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.

Evaluation benchmarks are at the core role for AI development.

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.

The Math on AI Agents Doesn't Add Up A research paper suggests AI agents are mathematically doomed to fail. The big AI companies promised us that 2025 would be "the year of the AI agents." It turned out to be the year of AI agents, and kicking the can for that transformational moment to 2026 or maybe later. But what if the answer to the question "When will our lives be fully automated by generative AI robots that perform our tasks for us and basically run the world?" is, like that New Yorker cartoon, "How about never?" That was basically the message of a paper published without much fanfare some months ago, smack in the middle of the overhyped year of "agentic AI." Entitled " Hallucination Stations: On Some Basic Limitations of Transformer-Based Language Models," it purports to mathematically show that "LLMs are incapable of carrying out computational and agentic tasks beyond a certain complexity."

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.

Despite their spectacular progress, language models still struggle on complex reasoning tasks, such as advanced mathematics.We consider a long-standing open problem in mathematics: discovering a Lyapunov function that ensures the global stability of a dynamical system. This problem has no known general solution, and algorithmic solvers only exist for some small polynomial systems.We propose a new method for generating synthetic training samples from random solutions, and show that sequence-to-sequence transformers trained on such datasets perform better than algorithmic solvers and humans on polynomial systems, and can discover new Lyapunov functions for non-polynomial systems.

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 introduce MLFMF, a collection of data sets for benchmarking recommendation systems used to support formalization of mathematics with proof assistants. These systems help humans identify which previous entries (theorems, constructions, datatypes, and postulates) are relevant in proving a new theorem or carrying out a new construction. Each data set is derived from a library of formalized mathematics written in proof assistants Agda or Lean. The collection includes the largest Lean 4 library Mathlib, and some of the largest Agda libraries: the standard library, the library of univalent mathematics Agda-unimath, and the TypeTopology library. Each data set represents the corresponding library in two ways: as a heterogeneous network, and as a list of s-expressions representing the syntax trees of all the entries in the library. The network contains the (modular) structure of the library and the references between entries, while the s-expressions give complete and easily parsed information about every entry.We report baseline results using standard graph and word embeddings, tree ensembles, and instance-based learning algorithms. The MLFMF data sets provide solid benchmarking support for further investigation of the numerous machine learning approaches to formalized mathematics. The methodology used to extract the networks and the s-expressions readily applies to other libraries, and is applicable to other proof assistants. With more than $250\,000$ entries in total, this is currently the largest collection of formalized mathematical knowledge in machine learnable format.