Ken Ono, the STEM Advisor to the Provost and Marvin Rosenblum Professor of Mathematics at the University of Virginia, has been named a runner-up for the 2025 Cozzarelli Prize in the physical sciences, an honor awarded by the Proceedings of the National Academy of Sciences for research teams whose articles in the journal have made outstanding contributions to their field. Ono’s paper, “Partitions Detect Primes,” co-authored with University of Cologne mathematicians Will Craig, a former UVA grad student, and Jan Willem van Ittersum, offers a new way of understanding prime numbers using the mathematical concept of partitions.
Prime numbers, which are divisible only by 1 and themselves, have puzzled mathematicians for centuries. They are fundamental to cryptography, computing and number theory, yet their distribution remains one of the biggest unsolved mysteries in mathematics. Ono’s research sheds new light on the puzzle by using partitions, which count how many ways a number can be split into smaller sums.
For example, the number 4 can be partitioned in five ways: as 4, as 3 + 1, as 2 + 2, as 2 + 1 + 1, and as 1 + 1 + 1 + 1. Ono and his collaborators discovered that partition numbers contain hidden clues about prime numbers, revealing a hidden connection between two seemingly unrelated areas of math. Their work introduces an infinite class of partition functions that can be assembled to list the primes in a completely new way.
“This paper connects two fundamental areas of number theory: prime numbers and partitions,” said Ono, a member of the faculty of the College and Graduate School of Arts & Sciences with joint appointments with UVA’s Department of Statistics, the UVA School of Data Sciences and the UVA School of Engineering and Applied Sciences’ Department of Electrical and Computer Engineering. “Although prime numbers have been studied for centuries, many of their most basic properties remain elusive. What we proved gives infinitely many new ways to detect prime numbers without having to check divisibility, which is one of the reasons primes are so difficult to detect.”
Where Math Meets National Security
The study of prime numbers is central to modern encryption and cybersecurity, making Ono’s work relevant to fields beyond pure mathematics. In addition to his work at UVA, Ono also serves on the advisory board of the National Security Agency, an organization that relies on prime numbers for cryptographic security. RSA encryption, a widely used encryption algorithm that secures banking, communications and classified government data, depends on the difficulty of factoring large prime numbers.
“In a few weeks, I’ll be giving a talk at Fort Meade on this subject. The good news is that the world will still be safe, but understanding primes remains a crucial area of research, especially in the era of quantum computing,” Ono said. “If someone successfully builds an efficient quantum computer, it would upend the way prime numbers are used in cryptography. That’s something the mathematical community is preparing for.”
A Prime Connection to Pop Culture
Ono’s research has drawn comparisons to Prime Target, the popular Apple TV+ series that follows a mathematician racing to solve a prime number-based puzzle before a global crisis unfolds. While the show brings drama and suspense to the world of number theory, Ono’s work demonstrates that the subject has the potential to be almost as exciting.
“If you're a fan of Prime Target, our paper is strikingly similar to the premise of the miniseries, where a brilliant student uncovers hidden patterns in prime numbers with world-changing consequences,” Ono said. “In reality, Hollywood takes some creative liberties. While our research reveals new patterns in primes, it doesn’t rise to the same level of breaking cryptographic security.”
A Legacy of Mathematical Excellence
Ono, a world-renowned number theorist, has made significant contributions to the study of partitions and primes throughout his career. His research builds on the legacy of mathematical giants like Srinivasa Ramanujan, whose work on partitions in the early 20th century continues to inspire discoveries today.
The recognition of Ono’s work as a Cozzarelli Prize finalist is particularly notable because it is the first pure mathematics papers to be honored in many years.
“The Proceedings of the National Academy of Sciences publishes over 3,000 papers each year, so being named a runner-up for the Cozzarelli Prize in the physical sciences is a tremendous honor for me and my co-authors,” Ono said. “This is the first pure mathematics paper to be recognized in many years, which makes the award even more special.”