/ Jana Völker

Lecture in Basel: Terence Tao and the notorious Collatz conjecture

Last Friday, February 14, 2020, Fields medallist Terence Tao gave a lecture at the University of Basel about the Collatz conjecture and mastered the feat of making advanced level mathematics accessible to everyone.

Mathematics isn't exactly known for creating popstars, but if you had to name one, it would be Terence Tao. The Fields medallist is probably the best mathematician of his generation and has been a professor at the University of California, Los Angeles since he was 24. His mathematical blog (on which he occasionally writes on topics other than mathematics) is very renowned. In addition to teaching and research, Tao has made it a habit to work on seemingly hopeless math problems for a few days a year, even if they are not related to his research focus.

The Collatz conjecture is one of these unsolved problems in mathematics. Let's think of any natural number. If it is even, divide it by two. If it is odd, multiply it by three and add one. Apply the same rules to your results over and over again. The Collatz conjecture predicts that at some point we reach the number one and are then caught in an endless loop (1, 4, 2, 1, 4, 2, 1, ...). Although these rules have been applied to more than a trillion numbers without finding an exception, no mathematical proof or general mathematical argument can be derived from the Collatz conjecture. Among the most recent challengers of the problem is Terence Tao. He recognized a connection between the Collatz conjecture and partial differential equations: The attempt to predict the future nature of a system and to check how and whether a pattern depends on the respective starting point. Although he did not expect to make great progress and did not solve the Collatz conjecture, he was still able to make the most significant progress in recent decades.

Last week Tao was a guest at the Department of Mathematics and Computer Science at the University of Basel and gave a lecture on his work on the Collatz conjecture. More than 500 national and international guests, including around 180 high school students, streamed into the auditorium hours before the event began. Because of the large number of guests, the lecture was also broadcasted in an adjoining lecture hall. During his lecture, Terence Tao mastered the feat of presenting advanced level mathematics in a way that is accessible to everyone. He managed to inspire and make the audience laugh so much that he was even asked for autographs and selfies after his lecture.