What if I solve the Riemann hypothesis

Riemann Hypothesis: Millennium problem remains unsolved

He was considered one of the most important mathematicians of his time. Accordingly, there was great excitement when Sir Michael Francis Atiyah announced at the Heidelberg Laureate Forum in September 2018 that he had proven the famous Riemann hypothesis. But it quickly became clear that Atiyah's work was flawed or at least incomplete. Experts are now certain: The Riemann hypothesis is still unsolved.

Atiyah died in January 2019 at the age of 89. He was one of the select few to receive both Nobel Prize-like awards in mathematics: the Fields Medal and the Abel Prize. The former is only awarded every four years to outstanding scientists who have not yet reached the age of 40. The Abel Prize, on the other hand, honors the life's work of important researchers.

This article is featured in Spectrum Compact, Prime Numbers - The Stars of Mathematics

Atiyah earned these awards for his work in the fields of algebraic topology, differential geometry and theoretical physics. Even in old age he was enthusiastic about mathematics: He took part in several international conferences - always surrounded by a bunch of young students with whom he discussed eagerly. The likeable mathematician was very popular among colleagues.

The puzzling distribution of prime numbers

Most recently he had dealt with the famous Riemann Hypothesis, which has puzzled mathematicians for more than 160 years. It says that a certain function ζ (z), the so-called zeta function, only for very specific values z0 equals zero. This may not sound particularly exciting at first, but this assumption has tangible consequences: If you know all the values ​​for which the zeta function is zero (the so-called zeros), you can deduce the distribution of the prime numbers very precisely.

In the meantime, the Riemann conjecture has made it into the seven "Millennium Problems" that the Clay Mathematics Institute named at the turn of the millennium. Proof of the 160-year-old riddle is rewarded with one million US dollars. In addition to scientific success, this is another incentive for many people to devote themselves to these problems. In the past few decades, there have been several attempts to prove the Riemann Hypothesis - but so far without success.

Atiyah's approach did not convince the mathematicians either. In a lecture in Heidelberg on September 24, 2018, he presented such alleged evidence, which consisted of just three lines. Some of his colleagues, including Richard Lipton from the Georgia Institute of Technology and Ken Reagon from the University of Buffalo, commented on his idea as not necessarily bad, after all, a similar approach in the field of complex analysis had already been successful. However, he missed a few essential steps.