Like physics, mathematics has its own set of “fundamental particles” – he prime numberswhich cannot be decomposed into smaller natural numbers. They can only be divided by themselves and 1.
And in a new development, it turns out that these mathematical “particles” offer new ways to approach some of the deepest mysteries in physics. Over the past year, researchers have discovered that formulas based on prime numbers can describe characteristics of black holes. Number theorists have spent hundreds of years deriving theorems and guesses based on prime numbers. These new connections suggest that the mathematical truths that govern prime numbers may also govern some fundamental laws of the universe. So can physics be expressed in terms of prime numbers?
black holes They are the sites of the most overwhelming gravitational force in the universe. At their centers are unique points called singularities, where classical physics predicts that gravity must be infinite, causing our understanding of space and time to crumble. But in the 1960s, physicists discovered that, immediately surrounding the singularity, a kind of chaos arises – and it looks remarkably like some kind of chaos recently found in prime numbers.
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Physicists hope to take advantage of this connection. “I would say that many high-energy physicists don’t know much about that aspect of number theory,” says Eric Perlmutter of the Saclay Institute for Theoretical Physics.
The fundamental conjecture of number theory about prime numbers is the Riemann hypothesis of 1859. In a handwritten paper, the German mathematician Bernhard Riemann provided a formula with two main terms. The first offered a surprisingly close estimate of how many prime numbers there are that are smaller than a given number. The second term is the zeta function, whose zeros (the places where the function is equal to zero) fit the original estimate. The mysterious way that zeta zeros always improve the estimate is the subject of the Riemann hypothesis. The hypothesis is so crucial to number theory that anyone who can prove it will win a million-dollar prize from the Clay Mathematics Institute.
In the late 1980s, physicists began to wonder if there was a physical system whose energy levels could be based on prime numbers. A colleague challenged physicist Bernard Julia of France’s École Normale Supérieure to find a physical analogue described by the zeta function. His solution was to propose a hypothetical type of particle with energy levels given by the logarithms of the prime numbers. Julia called these particles “primons” and a group of them “primon gas.” The partition function (a census of the possible states of a system) of this gas is exactly the Riemann zeta function.
At the time, Julia’s concept was a thought experiment: most scientists doubted that primorons really existed. But deep within black holes, a mathematical link awaited discovery. A little more than two decades later, physicists Yan Fyodorov of King’s College London, Ghaith Hiary of Ohio State University, and Jon Keating of the University of Oxford saw hints that fractal chaos emerges from fluctuations in the zeros of the zeta function, an idea that was conclusively demonstrated. tested in 2025.
Einstein’s general theory of relativity shows that the same chaos also arises near a singularity.
In a February 2025 preprint, University of Cambridge physicist Sean Hartnoll and graduate student Ming Yang brought Julia’s work to the real world. Within the chaos near a singularity, they discovered that a “conformal” symmetry emerges. Hartnoll compares conformal symmetry with the Dutch artist MC Escher’s famous bat drawings — the same structure is repeated at different scales. This scale symmetry, along with a little math, revealed a quantum system near the singularity whose spectrum is organized into prime numbers: a cloud of conformal primon gas.
Five months later, they uploaded a preprint with a new twist. The team, which now included physicist Marine De Clerck of the University of Cambridge, expanded its analysis to a five-dimensional universe instead of the usual four. They found that the extra dimension forced a new feature: Tracking the dynamics of the singularity now required a “complex” prime, known as a Gaussian prime, which includes an imaginary component (a number multiplied by the square root of –1). Gaussian primes can no longer be divided by other complex numbers. The authors called this system a “complex primon gas.”
“We don’t yet know whether the appearance of prime number randomness near a singularity has a deeper meaning,” Hartnoll says. “However, in my opinion, it is very intriguing that the connection extends to higher-dimensional theories of gravity,” including some candidates for a fully quantum mechanical theory of gravity.
And in a late 2025 preprint, Perlmutter proposed a new framework involving zeta zeros. He relaxed the restrictions on the zeta function so that it could depend not only on integers but on all real numbers, including irrational ones. Doing so opened up even more powerful zeta function techniques for understanding quantum gravity. Physicist Jon Keating of Oxford University, who was not involved in the new research, says broader perspectives like this can reveal new ways of tackling long-standing problems. “It’s only when you step back and look at the whole mountain that you think, ‘Oh, there’s a much better way to get there,'” he says.
Perlmutter cautiously hopes that the wave of primary physics will accelerate new discoveries, but the approach is one of many struggling for acceptance. “The kind of things we’re trying to understand, black holes in quantum gravity, are surely governed by some beautiful structures,” he says. “And number theory seems to be a natural language.”
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