Hannah Fry: 'AI can do some superhuman things - but so can forklifts' Mathematician Hannah Fry travels to the front lines of AI in her new BBC documentary AI Confidential with Hannah Fry. The chances are that you think about artificial intelligence far more today than you did five years ago. Since ChatGPT was launched in November 2022, we have become accustomed to interacting with AIs in most spheres of life, from chatbots and smart home tech to banking and healthcare. But such rapid change brings unexpected problems - as mathematician and broadcaster Hannah Fry shows in AI Confidential With Hannah Fry, a new three-part BBC documentary in which she talks to people whose lives have been transformed by the technology. She spoke to New Scientist about how we should view AI, its role in modern mathematics - and why it will upend the global economy.

This paper concerns the structure of learned representations in text-guided generative models, focusing on score-based models.

Paul Erdős was one of the most prolific mathematicians to ever live, known for showing up at the door of others in the field and declaring they should host and feed him while they do maths together. I come to you with something a little different for my latest maths column - a plea to Hollywood to make a comedy biopic about one of the greatest mathematicians of all time, Paul Erdős. Why is Erdős (pronounced "air-dish") deserving of such acclaim? With almost 1500 papers to his name, he is probably the most prolific mathematician that ever lived, and possibly that will ever live. Unsurprisingly, with that many papers, he is known for his work across many areas of maths, from probability to number theory to graph theory.

Axiom says its AI found solutions to several long-standing math problems, a sign of the technology's steadily advancing reasoning capabilities. Five years ago, mathematicians Dawei Chen and Quentin Gendron were trying to untangle a difficult area of algebraic geometry involving differentials, elements of calculus used to measure distance along curved surfaces . While working on one theorem, they ran into an unexpected roadblock: Their argument depended on a strange formula from number theory, but they were unable to solve or justify it. In the end, Chen and Gendron wrote a paper presenting their idea as a conjecture, rather than a theorem. Chen recently spent hours prompting ChatGPT in the hopes of getting the AI to come up with a solution to the still unsolved problem, but it wasn't working.

Amateur mathematicians are using artificial intelligence chatbots to solve long-standing problems, in a move that has taken professionals by surprise. While the problems in question aren't the most advanced in the mathematical canon, the success of AI models in tackling them shows that their mathematical performance has passed a significant threshold, say researchers, and could fundamentally change the way we do mathematics. The questions being solved by AI originate from Hungarian mathematician Paul Erdős, who was famous for his ability to pose useful but difficult questions during a career that spanned over six decades. "The questions tended to be very simple, but very hard," says Thomas Bloom at the University of Manchester, UK. By his death in 1996, there were more than 1000 of these unsolved Erdős problems, spanning a wide range of mathematical disciplines, from combinatorics (the study of combinations) to number theory.

Descriptive set theorists study the niche mathematics of infinity. Now, they've shown that their problems can be rewritten in the concrete language of algorithms. All of modern mathematics is built on the foundation of set theory, the study of how to organize abstract collections of objects. But in general, research mathematicians don't need to think about it when they're solving their problems. They can take it for granted that sets behave the way they'd expect, and carry on with their work. Descriptive set theorists are an exception. This small community of mathematicians never stopped studying the fundamental nature of sets--particularly the strange infinite ones that other mathematicians ignore. Their field just got a lot less lonely. In 2023, a mathematician named Anton Bernshteyn published a deep and surprising connection between the remote mathematical frontier of descriptive set theory and modern computer science.

In the mid-19th century, Bernhard Riemann conceived of a new way to think about mathematical spaces, providing the foundation for modern geometry and physics. Standing in the middle of a field, we can easily forget that we live on a round planet. We're so small in comparison to the Earth that from our point of view, it looks flat. The world is full of such shapes--ones that look flat to an ant living on them, even though they might have a more complicated global structure. Mathematicians call these shapes manifolds.

In 2025, the edges of mathematics came a little more sharply into view when members of the online Busy Beaver Challenge community closed in on a huge number that threatens to defy the logical underpinnings of the subject. This number is the next in the "Busy Beaver" sequence, a series of ever-larger numbers that emerges from a seemingly simple question - how do we know if a computer program will run forever? To find out, researchers turn to the work of mathematician Alan Turing, who showed that any computer algorithm can be mimicked by imagining a simplified device called a Turing machine. More complex algorithms correspond to Turing machines with larger sets of instructions or, in mathematical parlance, more states. For example BB(1) is 1 and BB(2) is 6, so making the algorithm twice as complex increases its runtime sixfold.

We investigate the mathematical capabilities of two iterations of ChatGPT (released 9-January-2023 and 30-January-2023) and of GPT-4 by testing them on publicly available datasets, as well as hand-crafted ones, using a novel methodology. In contrast to formal mathematics, where large databases of formal proofs are available (e.g., mathlib, the Lean Mathematical Library), current datasets of natural-language mathematics used to benchmark language models either cover only elementary mathematics or are very small. We address this by publicly releasing two new datasets: GHOSTS and miniGHOSTS. These are the first natural-language datasets curated by working researchers in mathematics that (1) aim to cover graduate-level mathematics, (2) provide a holistic overview of the mathematical capabilities of language models, and (3) distinguish multiple dimensions of mathematical reasoning. These datasets test on 1636 human expert evaluations whether ChatGPT and GPT-4 can be helpful assistants to professional mathematicians by emulating use cases that arise in the daily professional activities of mathematicians.

The era of hype first, think later. Demis Hassabis, CEO of Google DeepMind, summed it up in three words: "This is embarrassing." Hassabis was replying on X to an overexcited post by Sébastien Bubeck, a research scientist at the rival firm OpenAI, announcing that two mathematicians had used OpenAI's latest large language model, GPT-5, to find solutions to 10 unsolved problems in mathematics. "Science acceleration via AI has officially begun," Bubeck crowed. Put your math hats on for a minute, and let's take a look at what this beef from mid-October was about. Bubeck was excited that GPT-5 seemed to have somehow solved a number of puzzles known as Erdős problems.