A new discipline combines knowledge from number theory with dynamic systems, which play a particularly important role in physics. This opens up an unexpected connection between the two seemingly disparate fields and yields amazing results.
Joseph Silverman vividly remembers the moment that led him to found a new field of mathematics. It happened by accident on April 25, 1992, at a conference at Union College in Schenectady, New York. At that time he was listening to a lecture by his respected colleague John Milnor, who received the prestigious Fields Medal in 1962 and the Abel Prize in 2011. His presentation explored a topic in complex dynamics about which Silverman, a number theorist at Brown University, previously knew little. But as Milnor presented some of the basic ideas, Silverman discovered striking similarities to his own field. "Changing just a few words creates a completely analogous problem," he recalls.
Faced with this unexpected realization, Silverman left the room inspired. When he met Milnor at breakfast the following day, he sat down and peppered him with questions. During their conversation, the number theorist recognized more and more connections between the two areas that seemed so different. He therefore decided to create a dictionary that would translate between the most important contents and questions of dynamical systems and number theory.
At first glance, the two areas appear to have little to do with each other. But Silverman saw that they complemented each other in a special way. While number theory looks for patterns in sequences, dynamic systems generate such sequences - for example, by noting the position of a planet in space at regular time intervals. Both worlds thus merge as soon as one looks for the laws that govern the mysterious number sequences.
In the three decades that followed Milnor's lecture, mathematicians discovered increasing connections between the two fields. This created the basis for a completely new field: the so-called arithmetic dynamics. The range of the young discipline is constantly growing …
Article "Mathematicians Set Numbers in Motion to Unlock Their Secrets" translated and edited by "Spektrum der Wissenschaft" from "Quanta Magazine", an independent content magazine of the Simons Foundation dedicated to the dissemination of research in mathematics and has set the natural sciences as its goal.