Welcome to Quantum Magazine's podcast.

Each episode, we bring you stories about developments in science and mathematics.

I'm Susan Vallett.

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It helps people find the Quantum Magazine podcast. Joseph Silverman remembers when he began connecting the dots that would ultimately lead to a new

branch of mathematics. It was April 25, 1992, at a conference at Union College in Schenectady, New York.

It happened by accident while he was at a talk by decorated mathematician John Milner.

Milner worked in a field called Complex Dynamics, which Silverman knew little about.

Silverman says he noticed something, as Milner introduced some

basic ideas. So every time he stated a theorem or a lot of the theorems, my thought was, if you

just change a couple of the words, there's an analogous sort of problem in arithmetic geometry,

in number theory. Silverman, a mathematician at Brown University, asked Milner some follow-up questions over breakfast

the next day and then set to work pursuing the analogy. His goal was to create a dictionary

that would translate between dynamical systems and number theory. At first glance, the two look

like unrelated branches of mathematics. Most of the focus was sort of on the number theory side

for a while, at least from my perspective. And like we had a very successful conference, which pulled

together a lot of number theorists and algebraic

geometers, but not so much dynamicists, that first one.

...