## Wednesday, July 2, 2008

### Another Riemann Hypothesis Solution From Purdue?

Well, it seems that the mathematics department of the Purdue University is really obsessed with the as Xian-Jin Li published a proof of the legendary mathematical problem. However this is not the first time that Purdue disturbs the mathematical society with a Riemann Hypothesis solution. The most recent attempt was in June 2004 but was not convincing enough.

The Riemann function ζ(s) is a complex function and is defined as the sum of terms 1/(n^s) for all n to infinity. As a mathematical construct it seems to encode a great deal of information about number theory. One hit-example is the proof that there are no zeros of the ζ(s) function for which it holds: ζ(s)=0 => Re[s]=1. Here Re[.] is the real part of a complex number, e.g. if s=1+2.i then Re[s]=1. The above theorem is equivalent to the which states that from numbers 1 to N, there are approximately N/logN primes, and ad infinitum the ratio of the 'density' of primes to N/logN tends to 1.

Now the Riemann Hypothesis states that if ζ(s)=0 => Re[s]= 1/2. It has been haunting mathematics for centuries now and its solution will have an award of 1.000.000\$ from the Clay Mathematics Institute.

Now, many 'proofs' have been devised over the years which seems reasonable since many people have been obsessed with the problem. But it seems no other institution can match Purdue in its pursuit of the solution. The 'crusade' started with Professor of Mathematics at Purdue University. De Brange announced a solution in June 2004, which however fell in the dark by the mathematics community. The story continues with Xian-Jin Li who published yesterday a new proof of the hypothesis. You can find the document in ArXiv here. It is interesting to note that the Mathematics Genealogy Project reveals that Jin-Li is a student of De Brange in Purdue.

The proof is at the disposal of mathematicians who will try and test the correctness. It is an interesting case to have an eye on and who knows maybe Purdue took it right that time!