The proofs that earned EPFL professor Maryna Viazovska the Fields Medal in 2022 have reached a new milestone: their complete formalization by computer, achieved through a collaboration between mathematicians and artificial intelligence tools. In 2016, Maryna Viazovska solved the sphere packing problem in dimension 8, proving that the E lattice constitutes the densest possible arrangement. Shortly after, together with collaborators, she established an analogous result in dimension 24 using the Leech lattice. Her method provided an elegant solution to a problem studied for centuries, with close ties to applied fields such as error-correcting codes. For this major contribution, Viazovska was awarded the Fields Medal in 2022, the highest distinction in mathematics.

Some seemingly simple sequences of multiplication and addition grow so quickly that they question the very foundations of mathematics. Did you hear the one about the man who invented chess and got himself executed? Legend has it that a man called Sessa, who lived in India long ago, developed the rules for the game and presented them to a king. The king was delighted and offered the man his pick of reward. Sessa asked for a supposedly humble quantity of rice.

One of the most bitterly contested proofs in modern mathematics may be on the verge of being untangled. Two projects, both aiming to use a computer program to cast new light on the controversy, are now up and running - with one having operated in secret for more than two years already. The developments are a positive sign that the row might find a solution, say mathematicians. The saga began in 2012 when Shinichi Mochizuki at Kyoto University, Japan, claimed to have proved a famous idea called the ABC conjecture, posting a 500-page proof online. The conjecture is simple to state, concerning prime numbers involved in solutions to the equation a + b = c and how these numbers relate to each other.

Gödel's seminal work directly contradicted one of the great minds of mathematics and limited the field forever Kurt Gödel, the man who ruined mathematics, was one of the most important thinkers of the 20th century. He was born in 1906, smack-bang in the middle of the greatest crisis that maths has ever known. Just a few decades later, he would help resolve this turmoil, but in doing so doom mathematicians to a smaller world than the one that came before. Mathematics, as an intellectual framework, is incredibly powerful. The entire point is taking one set of logical ideas and using them to build another, making maths the closest thing we have to a cognitive perpetual-motion machine - there is always a new mathematical idea lurking across the horizon, and we just need to assemble the steps to get there.

Many people who try using AI are disappointed with the results and feel they can't trust a machine - but are there lessons we can learn from how AI is taking on mathematics? Have you ever received an email and had a sneaking suspicion it was written by AI, rather than lovingly handcrafted? Mathematicians have been wrestling with similar feelings for half a century, and have some lessons for the rest of us. It all began in 1976, when Kenneth Appel and Wolfgang Haken announced a proof of the four colour theorem, which states it takes a maximum of four shades to colour any map so that no two adjacent regions match. The theorem's simplicity meant mathematicians were expecting an elegant proof revealing a greater mathematical truth. Instead, they got 60,000 lines of impenetrable computer code.

In this interview series, we're meeting some of the AAAI/SIGAI Doctoral Consortium participants to find out more about their research. We sat down with Maxime Meyer to chat about his current research, future plans, and how he found the doctoral consortium experience. Could you start with an introduction to yourself, where you're studying and the topic of your research? My research focuses on large language models. Which aspect of large language models are you looking at?

The speed at which artificial intelligence is gaining in mathematical ability has taken many by surprise. Are the days of handwritten mathematics coming to an end? In March 2025, mathematician Daniel Litt made a bet. Despite the march of progress of artificial intelligence in many fields, he believed his subject was safe, wagering with a colleague that there was only a 25 per cent chance an AI could write a mathematical paper at the level of the best human mathematicians by 2030. Only a year later, he thinks he was wrong.

Chris Maddison was just an intern when he started working on the Go-playing AI that would eventually become AlphaGo. In March 2016, Google DeepMind's artificial intelligence system AlphaGo shocked the world. In a stunning five-match series of Go, the ancient Chinese board game, the AI beat the world's best player, Lee Sedol - a moment that was televised in front of millions and hailed by many as a historic moment in the development of artificial intelligence. Chris Maddison, now a professor of artificial intelligence at the University of Toronto, was then a master's student and helped get the project off the ground. Alex Wilkins: How did the idea for AlphaGo first come about?

Has the technology lived up to its potential? The first time that AlphaGo revealed its full power, it prompted a visceral reaction . Lee Sedol, the world's greatest player of the ancient Chinese board game Go, had grown visibly agitated at the artificial intelligence's prowess. The hushed crowd in downtown Seoul, South Korea, could barely contain its gasps. It was quickly dawning on Lee, and the tens of millions watching at home, that this AI was different to those that had come before. It wasn't just beating Lee, but it was doing so with an almost human-like aptitude.

What do a 20th-century physicist, an 18th-century statistician and an ancient Greek philosopher have in common? They all knew how to extrapolate with incredible accuracy. Suppose I showed you a box and asked you to guess what is inside, without providing any more details. You might think this is completely impossible, but the nature of the container provides some information - the contents must be smaller than the box, for example, while a solid metal box can hold liquids and withstand temperatures that a cardboard box would struggle with. Is there a way to describe this process of guessing with limited information in a mathematically sensible way?