A new proof demonstrates the power of arithmetic dynamics

Kelsey Houston-Edwards in Quanta:

Joseph Silverman remembers when he began connecting the dots that would ultimately lead to a new branch of mathematics: April 25, 1992, at a conference at Union College in Schenectady, New York.

It happened by accident while he was at a talk by the decorated mathematician John Milnor. Milnor’s subject was a field called complex dynamics, which Silverman knew little about. But as Milnor introduced some basic ideas, Silverman started to see a striking resemblance to the field of number theory where he was an expert.

“If you just change a couple of the words, there’s an analogous sort of problem,” he remembers thinking to himself.

Silverman, a mathematician at Brown University, left the room inspired. He asked Milnor 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.

More here.




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