23 Sept, 2018

I write this in some rush. It is just a few hours before what could be a monumental event in mathematics. A great mathematician is going to reveal what he claims is a solution to arguably the greatest unsolved problem in mathematics.

Sir Michael Atiyah is giving a talk in a few hours on his proof for Riemann Hypothesis at the Heidelberg Laureate Forum (HLF) in Heidelberg, Germany. The abstract of his talk is here. It is short and unequivocal.

There is a mixture of skepticism and excitement about the claim in the mathematical community.

Riemann Hypothesis is an old unsolved problem that has been elusive to great mathematicians over the years. It has its origin in a paper by the German mathematician Bernhard Riemann written in 1859. This makes the problem about 160 years old. The title of the Riemann’s paper approximately translated to English is “On the number of primes less than a given magnitude”. Riemann Hypothesis is an unproven statement made by Riemann in the paper about the distribution of zeros of a function of complex variable, famously known as the Riemann zeta function. As the title of Riemann’s paper indicates, the Riemann Hypothesis if proved correct has repercussions on knowledge of distribution of prime numbers.

For a claim on such a historical problem to be taken seriously now, it has to come from a serious mathematician. And, Sir Michael Atiyah is someone surely to fit the league. He has already won the top most honors in mathematics including the Field’s medal and Abel prize.

This proof if correct would be unconventional on several fronts. This would come from an 89 year old mathematician, while most mathematicians produce their best works when young – although, it is quite refreshing to see fruitful contributions from older mathematicians. Then, there is no sign of collaboration between Sir Atiyah and other mathematicians for this proof – no mathematician has openly commented on this yet. Then, the abstract of the talk claims that the proof is based on old ideas and methods developed in 1950’s or before. For a problem like Riemann Hypothesis, the above would be a very unlikely combination to lead to a proof.

Still, this is a serious claim at a serious venue! In the coming months, the proof will be subject to reviews by peer mathematicians. And, if the proof stands, the news would be big.

The forum organizers will have video of the talk available to public here shortly after the talk.

Moments like this are few and far between – Fermat’s last theorem was solved in 1994 and Poincare conjecture was proved in 2006. It is fascinating to be part of the excitement as such events unfold. I invite you to take a pause and absorb the happenings.

EDIT: The talk is available here.