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In the third episode of his new series, AfterMath, Edward Frenkel dives into the question of whether computers can ever reach the cognitive capacity of the human mind -- specifically, in the realm of mathematics. While computers excel at number crunching, they struggle with general mathematical statements. Edward introduces the concept of the Turing Wall, a fundamental limit to what computers can do with numbers, named in honor of Alan Turing, the father of modern computing. Frenkel further explores insights from Alfred Tarski's Undefinability Theorem (closely connected to Kurt Gödel's Incompleteness Theorems). And he also touches upon the limitations of Large Language Models, such as ChatGPT, in handling mathematical truths. At the end of the episode, Frenkel goes back to the 3D sphere he talked about in Episode #2. He gives a 4D spacetime demonstration of it, using... a balloon.
• Edward Frenkel's Official Website: https://edwardfrenkel.com
• Frenkel's X/Twitter: https://x.com/edfrenkel
• Edward Frenkel's LinkedIn https://www.linkedin.com/in/edfrenkel/
• Edward Frenkel's Instagram: https://www.instagram.com/edfrenkel
• Edward Frenkel's Facebook: https://www.facebook.com/edfrenkel/
• Edward Frenkel’s SoundCloud (DJ Moonstein): https://soundcloud.com/moonstein
Edward Frenkel’s book “Love and Math”: https://amzn.to/4evbBkS
5
99 ratings
In the third episode of his new series, AfterMath, Edward Frenkel dives into the question of whether computers can ever reach the cognitive capacity of the human mind -- specifically, in the realm of mathematics. While computers excel at number crunching, they struggle with general mathematical statements. Edward introduces the concept of the Turing Wall, a fundamental limit to what computers can do with numbers, named in honor of Alan Turing, the father of modern computing. Frenkel further explores insights from Alfred Tarski's Undefinability Theorem (closely connected to Kurt Gödel's Incompleteness Theorems). And he also touches upon the limitations of Large Language Models, such as ChatGPT, in handling mathematical truths. At the end of the episode, Frenkel goes back to the 3D sphere he talked about in Episode #2. He gives a 4D spacetime demonstration of it, using... a balloon.
• Edward Frenkel's Official Website: https://edwardfrenkel.com
• Frenkel's X/Twitter: https://x.com/edfrenkel
• Edward Frenkel's LinkedIn https://www.linkedin.com/in/edfrenkel/
• Edward Frenkel's Instagram: https://www.instagram.com/edfrenkel
• Edward Frenkel's Facebook: https://www.facebook.com/edfrenkel/
• Edward Frenkel’s SoundCloud (DJ Moonstein): https://soundcloud.com/moonstein
Edward Frenkel’s book “Love and Math”: https://amzn.to/4evbBkS
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