Google AI Nearly Misses IMO Gold Medal: Solves Problem in 19 Seconds, Shocking Judges, Geometric Ability Surpasses Humans

DeepMind's latest mathematical model has achieved an outstanding performance by winning a silver medal in the International Mathematical Olympiad (IMO). The model perfectly solved 4 out of 6 problems, missing the gold medal by just 1 point. Particularly impressive was its performance on Problem 4, where the model provided a solution in only 19 seconds, with a speed and quality of problem-solving that left human judges astounded.

AlphaProof

AlphaProof is a system capable of proving mathematical propositions in the formal language Lean. It combines a pre-trained large language model with the AlphaZero reinforcement learning algorithm.

To overcome the limitations of formal languages in machine learning due to limited human-written data, researchers bridged the gap between natural language and formal statements by:

  1. Fine-tuning the Gemini model to automatically translate natural language problem statements into formal statements
  2. Creating a large library of formalized problems of varying difficulty

When solving problems, AlphaProof generates candidate solutions and proves or disproves them by searching for possible proof steps in Lean.

AlphaGeometry 2

AlphaGeometry 2 is a neural-symbolic hybrid system trained from scratch using Gemini's language model. It can solve more difficult geometry problems than its predecessor, including those involving object motion, angles, ratios, and distance equations.

Key improvements include:

  1. Training on synthetic data an order of magnitude larger than the previous version
  2. A symbolic engine two orders of magnitude faster than before
  3. A novel knowledge-sharing mechanism allowing advanced combinations of different search trees to solve more complex problems

AlphaGeometry 2 has demonstrated impressive capabilities, solving 83% of IMO geometry problems from the past 25 years, compared to 53% for its predecessor. In this year's IMO, it solved Problem 4 in just 19 seconds after receiving the formalized question.

The AI's performance in the IMO demonstrates significant progress in mathematical reasoning capabilities, bringing AI closer to human-level problem-solving in advanced mathematics.