The Unconscious Mind and the Shadow Integration Process

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.

Edward Frenkel is a professor of mathematics at UC Berkeley, member of the American Academy of Arts and Sciences, winner of the Hermann Weyl Prize and the Euler Book Prize, and author of the international bestseller “Love and Math” which has been published in 19 languages.

Listen and Watch the Video on Spotify! https://tinyurl.com/AfterMathSeries

Episode 1 of AfterMath: https://youtu.be/7eejAeqYFCg

LINKS:

•⁠ ⁠Edward Frenkel's Official Website: https://edwardfrenkel.com

• Edward 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

A good introduction to Jungian psychology (with chapters by Carl Jung and Marie-Louise von Franz) is the book "Man and His Symbols": https://www.amazon.com/Man-His-Symbols-Carl-Jung/dp/0593499999/

Edward Frenkel's conversation with Curt Jaimungal on the TOE podcast about the Langlands Program:

Part 1: https://youtu.be/RX1tZv_Nv4Y

Part 2: https://youtu.be/0AC-Ol1z5vI

CREDITS:

Editing: Didi Kayling

Animation: Ross Flat Pack FX, Neda Divzad

For all business inquiries please contact frenkelmath@gmail.com or mike@omegamedia.io

© 2025 by Edward Frenkel

#science #math #mathematics #quantumphysics #philosophy #psychology #podcast #carljung