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The Dream: Riemann Hypothesis and F1 (RH Saga S1E1)

This is the first episode of the RH Saga. We embark on a journey into the world of L-functions, by introducing the Riemann Hypothesis and the dream of a new geometry over the "field with one element". The aim of RH Saga Season 1 is to map the landscape of L-functions, as a foundation for future in-depth exploration of some of the most immortal math problems of all time. This video is part of a PeakMath course. Join the journey at https://www.peakmath.org/ --- Chapters: 00:00 - Introduction to the RH Saga 01:50 - Introduction to Episode 1: The Dream 03:17 - Chapter 1: Intro to F1 07:58 - Summary of Chapter 1 09:26 - Chapter 2: Recap of RH 18:46 - Chapter 3: Proof of RH? 21:40 - Summary of Chapter 3 --- Links: 1. "Numbers as Functions" - Yuri Manin https://arxiv.org/pdf/1312.5160.pdf 2. "Riemann's Hypothesis" - Brian Conrey https://tinyurl.com/conrey90 3. SageMathCell https://sagecell.sagemath.org/ 4. SageMath https://www.sagemath.org/ 5. SageMathCell permalink for Riemann spectrum code https://tinyurl.com/e1-spectrum 6. SageMathCell permalink for cosine waves code https://tinyurl.com/e1-cosine --- Errata: Around 6:44: Just to clarify - the "fractional Gamma value" \Gamma(p/q) may not be a period in itself, but \Gamma(p/q)^q is certainly a period. --- Social: https://www.peakmath.org/ #RiemannHypothesis #F1Geometry #Mathematics #PeakMath #RHSaga