Mathematics has its own language, which is used by all other sciences to describe our world. It is very important to use it correctly, and to appreciate how it changes with time. This importance is growing rapidly with the ever wider use of large language models. There is great potential here, but also many pitfalls, as we will discuss in this lecture.
This talk will be geared towards a general audience.
Andrei Okounkov is currently the Samuel Eilenberg Professor of Mathematics at Columbia University. His work has revealed profound new connections between different areas of mathematics and has brought new insights into problems arising in physics. Although his work is difficult to classify because it touches on such a variety of areas, two clear themes are the use of notions of randomness and of classical ideas from representation theory. This combination has proven powerful in attacking problems from algebraic geometry and statistical mechanics.
In 2004, Okounkov received the European Mathematical Society Prize for work that “contributed greatly to the field of asymptotic combinatorics.” In 2006, he was awarded a Fields Medal, often described as the Nobel Prize for math, “for his contributions bridging probability, representation theory and algebraic geometry”, his work having revealed “profound new connections between different areas of mathematics.” He became a fellow of the American Academy of Arts and Sciences in 2016.