The Power of Complex Numbers

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Cardano wrote a book called Arzmagna which is like a great art of algebra and he was writing solutions for the cubic and cortical equations. In the process of solving these equations he came up with square root of an negative number specifically square root of minus 17. It took another two or three hundred years for mathematicians to figure that out but initially it looked like a completely crazy idea you know so all in all, complex numbers are not mysterious at all.

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