A completely new approach suggests the validity of the 110-year-old Lindelöf hypothesis, opening up the possibilities of new discoveries in quantum computing, number theory and cybersecurity

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Athanassios Fokas, a mathematician from the Department of Applied Mathematics and Theoretical Physics of the University of Cambridge and visiting professor in the Ming Hsieh Department of Electrical Engineering at the USC Viterbi School of Engineering has announced a novel method suggesting a solution to one of the long-standing problems in the history of mathematics, the Lindelöf Hypothesis.

The result, announced on June 25th, 2018, at the First Congress of the Greek Mathematical Society in Athens under the auspices of the president of Greece, Prokopios Pavlopoulos, has far reaching implications for fields like quantum computing, number theory, and encryption which forms the basis for cybersecurity.

Put forth in 1908 by Finnish topologist Ernst Leonard Lindelöf, the Lindelöf hypothesis is a conjecture about the rate of growth of the Riemann zeta function on the critical line implied by one of the most famous unsolved problems related to prime numbers, the Riemann Hypothesis, popularly referred to as the Holy Grail of math.

Lindelöf implies most of the claims of Riemann and Riemann fully implies Lindelöf, therefore a proof of Lindelöf equals a major breakthrough in the field of mathematics.

Bernhard Riemann reigns as the mathematician who made the single biggest breakthrough in prime number theory. Prime numbers – numbers like 2, 3, 5, 7 and 11 that are only divisible by 1 and itself – are ideal for things like RSA encryption, which protect our many online purchases. Prime numbers are literally the secret “keys” that hide your latest $35 Amazon purchase from prying eyes.

The Riemann zeta function is an almost magical tool in number theory used to investigate the properties of prime numbers. It has propelled scientific understanding in many fields, including biology, chemistry and physics, all without formal proof of Riemann’s famous hypothesis. “The failure of the Riemann Hypothesis,” wrote number theorist Enrico Bombieri, “would create havoc in the distribution of prime numbers.”


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