Institute for Advanced Study
The unexpected discovery by Montgomery and Dyson at teatime in the 1970s opened a tantalizing connection between prime numbers and mathematical physics that remains strange and mysterious today. Prime numbers are the building blocks of all numbers and have been studied for more than two thousand years, beginning with the ancient Greeks, who proved that there are infinitely many primes and that they are irregularly spaced.
More than forty years after the teatime conversation between Dyson and Montgomery, the answer to the question of why the same laws of distribution seem to govern the zeros of the Riemann zeta function and the eigenvalues of random matrices remains elusive, but the hunt for an explanation has prompted active research at the intersection of number theory, mathematical physics, probability, and statistics. The search is producing a much better understanding of zeta functions, prime numbers, and random matrices from a variety of angles, including analyzing various systems to see if they reflect Wigner’s prediction that the energy levels of large complex quantum systems exhibit a universal statistical behavior, a delicate balance between chaos and order defined by a precise formula.And this:
uasi-crystals were discovered in 1984 and exist in spaces of one, two, or three dimensions. Dyson suggests mathematicians obtain a complete enumeration and classification of all one-dimensional quasi-crystals, the most prevalent type, with the aim of identifying one with a spectrum that corresponds to the Riemann zeta function and one that corresponds to the L-functions that resemble the Riemann zeta function. If it can be proved that a one-dimensional quasi-crystal has properties that identify it with the zeros of the Riemann zeta function, then the Riemann Hypothesis will have been proved.This has been proved long before I arrived. Group theorists already know we need a dual rate quantizer to make groups, they shopwed this by showing that an invertable, constant scaled multiply is need to make groups.
Here is a secret for all you advanced scientists:
Prime numbers result because humans are efficient at making groups, we use the number system as enumerating indices to minimize redundancy. Use that principle, add the maximum entropy system of Shannon, and all these problems resolve.
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