A top mathematician showed that he solved a 160-year-old math problem at a lecture held in Germany on Monday.
Michael Atiyah, who has already won two of the biggest prizes in mathematics, the Fields Medal and Aber Prize, presented his work that proves the Riemann hypothesis at the Heidelberg Laureate Forum. He will receive a monetary prize if his solution is confirmed.
Riemann hypothesis, one of the last unsolved problems in math, was first proposed by German mathematician Bernhard Riemann in 1850.
The hypothesis relates to the distribution of prime numbers, which can only be divided by one or themselves. The hypothesis posits that the distribution of prime numbers in the number line is not random, but rather follows a pattern described by the equation known as the Riemann zeta function.
The pattern has so far been proven in 10,000,000,000,000 prime numbers but there is still no formal and indisputable proof that all primes follow the pattern. A $1 million prize will go to someone who can prove that the equation works to all prime numbers, and Atiyah thinks he has done this using a new approach.
Atiyah’s self-described “simple proof” that the hypothesis is correct is based on the works of two leading mathematicians of the 20th century, John von Neumann and Friedrich Hirzebruch.
“Nobody believes any proof of the Riemann hypothesis because it is so difficult,” Atiyah said during his presentation, as reported by the New Scientist. “Nobody has proved it, so why should anybody prove it now? Unless, of course, you have a totally new idea.”
Other experts, however, doubt the validity of the work citing that the 89-year-old has been committing mistakes in recent years.
“What he showed in the presentation is very unlikely to be anything like a proof of the Riemann hypothesis as we know it,” Jorgen Veisdal, of the Norwegian University of Science and Technology in Trondheim who has also studied the Riemann hypothesis, told Science Magazine.
Veisdal described Atiyah’s work as too vague and unspecific, and said that he needs to take a closer look at the written proof to make a definitive judgement.
Atiyah has produced several papers in recent years that make remarkable claims. Unfortunately, these have failed to convince his peers. His latest proof still has to undergo a rigorous peer review process to verify its validity, but the initial reaction is of cautious skepticism.
Nicholas Jackson, of Warwick University in the UK, said that the Riemann hypothesis is a notoriously difficult problem.
“Lots of other top-rate mathematicians have nearly but not quite managed to prove it over the years, only for a subtle flaw in the proof to become apparent,” he said.