How Random Matrix theory sheds a light on the laws underlying reality.
newscientist.com
newscientist.com
http://www.americanscientist.org/issues/num2/the-spectrum-of...
If you want to learn the actual math of random matrices, Terry Tao's notes are a good start:
http://terrytao.wordpress.com/category/teaching/254a-random-...
I find them really useful for staying up-to-date on a broad range of topics from which I can jump into further research if I find them interesting.
[1] Average people being defined as those without strong scientific training, and therefore more likely to make inferences that may not be reasonable.
Frinstance, New Scientis starts an article on the fairly prosaic subject of random matrix theory with this paragraph:
"SUPPOSE we had a theory that could explain everything. Not just atoms and quarks but aspects of our everyday lives too. Sound impossible? Perhaps not."
Also: ...has computed the locations of as many as 10^23 zeros of the Riemann zeta function and found a near-perfect agreement with random matrix theory.
I think that when you're talking about mathematics, "near-perfect agreement" is synonymous with "not in agreement".
http://arxiv.org/PS_cache/arxiv/pdf/0910/0910.1205v1.pdf
The first pages are a quick overview of the math behind random matrix theory, if you're curious.