The PI's work concerns deterministic systems whose small-scale behavior is designed to mimic the average case behavior of random systems. In many cases the large-scale behavior of such "quasirandom" systems reproduces interesting aspects of the large-scale behavior of the random systems they mimic. At the same time, quasirandom systems exhibit many rich and complex patterns specific to the deterministic context, and these patterns demand explanation.
One reason for studying quasirandom systems is that they may have applications to Monte Carlo simulation: it could be that for many random systems of interest to scientists, the best way to get statistical information about the system is to replace it by a quasirandom analogue. But in the longer run the real significance of the PI's work may be the way it shows that many of the theorems of probability theory remain true when they are recast as statements about discrepancy, with no mention of probability at all. Such a radical revision of probability theory seems necessary if we are ever to understand how non-random mathematical objects (like the digits of pi) behave "as if they were random".
