14 Feb 2020
Universität Basel, Kollegienhaus, Aula, Petersplatz 1, Basel
Natur & Technik
The notorious Collatz conjecture
Lecture by Fields medalist Professor Terence Tao, University of California, Los Angeles
Start with any natural number. If it is even, divide it by two. If instead it is odd, multiply it by three and add one. Now repeat this process indefinitely. The Collatz conjecture asserts that no matter how large an initial number one starts with, this process eventually reaches the number one (and then loops back to one indefinitely after that).
This conjecture has been tested for quintillions of initial numbers, but remains unsolved in general; it is perhaps one of the simplest to state problems in all of mathematics that remains open; it is also one of the most notorious “mathematical diseases” that can lure professional and amateur mathematicians alike into devoting hours of futile effort into trying to solve the problem.
While it is itself mostly a curiosity, and the full resolution still remains well out of reach of current technology, the Collatz problem is a model example of the more general concept of a dynamical system, which occurs throughout mathematics and science; and so progress on the Collatz conjecture can shed some light on the more general problem of understanding dynamical systems.
In this lecture we give some of the history of the Collatz conjecture and some of its variants, and also describe some recent partial results on the problem.
Department of Mathematics and Computer Science
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