.youtube.com/watch?v=N0Ho0XGuXZs But what is the Riemann zeta function? Visualizing analytic continuation — 3Blue1Brown https://www.youtube.com/watch?v=sD0NjbwqlYw&t How The Riemann Zeta Function Encodes The Prime Numbers — CMMath https://www.youtube.com/watch?v=9vs0OpmcjXY What is the Riemann Hypothesis REALLY about? — HexagonVideos https://www.youtube.com/watch?v=smAfvRTfPJY