Friends often send me bits and pieces of science or mathematics via internet links. It’s surprising how perceptive these friends can be.
Recently one of them sent me a link about a proposed solution to the world’s most difficult problem. It is called the Riemann Hypothesis (RH). Instant fame and $1,000,000 awaits anyone solving it. It is the Holy Grail of problems. It is at the heart of some of the most intricate and useful areas of science and mathematics. Many researchers say “If the Riemann Hypothesis is true, then thus and so follows”
The problem is named after Bernard Riemann, who proposed it in an 1859 lecture and short paper. It is now famous. He took what is known as the Zeta function studied first by Euler, my favorite mathematician and scientist and then almost every good mathematician up to today has followed the ‘siren’s song’.
A still alive great mathematician Michael Atiyah age 89 recently lectured at a Heidelberg Laureate Forum. In the lecture he shocked the world by claiming that he had solved the RH. Waves of speculation now circle the globe.
There are always proposed solutions in circulation, which turn out to be incorrect. But, Atiyah is not an ordinary person. He is far from a crackpot. He ranks up near or at the top of living mathematicians. He has won both the Fields Medal and the Abel Medal for his work. That’s the equivalent of the Nobel Prize twice over.
I won’t state the problem. To tell you what it is in any detail takes too much time and space for this short write-up. For some information on it, Click HERE
You will quickly see that few experts believe he has solved the problem.
To understand the problem has taken me since 1965. I’ve had help in understanding it by reading good books about it including a book called ‘Prime Obsession’ by John Derbyshire. This book weaves heavyweight mathematics in with historical context, which is always good to do.
I have not examined Atiyah’s proof, because he has not written it up in any detail. Also the path to his proposed solution is not one that I’ve traveled.
What intrigues me is that such a famous man as Atiyah has ‘blitzed’ the world at 89 with his proposal. I hope he has done it, but it is a long shot. He points to work done many years ago by John von Neumann and Friedrich Hirzebruch in physics. This pushes his solution right into the interactions between light and matter. In other words, we are now swimming in the deep water of physics and probably quantum physics and research done more than 70 years ago.
What is so interesting about this problem? Well, it deals with the distribution of the prime numbers and gives us a tantalizing hint that the primes may follow some as yet unknown rule as to their structure and distribution. This rule would have dramatic implications in physics and even code breaking.
I’ve somehow fallen prey to this problem too. I found in 1965 some things that are new and quite beautiful and they lead to the Riemann Hypothesis and primes along another path. I make no claim on a solution. The work done has discovered totally unknown things, however. They don’t constitute a proof, but deal with Riemann and Euler’s work. I’m going to write all this up properly in the next few months.
In the meantime, I’m rooting for an 89 year old man