In a landmark achievement, AI models from Google and OpenAI have attained gold medal status at the International Mathematical Olympiad (IMO), signaling a significant leap in the mathematical capabilities of artificial intelligence. This marks the first instance of AI systems surpassing the gold-medal scoring threshold in this prestigious competition for high school students.

The International Mathematical Olympiad is the world's most prestigious mathematics competition for young mathematicians. Since 1959, the annual competition has brought together pre-university students from various countries, each represented by six elite mathematicians. These students tackle six exceptionally challenging problems spanning algebra, combinatorics, geometry, and number theory.

This year, the 66th IMO was hosted in Queensland, Australia, with 641 students from 112 countries participating. The competition consists of two sessions, where participants are given 4.5 hours to solve three complex math problems in each session.

Google's DeepMind AI unit and OpenAI independently developed AI models that achieved gold medal scores at the IMO. An advanced version of Google's Gemini Deep Think model and OpenAI's experimental reasoning model each solved five out of the six problems, earning 35 out of a possible 42 points. This score is the cut-off for winning a gold medal this year. For each problem, three former IMO medalists independently graded the model's submitted proof. In comparison, approximately 11% (67 of 630) of the human contestants achieved gold-medal scores, and five contestants achieved perfect scores of 42 points.

The AI models' success is attributed to their use of general-purpose "reasoning" models, which process mathematical concepts using natural language. This approach contrasts with previous AI attempts that relied on specialized formal languages and symbolic manipulation. Google's Gemini model, for example, operated end-to-end in natural language, producing mathematical proofs directly from the official problem descriptions within the 4.5-hour time limit. The advanced Gemini model was trained using novel reinforcement learning techniques. These techniques leverage multi-step reasoning, problem-solving, and theorem-proving data. OpenAI's breakthrough was achieved with a new experimental model centered on massively scaling up “test-time compute”. This involved allowing the model to "think" for longer periods and deploying parallel computing power to run numerous lines of reasoning simultaneously.

The implications of these achievements are far-reaching. Experts suggest that AI is less than a year away from assisting mathematicians in cracking unsolved research problems. Google researchers believe that AI models' capabilities can extend to other fields, such as physics. According to Junehyuk Jung, a math professor at Brown University and visiting researcher at Google's DeepMind, the ability to solve hard reasoning problems in natural language will enable collaboration between AI and mathematicians.

Despite the impressive performance of AI, humans still hold an edge in certain areas. While the AI models achieved gold-level scores, they did not attain perfect scores, unlike five human contestants. This highlights the importance of human intuition and problem-solving skills in complex reasoning tasks. Contest organizers could not verify how much computing power had been used by the AI models or whether there had been human involvement.

Regardless, the progress made by AI in mathematical problem-solving is undeniable. As IMO President Gregor Dolinar stated, "It is very exciting to see progress in the mathematical capabilities of AI models". Demis Hassabis, CEO of Google DeepMind, echoed this sentiment, emphasizing that their solutions were clear, precise, and easy to follow.

These breakthroughs signify a major step forward in the development of AI systems capable of rivalling human intelligence. As AI continues to evolve, its ability to tackle complex mathematical problems will likely lead to further advancements in various fields, accelerating scientific discovery and innovation.