The most extreme promises'AI-assisted resolutions to some of the hardest problems in mathematics'may well turn out to be empty hype. But a number of AI-written solutions, albeit to far less lauded problems, have checked out. These were answers to a number of the Erdos Problems'more than 1,000 mathematical questions set forth by the Hungarian mathematician Paul Erdos'written with generative-AI models including ChatGPT. OpenAI quickly claimed a victory: 'GPT-5.2 Pro for solving another open Erdos problem,' OpenAI President Greg Brockman posted on X in January. 'Going to be a wild year for mathematical and scientific advancement!' (OpenAI and The Atlantic have a corporate partnership.) Much of the excitement around the news has stemmed from the adjudicator of these AI-written proofs: Terence Tao, a professor at UCLA who is widely considered to be the world's greatest living mathematician. His stamp of approval seemingly legitimizes the greatest promise of generative AI'to push the frontier of human knowledge and civilization. When I called Tao earlier this month to get his take on what AI can offer mathematics, he was more tempered. The AI-generated Erdos solutions are impressive, he told me, but not overwhelmingly so: The bots have functionally landed some 'cheap wins,' Tao said....

One of the biggest stories in science is quietly playing out in the world of abstract mathematics. Over the course of last year, researchers fulfilled a decades-old dream when they unveiled a proof of the geometric Langlands conjecture ' a key piece of a group of interconnected problems called the Langlands programme. The proof ' a gargantuan effort ' validates the intricate and far-reaching Langlands programme, which is often hailed as the grand unified theory of mathematics but remains largely unproven. Yet the work's true impact might lie not in what it settles, but in the new avenues of inquiry it reveals. Proving the geometric Langlands conjecture has long been considered one of the deepest and most enigmatic pursuits in modern mathematics. Ultimately, it took a team of nine mathematicians to crack the problem, in a series of five papers spanning almost 1,000 pages1'5. The group was led by Dennis Gaitsgory at the Max Planck Institute for Mathematics in Bonn, Germany, and Sam Raskin at Yale University in New Haven, Connecticut, who completed his PhD with Gaitsgory in 2014....

A shard of smooth bone etched with irregular marks dating back 20,000 years puzzled archaeologists until they noticed something unique ' the etchings, lines like tally marks, may have represented prime numbers. Similarly, a clay tablet from 1800 B.C.E. inscribed with Babylonian numbers describes a number system built on prime numbers. As the Ishango bone, the Plimpton 322 tablet and other artifacts throughout history display, prime numbers have fascinated and captivated people throughout history. Today, prime numbers and their properties are studied in number theory, a branch of mathematics and active area of research today. Informally, a positive counting number larger than one is prime if that number of dots can be arranged only into a rectangular array with one column or one row. For example, 11 is a prime number since 11 dots form only rectangular arrays of sizes 1 by 11 and 11 by 1. Conversely, 12 is not prime since you can use 12 dots to make an array of 3 by 4 dots, with multiple rows and multiple columns. Math textbooks define a prime number as a whole number greater than one whose only positive divisors are only 1 and itself....

The growth of rose petals exploits a geometric trick previously unobserved in nature, physicists have found. Using theoretical analysis, computer simulations and experiments with rubbery plastic sheets, they established that as the petals curl outwards, mechanical feedback regulates their growth, leading to the formation of rolled edges and pointed corners at their tips. The findings, described in Science on 1 May1, could one day have applications in engineering and architecture. 'You might learn new principles and then implement them in manmade structures,' says Eran Sharon, an experimental physicist at the Hebrew University of Jerusalem. Geometric patterns are known to affect developing organisms. But in all previously observed cases, the principles had to do with the 'intrinsic' geometry of surfaces. Intrinsic features are those related to the distances between points on the surface, as would be measured by an ant walking on it. But a surface of a given intrinsic geometry can have multiple ways of existing in 3D ' or 'extrinsic' geometries. For example, a sheet of paper can be laid flat or curled up into a cylinder; and an ant walking on it would not notice any changes in the distances it covers, even though points on the sheet could be closer to or farther from each other in 3D space....