\n<\/p>\n
Like physics, math has its own set of \u201cfundamental particles\u201d\u2014the prime numbers, which can\u2019t be broken down into smaller natural numbers. They can only be divided by themselves and 1.<\/p>\n
And in a new development, it turns out these mathematical \u201cparticles\u201d are offering new ways to tackle some of physics\u2019 deepest mysteries. Over the past year, researchers have found that formulas based on the prime numbers can describe features of black holes. Number theorists have spent hundreds of years deriving theorems and conjectures based on the primes. 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 primes?<\/p>\n
Black holes are the sites of the universe\u2019s most crushing gravitational force. At their centers lie single points called singularities, where classical physics predicts that gravity must be infinite, causing our understanding of space and time to break down. But in the 1960s, physicists found that, immediately surrounding the singularity, a type of chaos emerges\u2014and it looks remarkably similar to a kind of chaos recently found in the primes.<\/p>\n
If you’re enjoying this article, consider supporting our award-winning journalism by subscribing. By purchasing a subscription you are helping to ensure the future of impactful stories about the discoveries and ideas shaping our world today.<\/p>\n
Physicists hope to make use of the connection. \u201cI\u2019d say many high-energy physicists don\u2019t actually know much about that side of number theory,\u201d says Eric Perlmutter of the Institute of Theoretical Physics, Saclay.<\/p>\n
Number theory\u2019s foundational conjecture on primes is the 1859 Riemann hypothesis. In a hand-written paper, German mathematician Bernhard Riemann provided a formula with two main terms. The first offered a startlingly close estimate for how many prime numbers exist 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) tune up the original estimate. The mysterious way in which the 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 earn a $1-million Clay Mathematics Institute prize.<\/p>\n
In the late 1980s physicists started to wonder if there was a physical system whose energy levels might be based on the prime numbers. Physicist Bernard Julia of the \u00c9cole Normale Sup\u00e9rieure in France was challenged by a colleague to find a physics analogue described by the zeta function. His solution was to propose a hypothetical kind of particle with energy levels given by the logarithms of prime numbers. Julia called these particles \u201cprimons\u201d and a group of them a \u201cprimon gas.\u201d The partition function\u2014a census of a system\u2019s possible states\u2014of this gas is exactly the Riemann zeta function.<\/p>\n
At the time, Julia\u2019s concept was a thought experiment\u2014most scientists doubted that primons actually existed. But deep inside black holes, a mathematical link awaited discovery. A little more than two decades later, physicists Yan Fyodorov of King\u2019s College London, Ghaith Hiary of Ohio State University and Jon Keating of the University of Oxford saw hints that fractal chaos emerges from the fluctuations of the zeta function\u2019s zeros, an idea that was conclusively proven in 2025.<\/p>\n
Einstein\u2019s general theory of relativity shows that the same chaos also arises near a singularity.<\/p>\n
In a February 2025 preprint, University of Cambridge physicist Sean Hartnoll and graduate student Ming Yang brought Julia\u2019s work into the real world. Inside the chaos close to a singularity, they found that a \u201cconformal\u201d symmetry emerges. Hartnoll likens conformal symmetry to Dutch artist M. C. Escher\u2019s famous drawings of bats\u2014the same structure repeats on different scales. This scaling symmetry, together with a bit of math, revealed a quantum system near the singularity whose spectrum organizes into prime numbers\u2014a conformal primon gas cloud.<\/p>\n
Five months later, they uploaded a preprint with a new twist. The team, which now included University of Cambridge University physicist Marine De Clerck, expanded their analysis to a five-dimensional universe instead of the usual four. They found that the extra dimension forced a new feature: keeping track of the singularity\u2019s dynamics now required a \u201ccomplex\u201d prime number, known as a Gaussian prime, that includes an imaginary component (a number multiplied by the square root of \u20131). Gaussian primes can\u2019t be divided any further by other complex numbers. The authors dubbed this system a \u201ccomplex primon gas.\u201d<\/p>\n
\u201cWe don\u2019t know yet whether the appearance of prime number randomness close to a singularity has a deeper meaning,\u201d Hartnoll says. \u201cHowever, to my mind, it is very intriguing that the connection extends to higher dimensional theories of gravity,\u201d including some candidates for a fully quantum mechanical theory of gravity.<\/p>\n
And in a late 2025 preprint, Perlmutter proposed a new framework involving the zeta zeros. He relaxed the restrictions on the zeta function so it could rely not just on integers but on all real numbers, including irrationals. Doing so opened up even more powerful zeta function techniques to understand quantum gravity. Physicist Jon Keating of the University of Oxford, who was not involved in the new research, says that broader perspectives such as this can reveal new ways to tackle long-standing problems. \u201cIt\u2019s only when you step back and look at the whole mountain that you think, \u2018Ah, there\u2019s a much better way to get up over there,\u2019\u201d he says.<\/p>\n
Perlmutter cautiously hopes the flurry of prime physics will hasten new discoveries, but the approach is one of many fighting for acceptance. \u201cThe kinds of things we\u2019re trying to understand, black holes in quantum gravity, are surely governed by some beautiful structures,\u201d he says. \u201cAnd number theory seems to be a natural language.\u201d<\/p>\n
If you enjoyed this article, I\u2019d like to ask for your support. Scientific American<\/span> has served as an advocate for science and industry for 180 years, and right now may be the most critical moment in that two-century history.<\/p>\n I\u2019ve been a Scientific American<\/span> subscriber since I was 12 years old, and it helped shape the way I look at the world. SciAm <\/span>always educates and delights me, and inspires a sense of awe for our vast, beautiful universe. I hope it does that for you, too.<\/p>\n If you subscribe to Scientific American<\/span>, you help ensure that our coverage is centered on meaningful research and discovery; that we have the resources to report on the decisions that threaten labs across the U.S.; and that we support both budding and working scientists at a time when the value of science itself too often goes unrecognized.<\/p>\n In return, you get essential news, captivating podcasts, brilliant infographics, can’t-miss newsletters, must-watch videos, challenging games, and the science world’s best writing and reporting. You can even gift someone a subscription.<\/p>\n There has never been a more important time for us to stand up and show why science matters. I hope you\u2019ll support us in that mission.<\/p>\n","protected":false},"excerpt":{"rendered":" Like physics, math has its own set of \u201cfundamental particles\u201d\u2014the prime numbers, which can\u2019t be broken down into smaller natural numbers. They can only be divided by themselves and 1. And in a new development, it turns out these mathematical \u201cparticles\u201d are offering new ways to tackle some of physics\u2019 deepest mysteries. Over the past<\/p>\n","protected":false},"author":1,"featured_media":45790,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"footnotes":""},"categories":[58],"tags":[706,4104,4240,5076,1353],"class_list":{"0":"post-45789","1":"post","2":"type-post","3":"status-publish","4":"format-standard","5":"has-post-thumbnail","7":"category-science","8":"tag-black","9":"tag-hiding","10":"tag-holes","11":"tag-numbers","12":"tag-prime"},"_links":{"self":[{"href":"https:\/\/naijaglobalnews.org\/index.php?rest_route=\/wp\/v2\/posts\/45789","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/naijaglobalnews.org\/index.php?rest_route=\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/naijaglobalnews.org\/index.php?rest_route=\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/naijaglobalnews.org\/index.php?rest_route=\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/naijaglobalnews.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcomments&post=45789"}],"version-history":[{"count":0,"href":"https:\/\/naijaglobalnews.org\/index.php?rest_route=\/wp\/v2\/posts\/45789\/revisions"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/naijaglobalnews.org\/index.php?rest_route=\/wp\/v2\/media\/45790"}],"wp:attachment":[{"href":"https:\/\/naijaglobalnews.org\/index.php?rest_route=%2Fwp%2Fv2%2Fmedia&parent=45789"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/naijaglobalnews.org\/index.php?rest_route=%2Fwp%2Fv2%2Fcategories&post=45789"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/naijaglobalnews.org\/index.php?rest_route=%2Fwp%2Fv2%2Ftags&post=45789"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}