aftermath by Edward Frenkel

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.

In the second episode of his new series, the AfterMath, Edward Frenkel talks about a unification of mathematics and analytic psychology. Following Carl Jung, Edward proposes that all mathematical objects and ideas come from archetypes in our Collective Unconscious (a common psychic realm to which our individual minds are connected). After a brief introduction to Jungian psychology, covering such topics as the Collective Unconscious and its building blocks called the archetypes, with special attention to the archetype of the Shadow, Frenkel talks about a specific mathematical archetype: the archetype of Flat Space. He explains what it means for humans to be "under the spell of this archetype," what it means to "project" this archetype, and what it means to "integrate" this archetype. He argues that when we integrate mathematical archetypes, new dimensions of reality open up to us.

This is the pilot episode of Edward Frenkel’s new YouTube show/podcast “AfterMath” which will explore revolutionary ideas in mathematics, quantum physics, philosophy, and Jungian psychology, as well as interconnections between these subjects. In this episode, Edward explains in simple and accessible terms – based on mathematics! – that our minds are connected to each other at a much deeper level than is ordinarily understood.