Speaker: Eben Blaisdell

Abstract: We’ve all multiplied integers by hand, and the grade school method is intuitive and efficient enough for most practical purposes.  In 1960, the legendary Andrey Kolmogorov conjectured that this everyday algorithm was optimal.  Amazingly, less than a week after this conjecture was posed publicly, a 23 year old Anatoly Karatsuba would give a counterexample: a novel elegant elementary way to multiply large numbers.  This set off a decades-long hunt for more (asymptotically) efficient algorithms that has seen progress as recently as 2019.  We will look at several ways to multiply natural numbers, and motivate some interesting mathematics along the way.