Event Type:

Department Colloquium

Date/Time:

Tuesday, November 29, 2005 - 07:00

Location:

Kidd 364

Guest Speaker:

Institution:

Lawrence Berkeley National Laboratory

Abstract:

The past ten years or so have seen the flowering of "experimental mathematics", namely the usage of modern computer technology as an active agent in mathematical research. This talk summarizes some of the recent developments in this field. Perhaps the most notable result is the discovery of a new formula for pi, by means of a computer program implementing the "PSLQ" integer relation algorithm. This new formula has the remarkable property that it permits one to calculate binary or hexadecimal digit of pi beginning at an arbitrary position n, without having to calculate any of the first n-1 digits. More recently, it has been found that this formula has implications for the age-old question of whether mathematical constants such as pi and log(2) are "normal", or in other words have digit expansions that are "random" in a specific sense. These methods have led to the proof of normality for an uncountably infinite collection of explicit real constants (sadly not yet including pi). This proof, which was quite difficult in its original form, can now be established very simply by means of a "hot spot" lemma, thus giving hope that these techniques can eventually be extended to establish normality for pi and log(2).