Vietnamese scientists build Olympian AI math model

Trinh Hoang Trieu, 29, Luong Minh Thang, 36, and Le Viet Quoc, 42, collaborated to build the AI system AlphaGeometry with a team of several other scientists. Trieu received his doctorate from New York University, Thang’s is a Stanford University degree, and along with Quoc, all three are AI experts at Google DeepMind.

AlphaGeometry was able to solve 25 out of 30 geometry problems used by the International Mathematical Olympiads (IMO) of in 2000-2022 period, all within the standard time period.

A previous system developed in the 1970s, which was at the time thought to be the world’s strongest geometry theorem prover, solved only 10, as reported by the New York Times. On average, an IMO gold medalist can solve 25.9 problems, according to experts.

“This [AlphaGeometry’s Olympiad score] is something unimaginable,” Quoc said on Thursday. He explained that AI can solve one-step problems very well, but mathematical problems tend to involve hundreds of steps before they can be solved.

An Olympiad typically presents six problems, including two geometry problems, meaning AlphaGeometry can manage a third of those problems. The team responsible for building AlphaGeometry has also claimed that it is first AI model in the world capable of solving more problems than the bronze medalists of the IMO 2000 and 2015.

“It absolutely makes sense when AI researchers take on the challenges of IMO geometry problems, as finding their solutions is a bit similar to chess, where we have few appropriate moves in each step. But I’m still surprised that they could pull it off,” said Professor Ngo Bao Chau of the Math department at Chicago University.

AlphaGeometry is the combination of a neural language model and a symbolic engine, which is then calibrated to solve geometric problems. The neural network is trained on 100 million geometric proofs without human examples. If the neural network cannot solve a problem, it will suggest ways to improve the proof arguments, such as by drawing additional lines or circles.

What makes the AI model special is the fact that it is trained only on synthetic data made from scratch. Trieu said it can generate high-quality data without using data from human examples, something that other AI models like ChatGPT or Gemini have not been able to do yet.

“Simply speaking, AlphaGeometry can generate answers out of nothing. Other existing AI models will find existing answers, or answers that are similar to a human’s,” Thang said.

Trieu said he had been conceiving ideas for AlphaGeometry since 2019, while he was looking for a graduation research topic at New York University.

“I thought back to when I was in high school, when I loved to solve geometric problems, but was not good enough to participate in national exams. So, I decided to pursue that, starting with a model that can solve simple problems,” said Trieu, a former student at the Ho Chi Minh City University of Science.

Quoc and Thang, former math-major students at the Quoc Hoc-Hue High School For The Gifted and the VNU-HCM High School for the Gifted, were intrigued by Trieu’s ideas. Trieu later joined Google DeepMind and has been working there since 2021.

By July 2022, after 10 versions, AlphaGeometry had solved its first problems. The breakthrough came to the team three months later, when an IMO geometry problem was solved.

Trieu said the AI model can be used as a guiding system that supports high school students with geometric problems.

Evan Chen, a researcher at the Massachusetts Institute of Technology and gold medalist at the 2014 IMO, said he was surprised to see what AlphaGeometry could do. Chen said a computer program solves geometry problems through coordinates and algebra, while AlphaGeometry uses pure geometrical principles, similar to what students typically learn.

“I’m curious to see how AlphaGeometry can achieve this,” Chen said.

A month ago, when Thang returned to the VNU-HCM High School for the Gifted, he showed Dr. Le Ba Khanh Trinh how the AI solved a problem at the IMO 2015. It was one of the most difficult geometry problems seen at the IMO. AlphaGeometry reached a solution after 109 steps.

“Trinh was impressed by how it solved the problems through very simple principles, but he was not quite satisfied, as he believed solutions should have a certain beauty and soul to it, and there needs to be interconnection,” Thang said. Trinh once secured a gold medal at the IMO 1979 with a perfect score, and was the only Vietnamese to win a special prize at the IMO for a succinct and beautiful solution for a geometry problem.

Researchers have also said this might be a direction for the continued development of AlphaGeometry, and they hoped that further developments can help the AI assist humans in solving the seven Millennium Prize Problems.

Quoc said he was proud that their work was published in Nature, a top-tier journal. He said AI can not only solve math problems, but maybe also advance humanity as a whole.

“Because math is the language of science and technology,” he said. “So, doing math is the way to push these fields to develop.”