Euclidean Geometry: A Game of Mirrors

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In mathematics there are many choices and so Euclidean geometry is actually good illustration of this because Euclid had five axioms four of them were kind of obvious like the one I just mentioned. The fifth which came to be known famously as the fifth postulate was that if you have a line and you have a point outside of this line there is a unique line passing through that point meaning that doesn't intersect it. For many for many centuries after that mathematicians were trying to derive this axiom from other axioms which were more obvious and they failed. It was only almost 2000 years later that mathematicians realized that you can’t not only you cannot derive but you can

Edward Frenkel is a mathematician at UC Berkeley working on the interface of mathematics and quantum physics. He is the author of Love and Math: The Heart of Hidden Reality. Please support this podcast by checking out our sponsors:
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OUTLINE:
Here’s the timestamps for the episode. On some podcast players you should be able to click the timestamp to jump to that time.
(00:00) – Introduction
(05:54) – Mathematics in the Soviet Union
(16:05) – Nature of reality
(27:23) – Scientific discoveries
(40:45) – Observing reality
(56:57) – Complex numbers
(1:05:42) – Imagination
(1:13:33) – Pythagoreanism
(1:21:28) – AI and love
(1:34:07) – Gödel’s Incompleteness Theorems
(1:54:32) – Beauty in mathematics
(1:59:02) – Eric Weinstein
(2:20:57) – Langlands Program
(2:27:36) – Edward Witten
(2:30:41) – String theory
(2:36:10) – Theory of everything
(2:45:03) – Mathematics in academia
(2:50:30) – How to think
(2:56:16) – Fermat’s Last Theorem
(3:11:07) – Eric Weinstein and Harvard
(3:18:32) – Antisemitism
(3:38:45) – Mortality
(3:46:42) – Love