I'm listening to my favorite pocast, In Our Times -- this one's on Prime Numbers. They start with Euclid, and work their way up to the Reimann-Zeta functions and beyond. Things get weird. The primes seem randomly distributed, with a probability of discovery that falls as the log of the number considered. Random and unpredictable, and yet the related Reimann-Zeta function has a very predictable component ... Where does the randomness come from? (It sounds like the imaginary component of the imaginary numbers in the RZ function hold the random component, but our lecturers didn't delve into that topic.)
This is the great dream for mathematicians then, that there is some method to transform the seemingly perfect randomness of the primes into something that's utterly predictable. True, this could devastate the world economy (encryption relies on the unpredictability of primes), but it would mean mathematical glory.
Randomness and utter predictability. It reminds me of Einstein's wistful declaration 'God does not play dice with the universe'. Surely he must have looked to the Reimann-Zeta function as a way to bring order from apparent chaos -- alas, to no avail.
In the age of Google, one can quickly ask if anything has come up recently. I did find this page. Physicists continue to play with these tempting toys ...
I do recommend listening to In Our Times ...
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