An artificial intelligence model developed by Alphabet Inc.’s Google DeepMind unit has won a gold medal in the International Mathematical Olympiad.

The company announced the achievement today, two days after OpenAI disclosed that it has reached the same milestone. However, the ChatGPT developer reportedly earned its gold medal in a different manner. Whereas Google’s AI model underwent the same evaluation as human test takers, OpenAI’s submission was graded by a group of former contest participants.

The International Mathematical Olympiad, or IMO, is a prestigious math competition for high school students. Participating countries each send six contestants who must solve six questions in 4.5 hours. This year, 67 of the 630 participants won a gold medal.

IMO questions are relatively narrow in scope. They primarily focus on four branches of mathematics taught in high school: algebra, combinatorics, geometry and number theory. Nevertheless, the proofs necessary to solve the problems are highly complicated. Each proof comprises multiple pages of dense mathematical formulae accompanied by natural language explanations.

Google used an algorithm based on its Gemini series of large language models to win the gold medal. The LLM is equipped with Deep Think, a feature that the search giant debuted in May. The capability allows an AI to generate multiple potential answers to a prompt instead of the usual one and then combine them.

Google honed the AI’s math capabilities using reinforcement learning, a common approach to training reasoning models. In a reinforcement learning project, researchers give an LLM sample questions and provide feedback on the quality of each response. The LLM then analyzes the feedback to find ways of improving its capabilities.

Google taught Gemini using a “curated corpus of high-quality solutions to mathematics.” The company’s researchers didn’t simply include a set of math problems and their solutions, but also provided information on the intermediate steps necessary to reach each given solution. Additionally, they added in “general hints and tips” on how to tackle IMO questions.

Google’s model answered five of the six questions in this year’s contest correctly. The sixth problem, the most complicated in the set, required calculating the number of tiles needed to cover a two-dimensional space. It was solved correctly by five of the 630 students who participated.

In last year’s IMO contest, two Google-developed AI models jointly earned a silver medal by solving four of the six problems. One of the algorithms was optimized to answer geometry questions while the other focused on generating proofs. According to DeepMind, accuracy is only one of the metrics by which its Gemini model outperforms those algorithms.

“AlphaGeometry and AlphaProof required experts to first translate problems from natural language into domain-specific languages, such as Lean, and vice-versa for the proofs. It also took two to three days of computation,” DeepMind researchers detailed in a blog post. “Our advanced Gemini model operated end-to-end in natural language, producing rigorous mathematical proofs directly from the official problem descriptions – all within the 4.5-hour competition time limit.”

Google plans to roll out the AI model in phases. It will first test the algorithm with a group of mathematicians before making it available in Google AI Ultra, a $250 subscription announced earlier this year. The plan increases the usage limits of the company’s Gemini AI assistant and provides access to a number of other AI services.

Image: Google