Thoughts about Primes and Knots

Abstract: Knots and their exquisitely idiosyncratic properties, are the vital essence of three-dimensional topology. Primes and their exquisitely idiosyncratic properties, are the vital essence of number theory. A striking (and extremely useful) analogy between Knots and Primes helped me as I became as passionate about number theory as I was (and still am) about knots. I’m delighted to have been asked by Shekhar and Chi-Yun to be part of the ‘experiment’ in this (experimental) series of talks: CHAT: Career, History and Thoughts to think again about this, and take part in a Q&A with people in the seminar.

number theory

Audience: researchers in the discipline

( video )

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CHAT (Career, History And Thoughts) series

Series comments: The CHAT series invite established professors to talk about either (1) their math career in general (2) their theorems or theories, but explained from a personal and historical perspective, like how they came up with the problem, what the Aha! moment was like, how the problem changes from its initial form to the published rigorous form.

The idea is that instead of talking about their latest theorems, the speakers would take a step back and talk about the trajectory of an idea, the path to the discovery of a theorem, the influence of ideas learned through a paper or a chance conversation with a colleague, and the hazards met and overcome along the way.

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