Back to my Maths degree for this bit of news. Slashdot’s reporting the claim that the Riemann hypothesis has been proven by Louis de Branges de Bourcia at Purdue University.
The Riemann hypothesis is all about solutions to a function called the zeta function. Riemann, back in the 19th Century, noticed that solutions to the function seemed to be related to the distribution of prime numbers — and prime number distribution has been a puzzle for ages. As Wikipedia says,
the zeros of the zeta function can be regarded as the harmonic frequencies in the distribution of primes
— which sounds lovely even if I only dimly see what it’s suggesting. There’s a $1million prize for the solution so if you’d like to check the proof you’ll be helping Louis.
The Riemann Hypothesis was the 8th of David Hilbert’s list of outstanding problems in maths and you can read more about it here or on Wikipedia’s entry about the Riemann Hypothesis.
For all you die-hard maths fans:
A Riemann zeta function is a function which is analytic in the complex plane, with the possible exception of a simple pole at one, and which has an Euler product and a functional identity. The functions originate in an adelic generalization of the Laplace transformation which is defined using a theta function. Hilbert spaces, whose elements are entire functions, are obtained on application of the Mellin transformation. Maximal dissipative transformations are constructed in these spaces which have implications for zeroes of zeta functions. The zeros of a zeta function in the critical strip are simple and lie on the critical line. The Euler zeta function, Dirichlet zeta functions, and modular zeta functions are examples of Riemann zeta functions. An application is a construction of Riemann zeta functions in the quantum theory of electrons in the atom.
Ok?
