Unlock the Editor’s Digest for free
Roula Khalaf, Editor of the FT, selects her favourite stories in this weekly newsletter.
Google DeepMind has used artificial intelligence to all but match the geometry problem-solving skills of the world’s brightest students, advancing the prized quest to apply the fast-growing technology to complex maths.
AlphaGeometry, the tech giant’s system, correctly answered 25 of 30 questions from the high school International Mathematical Olympiad, according to a paper published in Nature on Wednesday.
The performance, close to the gold medal-winning standard of human competitors, highlights both AI’s growing proficiency in maths and the obstacles that remain. The challenges of reasoning and learning presented by complex maths make it an important test in the effort to create an artificial general intelligence (AGI) that can equal or outstrip humans.
“This is a crucial step towards building an AGI,” said Quoc V Le, a DeepMind researcher. “This is another example that reinforces how AI can help us advance science — and better understand the underlying processes that determine how the world works.”
AlphaGeometry is a so-called neuro-symbolic system that deploys a combination of language learning and deductive reasoning. The company compares the hybrid method to “Thinking, Fast and Slow”, the phrase coined by psychologist Daniel Kahneman to describe the power of harnessing fast pattern recognition to more deliberative logical thinking.
The approach delivers what Trieu H Trinh, another member of the DeepMind research team, describes as “the best of both worlds” to solving problems in geometry. The field is at once familiar to all of us at the everyday level of observation of shapes and space, yet is underpinned by an intricate scaffolding of mathematical theory.
The researchers built a trove of 100mn examples of synthetic geometry data as the information set to train the system to work. Its 25-out-of-30 performance was close behind the 25.9 for a benchmark of human winners in mathematical Olympiads from 2000 to 2022 — and well ahead of the score of 10 achieved by the previous state-of-the-art automated system.
AlphaGeometry nonetheless found some problems laborious and others confounding. It was unable to solve a conundrum of intersecting circles cracked in the 1979 Olympiad by the Vietnamese mathematician Lê Bá Khánh Trình — who was an inspiration to some of the researchers.
The even bigger goal for DeepMind and other researchers is to create AI systems that can deal with maths problems that have proven beyond the human mind.
Mikhail Burtsev, a Landau AI Fellow at the London Institute for Mathematical Sciences, said the DeepMind work was a big step forward — but “only within the limits of the challenge it sets itself”.
“The steeper challenge remains,” he said. “That is, to find out if an AI can discover new mathematics to solve a question that has never yet been answered.”
The prospect of an iconic moment of an AI maths system taking on and beating a human rival, as the chess computer Deep Blue did with world champion Garry Kasparov in 1997, remains elusive.
DeepMind said it had no plans yet to enter the International Mathematical Olympiad — although the company did not rule it out as it pushes ever further into the exacting realm of maths.
