AI Closes In On Math’s Biggest Target | World Science Festival
From World Science Festival.
Watch this video on YouTube ↗
AI just took an unprecedented step toward solving what is arguably math’s most towering problem: to prove the Riemann Hypothesis, which holds the key to the distribution of prime numbers. Alex Kontorovich, professor of mathematics at Rutgers University, joins Brian Greene to explain the result, and what it means for a field that has worked on these questions for more than a century.
Kontorovich lays out the connection between prime numbers and the Riemann zeta function, then explains what the new proof establishes and what it leaves open. He and Brian turn to the harder question of what mathematics becomes when machines can produce theorems that humans pursued for lifetimes. Kontorovich, argues that the value of a mathematician is shifting toward understanding and communication, and lays out why he remains optimistic about where mathematics is headed.
This program is part of the Rethinking Reality series, supported by the John Templeton Foundation.
ABOUT WORLD SCIENCE FESTIVAL:
The World Science Festival (WSF) is a multimedia organization bringing the most transformative ideas in science to global audiences. Through long- and short-form videos spanning physics, cosmology, quantum mechanics, biology, neuroscience, consciousness, medicine, space exploration, the dilemma of free will, artificial intelligence, engineering, robotics, and beyond. WSF gathers world-renowned scientists, artists, and thinkers for dynamic discussions, debates, lectures, performances, films, and immersive live experiences.
Founded in 2008 and headquartered in New York City, the World Science Festival is a production of the World Science Foundation, a 501(c)(3) nonprofit organization. Our mission is to cultivate a public informed by science, inspired by its wonder, convinced of its value, and prepared to engage with its implications for the future. With live events reaching millions worldwide and hundreds of millions of digital views, WSF continues to expand its global impact through festivals, educational initiatives like World Science U, and digital content that explores the near and far future of our world.
FOLLOW WORLD SCIENCE FESTIVAL:
Website: https://worldsciencefestival.com/
Instagram: https://www.instagram.com/worldscifest/
TikTok: https://www.tiktok.com/@worldscifest
X(Twitter): https://twitter.com/worldscifest
Facebook: https://www.facebook.com/worldsciencefestival
LinkedIn: https://www.linkedin.com/company/world-science-festival
CHAPTERS:
00:00 AI’s Big Step Toward the Riemann Hypothesis
03:30 Is Math Feeling the AI Shock More Than Any Other Field?
07:20 From Math Olympiad Problems to Gold Medals
09:41 How Large Language Models Actually Do Math
11:49 Lean: How a Computer Checks a Proof
13:35 The Prime Number Theorem Project
19:27 Lean, Mathlib, and Teaching Math to a Computer
22:34 Why Should We Care Where the Primes Are?
24:12 Euclid’s Fifth Postulate and the Value of “Useless” Knowledge
27:44 What Is the Zeta Function?
32:04 How the Zeta Function Connects to Prime Numbers
35:55 Why Use Complex Numbers?
41:41 The Zeros of the Zeta Function and Why They Matter
48:19 Checking Trillions of Zeros
56:03 Is AI Just Building on Human Work?
57:16 The Lean Certification
59:08 Why the Full Riemann Hypothesis Is Still Open
1:01:17 Could AI Do Math or Physics Starting From Scratch?
1:08:00 Is AI Now the Greatest Mathematician of All Time?
1:09:43 Do Human Experts Still Matter?
1:11:31 What Do We Lose If Humans Stop Proving Theorems?
1:14:47 Will Math Departments Still Exist?
1:20:29 The One Thing AI Can’t Do for You
1:21:45 Advice for Students in the Age of AI
1:22:58 Rethinking the Math PhD
1:25:52 Will Communication Matter More Than Discovery?
AI Closes In On Math's Biggest Target | World Science Festival
https://www.youtube.com/channel/UCShHFwKyhcDo3g7hr4f1R8A
Kontorovich lays out the connection between prime numbers and the Riemann zeta function, then explains what the new proof establishes and what it leaves open. He and Brian turn to the harder question of what mathematics becomes when machines can produce theorems that humans pursued for lifetimes. Kontorovich, argues that the value of a mathematician is shifting toward understanding and communication, and lays out why he remains optimistic about where mathematics is headed.
This program is part of the Rethinking Reality series, supported by the John Templeton Foundation.
ABOUT WORLD SCIENCE FESTIVAL:
The World Science Festival (WSF) is a multimedia organization bringing the most transformative ideas in science to global audiences. Through long- and short-form videos spanning physics, cosmology, quantum mechanics, biology, neuroscience, consciousness, medicine, space exploration, the dilemma of free will, artificial intelligence, engineering, robotics, and beyond. WSF gathers world-renowned scientists, artists, and thinkers for dynamic discussions, debates, lectures, performances, films, and immersive live experiences.
Founded in 2008 and headquartered in New York City, the World Science Festival is a production of the World Science Foundation, a 501(c)(3) nonprofit organization. Our mission is to cultivate a public informed by science, inspired by its wonder, convinced of its value, and prepared to engage with its implications for the future. With live events reaching millions worldwide and hundreds of millions of digital views, WSF continues to expand its global impact through festivals, educational initiatives like World Science U, and digital content that explores the near and far future of our world.
FOLLOW WORLD SCIENCE FESTIVAL:
Website: https://worldsciencefestival.com/
Instagram: https://www.instagram.com/worldscifest/
TikTok: https://www.tiktok.com/@worldscifest
X(Twitter): https://twitter.com/worldscifest
Facebook: https://www.facebook.com/worldsciencefestival
LinkedIn: https://www.linkedin.com/company/world-science-festival
CHAPTERS:
00:00 AI’s Big Step Toward the Riemann Hypothesis
03:30 Is Math Feeling the AI Shock More Than Any Other Field?
07:20 From Math Olympiad Problems to Gold Medals
09:41 How Large Language Models Actually Do Math
11:49 Lean: How a Computer Checks a Proof
13:35 The Prime Number Theorem Project
19:27 Lean, Mathlib, and Teaching Math to a Computer
22:34 Why Should We Care Where the Primes Are?
24:12 Euclid’s Fifth Postulate and the Value of “Useless” Knowledge
27:44 What Is the Zeta Function?
32:04 How the Zeta Function Connects to Prime Numbers
35:55 Why Use Complex Numbers?
41:41 The Zeros of the Zeta Function and Why They Matter
48:19 Checking Trillions of Zeros
56:03 Is AI Just Building on Human Work?
57:16 The Lean Certification
59:08 Why the Full Riemann Hypothesis Is Still Open
1:01:17 Could AI Do Math or Physics Starting From Scratch?
1:08:00 Is AI Now the Greatest Mathematician of All Time?
1:09:43 Do Human Experts Still Matter?
1:11:31 What Do We Lose If Humans Stop Proving Theorems?
1:14:47 Will Math Departments Still Exist?
1:20:29 The One Thing AI Can’t Do for You
1:21:45 Advice for Students in the Age of AI
1:22:58 Rethinking the Math PhD
1:25:52 Will Communication Matter More Than Discovery?
AI Closes In On Math's Biggest Target | World Science Festival
https://www.youtube.com/channel/UCShHFwKyhcDo3g7hr4f1R8A
