Real Applications of Non-Real Numbers


October 10, 2012


The system of real numbers are defined mathematically as a “completion’ of the rational numbers. But this is not the only way to do it! In fact there are infinitely many others completions- the so called “p-adic numbers”. These numbers were defined for pure mathematical reasons and have been a subject of research for a century. But in the last 3 decades they have found ‘real world’ applications in computer science, construction of networks, algorithms etc. We will try to tell the story in a way which hopefully will make sense also to non-mathematicians.


Alex Lubotzky

Alex Lubotzky is the Weil Professor of Mathematics at the Hebrew University of Jerusalem and an adjunct prof. of math at Yale University. He got his PhD. from Bar-Ilan University in 1980. Following an army service he joined the Hebrew University in 1983.His main area of research is group theory which he likes to combine with other areas like geometry, number theory, combinatorics and computer science. One of his best known works is the construction of Ramanujan graphs (which are optimal expanders) jointly with Phillips and Sarnak. This opened a world of connections between graph theory and representation theory. Lubotzky is an Honorary Foreign Member of the American Academy of Arts and Science and in 2006 he received an honorary degree from the University of Chicago for his contributions to modern mathematics.