The world's first AI to win a gold medal in the IMO has emerged. Google's Gemini shattered the myth of the International Mathematical Olympiad, scoring 35 points and astonishing the judges.

Google DeepMind has won a gold medal in the IMO and received official certification from the IMO! The new model, Gemini Deep Think, solved 5 problems in 4.5 hours using only natural language and scored 35 points. This time, the specific problem-solving process has also been made public.

Today, Google DeepMind officially announced that it has won a gold medal in the IMO!

With Gemini Deep Think (Advanced Version), a general model, they successfully cracked the first 5 problems and scored 35 points (out of a full score of 42). 

Moreover, the AI reached the gold medal standard in the IMO within the limit of 4.5 hours.

Most importantly, Gemini solved the problems using only pure natural language - English.

Different from OpenAI, this result has been officially certified by the IMO organizing committee.

Demis Hassabis issued two statements in a row, repeatedly emphasizing that "Google's model is the first AI system to receive official gold medal-level recognition."

Google DeepMind Officially Wins the Gold Medal

As the Olympics of the mathematical world, the IMO has been held annually since 1959, attracting outstanding students from all over the world every year.

Contestants are required to solve 6 in-depth mathematical problems within 4.5 hours, covering algebra, geometry, combinatorics, and number theory.

Moreover, only the top 8% of the contestants can win a gold medal, which symbolizes supreme academic honor.

In recent years, the IMO has gradually become a testing ground for AI capabilities. Mathematical problems not only require logical reasoning but also test creative thinking and rigor, which pose extremely high requirements for AI systems.

In 2024, AlphaProof and AlphaGeometry 2 cracked 4 out of 6 problems and scored 28 points, reaching the silver medal level.

This breakthrough using professional "formal language" indicates that AI is beginning to approach the mathematical reasoning ability of top humans.

Today, Gemini Deep Think has set another milestone by perfectly cracking 5 problems and entering the gold medal ranks.

So, how did this model achieve this?

We hereby confirm that Google DeepMind has reached a much-anticipated milestone, scoring 35 points in a competition with a full score of 42 - which is enough to win a gold medal.

Their solutions are amazing in many aspects. The IMO judges believe that these solutions are clear in thinking, precise in expression, and most of the content is easy to understand.

- Professor Gregor Dolinar, Chairman of the IMO

Solving Problems with Natural Language, End-to-End Reasoning

Before AlphaProof and AlphaGeometry 2 solved the IMO problems, experts were required to translate the problems into "formal language," such as Lean.

Moreover, the same was true for the proof process, which required two to three days of computation time.

This year, Gemini Deep Think runs end-to-end entirely in natural language, directly generating rigorous mathematical proofs from the official problem descriptions and completing them within the 4.5-hour competition time limit.

Borrowing Karpathy's classic quote, "English is a popular programming language." Now it seems that's really the case.

Deep Think Mode

The reason for winning the gold medal is that the team used an advanced version of Gemini Deep Think - an enhanced reasoning mode for complex problems.

Moreover, combined with parallel thinking technology, the model is allowed to explore multiple problem-solving paths simultaneously and finally integrate the optimal answer.

This multi-threaded reasoning method breaks through the limitations of traditional single linear thinking.

In order to fully utilize the reasoning ability of Deep Think, Google also conducted novel reinforcement learning training on Gemini, allowing it to use more data on multi-step reasoning, problem-solving, and theorem proving.

In addition, the Google research team further upgraded the Gemini version in the following ways: 

· More thinking time

· Access to a set of high-quality solutions to past problems

· Providing general tips and techniques for solving IMO problems

This combination of "training + knowledge base + strategy" allows Gemini to shine on the IMO stage.

It is worth mentioning that next, Google will provide this version of the Deep Think model to a group of testers, such as mathematicians, and then launch it to Google AI Ultra subscribers.

Problem-Solving Process

Let's take a look at the specific problem-solving process of Google Gemini Deep Think this time.

Official report: https://storage.googleapis.com/deepmind-media/gemini/IMO_2025.pdf

For the first problem, an analytic geometry problem, the model's solution is to let n > 3 be a given integer.

The proof idea is to simplify the problem to the specific case where n = k and all lines must be sunlines. Specifically, let C(k) denote "P can be covered by k different sunlines," and define P_0 = ø.

Then the model sets up a lemma: In the set L, all N_v vertical lines must be {x = 1, 2, ..., N_v}, all N_H horizontal lines must be {y = 1, 2, ..., N_H}, and all N_D diagonal lines must be lines of the form x + y = s, where s ranges from n + 2 - N_D, ..., n + 1.

Then, the model proves this lemma.

Next, the model proves Theorem 1: When n ≥ 3 and 0 ≤ k ≤ n, if there exists a set of n different lines that exactly cover the point set P_n, and exactly k of them are sunlines, then the necessary and sufficient condition is that the proposition C(k) is true.

Next, the model analyzes the core problem C(k): For which k > 0 can the point set P_k be exactly covered by k sunlines?

Finally, the model successfully proves that the necessary and sufficient condition for C(k) to hold is k ∈ {0, 1, 3}, thus proving that the only possible numbers of sunlines are 0, 1, or 3.

For the second problem, a plane geometry problem, the model divides the proof process into five steps.

Step 1: Determine that point P is the excenter of △AMN.

Step 2: Find ∠EBF.

Step 3: Introduce the auxiliary point V and its properties.

Step 4: Point V lies on the circumcircle Σ.

Step 5: The orthocenter H and the tangent condition.

Finally, the model proves that the line VH is the tangent to the circle Σ at point V, thus completing the proof.

The third problem is a function problem.

In the problem-solving process, the model divides the key steps into three steps.

First, it determines the properties and classification of the Bonza function.

In the second and third steps, the model completes the upper bound proof c ≤ 4 and the lower bound proof c ≥ 4, respectively.

The final conclusion is that the smallest real constant c that satisfies the condition is c = 4.