Google Unveils Groundbreaking Math AI: Solving Complex Problems in Seconds

AlphaProof and AlphaGeometry 2, two new AI systems from Google DeepMind, did very well in the International Mathematical Olympiad by solving challenging problems. AlphaProof solved the competition’s hardest problem, and AlphaGeometry 2 got a lot better at solving geometry problems.

The IMO is the biggest and most prestigious competition for young mathematicians. Since 1959, the competition has taken place annually. There are six challenging problems that competitors must solve. All of them add up to 42 points, with seven each.

This year, you need at least 29 points to win the gold medal. 58 out of the 609 contestants achieved this in the real competition. Google DeepMind said, “We got 28 out of 42 points, which is the same level as a silver medalist in the competition.”

To better understand this accomplishment, it’s helpful to know that some of the best high school mathematicians train for thousands of hours to solve six tough problems in algebra, combinatorics, geometry, and number theory. Students have to turn in their answers in two sessions, each lasting 4.5 hours.

At least not yet; AI is slower than humans. Google stated, “We solved one problem in minutes, but others took up to three days to solve.” One AI, AlphaProof, is a new formal math reasoning system based on reinforcement learning. The other AI, AlphaGeometry 2, is an improved version of our geometry-solving system.

AlphaProof found the right answer to two algebra problems and one number theory problem and showed that it was correct. Google says that this was the competition’s hardest problem, which only five humans were able to solve.

AlphaGeometry 2 also proved the geometry problem at the same time. The two combinatorics problems remain unsolved. Prof. won an IMO gold medal and a Fields Medal. Sir Timothy Gowers, said, “The fact that the program can come up with a construction like this that isn’t obvious is very impressive and well beyond what I thought was state of the art.”

The AlphaProof system learns to show that mathematical claims are true. It combines Gemini, a large language model that can make up plausible but wrong arguments, with AlphaZero, an AI that was previously proficient at Go, chess, and shogi. “When given a problem, AlphaProof comes up with possible solutions, and then checks to see if they are true by looking through possible proof steps in Lean.”

AlphaProof and AlphaGeometry2

Each discovered and confirmed proof, according to Google DeepMind, strengthens AlphaProof’s language model and improves its ability to tackle future, more challenging problems. AlphaGeometry2 is a neuro-symbolic hybrid system that is two times faster and much better than the first version.

Before this year’s competition, AlphaGeometry 2 could solve 83% of all IMO geometry problems from the last 25 years, while its predecessor could only solve 53% of those problems. This system fixed one problem for IMO 2024 in 19 seconds.

Google is going to share more technical information about AlphaProof and make tools for mathematicians to test hypotheses and quickly finish parts of proof that take a lot of time.