# Experimental Mathematics Meets Mathematical Physics

*by David H Bailey*

*Institution:*Lawrence Berkeley Laboratory, USA

*Date: Thu 20th August 2009*

*Time: 3:15 PM*

*Location: Old Geology theatre 1, The University of Melbourne*

*Abstract*: High-precision arithmetic has been called the "electron microscope"

of experimental mathematics. The general approach is to compute some

mathematical expression to very high precision (typically several hundred digits)

for some specific choice of parameters, then apply an integer relation algorithm

such as "PSLQ" to find a relation linking this object or expression and other

known mathematical entities. Relations and formulas that are numerically

discovered in this manner must then be proven rigorously.

One particularly fruitful area for this methodology is the evaluation of definite integrals,

such as those that arise in mathematical physics. Literally hundreds of new and

intriguing results, specific and general, have been found in this manner, including

results in Ising theory, quantum field theory and even computational biology.

Progress in this arenas has been hampered by long run times required to evaluate

high-dimensional integrals. However, with the increasing availability of highly parallel

computer systems, many of these integrals can now be evaluated.

Nonetheless, new techniques are required to further advance the state of the art.

*For More Information:* contact Iwan Jensen. email: I.Jensen@ms.unimelb.edu.au