# Visiting professor solves one of math’s long-standing mysteries

## Athanassios Fokas’ breakthrough on the Lindelöf hypothesis may have far-reaching implications for fields like cybersecurity and quantum computing

A visiting professor in the Ming Hsieh Department of Electrical Engineering at the USC Viterbi School of Engineering has solved one of mathematics’ long-standing problems, the Lindelöf hypothesis.

The solution by Athanassios Fokas, a mathematician from the University of Cambridge, has far-reaching implications for fields including cybersecurity and quantum computing.

Put forth in 1908 by Finnish topologist Ernst Leonard Lindelöf, the Lindelöf hypothesis is related to one of the most famous unsolved problems related to prime numbers, the Riemann hypothesis — often called the Holy Grail of math.

Prime numbers — numbers like 2, 3, 5, 7 and 11 that are only divisible by 1 and itself — are ideal for things like the encryption that protects online transactions. Prime numbers are literally the secret “keys” that hide your latest $35 Amazon purchase from prying eyes.

## New approach to Lindelöf hypothesis

“My approach was completely different from the usual approaches used,” said Fokas, a world expert in asymptotics, an applied mathematical domain that helps scientists answer questions about the behavior of functions when a parameter is very large. The work was first published in arXiv.

Fokas’ work is a step toward proving the Riemann hypothesis, which would allow mathematicians to better describe how the prime numbers are placed among whole numbers. The Riemann hypothesis has been dubbed so important to the field of mathematics and so difficult to prove that the Clay Mathematics Institute has offered $1 million to the first person to prove it.

Fokas is a senior fellow of the U.K.’s Engineering and Physical Sciences Research Council. In 2000, Fokas was awarded the Naylor Prize, one year after the London Mathematical Society awarded the same prize to Stephen Hawking. His “Fokas Method” for solving partial differential equations has replaced methods discovered in the 18th century and used for over 250 years.

*Parts of this work were jointly researched with several mathematicians, including Jonathan Lenells of the Royal Institute of Technology (KTH) Sweden; Konstantinos Kalimeris, senior scientist at The Johann Radon Institute for Computational and Applied Mathematics, Austrian Academy of Sciences; Anthony Ashton and Arran Fernandez of the University of Cambridge; and Euan Spence of the University of Bath.*

An extended version of this story appears on the USC Viterbi website.

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