Like physics, mathematics also has its own set of “fundamental particles” – prime numbers, which cannot be divided into smaller natural numbers. These can be divided only among themselves and 1.
And in a new development, it turns out that these mathematical “particles” are offering new ways to tackle some of physics’ deepest mysteries. In the past year, researchers have discovered that formulas based on prime numbers can describe the characteristics of black holes. Number theorists have spent hundreds of years deriving theorems and conjectures based on prime numbers. These new connections suggest that the mathematical truths that govern prime numbers may also govern some of the fundamental laws of the universe. So can physics be expressed in terms of prime numbers?
Black holes are the sites of the most powerful gravitational force in the universe. They contain single points at their centers called singularities, where classical physics predicts gravity should be infinite, breaking down our understanding of space and time. But in the 1960s, physicists discovered that, immediately around the singularity, a kind of chaos ensues-And it looks remarkably similar to a type of chaos recently found in the Primes.
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Physicists hope to make use of the connection. “I would say that many high-energy physicists don’t really know much about that side of number theory,” says Eric Perlmutter of the Sackley Institute for Theoretical Physics.
The fundamental conjecture of number theory on prime numbers is the 1859 Riemann hypothesis. In a handwritten paper, the German mathematician Bernhard Riemann provided a formula with two key terms. The first offered a surprisingly close estimate of how many prime numbers exist that are smaller than a given number. The second term is the zeta function, whose zero (the place where the function is equal to zero) accommodates the original estimate. The mysterious way in which zeta zero always improves the estimate is the subject of the Riemann hypothesis. This hypothesis is so important to number theory that anyone who can prove it will earn a $1 million Clay Mathematics Institute prize.
In the late 1980s physicists began to wonder whether there were any physical systems whose energy levels could be based on prime numbers. Bernard Julia, a physicist at the École Normale Supérieure in France, was challenged by a colleague to find a physics analog described by the zeta function. His solution was to propose a hypothetical type of particle with energy levels given by the logarithm of prime numbers. Julia called these particles “primones” and their group “primone gas”. The partition function of this gas – the enumeration of possible states of the system – is exactly the Riemann zeta function.
At the time, Julia’s concept was a thought experiment – most scientists doubted that prions actually existed. But inside the black hole, a mathematical link was waiting to be discovered. A little more than two decades later, physicists Yan Fyodorov of King’s College London, Gaither Hyeri of Ohio State University, and John Keating of the University of Oxford saw hints that fractal chaos emerges from fluctuations of the zeros of the zeta function, an idea that was conclusively proven 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 Bringing Julia’s work into the real world. Inside chaos near a singularity, they found that an “analogous” symmetry emerges. Hartnoll compares analog symmetry to that of the Dutch artist MC Escher’s famous paintings of bats-The same structure is repeated on different scales. This scaling symmetry, with a little mathematics, revealed a quantum system near the singularity whose spectrum is organized into prime numbers – an analogous primordial gas cloud.
Five months later, he uploaded a preprint with a new twist. The team, which also included physicist Marine de Klerk, now of the University of Cambridge, extended their analysis to a five-dimensional universe instead of the usual four. He found that Extra dimension forced a new feature: Tracking the dynamics of the singularity now requires a “complex” prime, known as a Gaussian prime, which includes an imaginary component (a number multiplied by the square root of -1). Gaussian prime numbers cannot be divided by other complex numbers. The authors dubbed this system the “complex primordial gas”.
“We don’t yet know whether the presence of prime number randomness close to a singularity has any deeper meaning,” says Hartnoll. “However, in my view, it is very interesting that the connection extends to higher dimensional theories of gravity,” including some candidates for a full quantum mechanical theory of gravity.
And in preprint late 2025, Perlmutter proposed a new framework Zeta zero is included. He relaxed the restrictions on the zeta function so that it could rely not only on integers but also on all real numbers, including irrationals. Doing so opened up even more powerful zeta function techniques for understanding quantum gravity. John Keating, a physicist at the University of Oxford who was not involved in the new research, says such a comprehensive approach could reveal new ways to tackle long-standing problems. “It’s only when you step back and look at the whole mountain that you think, ‘Ah, there’s a better way to get up there,'” he says.
Perlmutter is cautiously hopeful that the shake-up of major physics will spur new discoveries, but the approach is just one of many fighting for acceptance. “The kinds of things we’re trying to understand, black holes in quantum gravity, are certainly governed by some beautiful structures,” he says. “And number theory appears to be a natural language.”
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