Riemann surfaces

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http://youtube.com/watch?v=zlm1aajH6gY

The Riemann Hypothesis is the most notorious unsolved problem in all of mathematics. Ever since it was first proposed by Bernhard Riemann in 1859, the conjecture has maintained the status of the Holy Grail of mathematics. The person who solves it will win a $1 million prize from the Clay Institute of Mathematics. So, what is the Riemann Hypothesis? Why is it so important? What can it tell us about the chaotic universe of prime numbers? And why is its proof so elusive? Alex Kontorovich, professor of mathematics at Rutgers University, breaks it all down in this comprehensive explainer. • 00:00 A glimpse into the mystery of the Riemann Hypothesis • 01:42 The world of prime numbers • 02:30 Carl Friedrich Gauss looks for primes, Prime Counting Function • 03:30 Logarithm Function and Gauss's Conjecture • 04:39 Leonard Euler and infinite series • 06:30 Euler and the Zeta Function • 07:30 Bernhard Riemann enters the prime number picture • 08:18 Imaginary and complex numbers • 09:40 Complex Analysis and the Zeta Function • 10:25 Analytic Continuation: two functions at work at once • 11:14 Zeta Zeros and the critical strip • 12:20 The critical line • 13:04 Riemann's Hypothesis shows the distribution of prime numbers can be predicted • 14:59 The search for a proof of the Riemann Hypothesis • Read more at Quanta Magazine: https://www.quantamagazine.org/how-i-... • VISIT our Website: https://www.quantamagazine.org • LIKE us on Facebook: / quantanews • FOLLOW us Twitter: / quantamagazine • Quanta Magazine is an editorially independent publication supported by the Simons Foundation: https://www.simonsfoundation.org/

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