Bernhard Riemann formulated his hypothesis about prime numbers in 1859. 160 years later, mathematician Sir Michael Atiyah claims he solved the million-dollar-worth problem.
The Riemann hypothesis remained unsolved for 160 years. The German mathematician formulated the problem in 1859 when looking at the ever-growing distance between prime numbers along the numerical scale. Riemann created a formula, the Riemann Zeta Function, to explain the distribution of prime numbers. However, it remained to be demonstrated if the Riemann’s formula could be proven out in infinity. The Riemann’s hypothesis is one of the Millennium Prize Problems, stated by the Clay Mathematics Institute, and its solution is worth 1 million dollars.
Now, the mathematician Sir Michael Atiyah claims he has it. In a presentation at the Heidelberg Laureate Forum in Germany, the British-Lebanese mathematician presented his “simple proof“ to the Riemann hypothesis.
Atiyah is an acclaimed mathematician who has won the prestigious Fields Medal in 1966 and the Abel Prize in 2004.
But, in recent years, he has been criticized for basing his solutions to old mathematical problems on flimsy arguments. Following his talk at Heidelberg, economist Jørgen Veisdal told Science Magazine that Atiyah‘s “presentation is very unlikely to be anything like a proof of the Riemann hypothesis as we know it”. Mathematician John Baez wrote on Twitter: “I bet that Atiyah’s claimed proof, if and when he writes it up, will not convince experts.”
Atiyah himself seems well aware that he might be the target of criticism; “I am throwing myself to the lions”, he wrote before his presentation, “I hope to emerge unscathed”.
Sir Atiyah’s paper (PDF): The Riemann Hypothesis
Dwilewicz, R. J., & Minác, J. (2009). Values of the Riemann zeta function at integers. Materials matematics, 0001-26. (OPEN ACCESS);
Riemman Hypothesis likely remains unsolved despite claimed proof; New Scientist; Retrieved: 27/09/2018;
Skepticism surrounds renowned mathematician’s attempted proof of 160-year-old hypothesis (Science Mag); Retrieved: 27/09/2018