Global AI models dominate IMO 2026 with perfect scores

In July in Shanghai, heat waves roll in.

The 67th International Mathematical Olympiad has officially concluded, with China winning first place with 232 points. Three teenagers achieved a perfect score of 42.

As the applause in the live event still echoed, another impressive achievement quietly appeared on GitHub.

Former Google engineer Deedy Das conducts an AI showdown: 7 cutting-edge large models independently tackle all six problems from IMO 2026.

Claude Fable 5 scored a perfect 42 points in just 2.5 hours, costing $51.

The GPT-5.6 Sol xhigh version also achieved a perfect score, taking just 3.8 hours and reducing costs to an extremely low $20.

Kimi K3 followed closely behind, achieving a perfect score after 17.4 hours of competition and spending $31.

Including the independently submitted AxiomProver, all four parties have achieved a perfect score.

For reference, over the past seven IMOs, with 4,347 human participants, only 30 achieved a perfect score—representing a rate of 0.69%.

The results show not only a 14-point gap between the perfect score of 42 and the fourth-place score of 28, but also that the three perfect-score models reached the top in entirely different ways.

Claude Fable 5 performed cleanly and efficiently. Over 9 dialogue rounds, it produced 6 effective outputs, with a single session lasting up to 73 minutes (P3), generating a total of 700,000 tokens.

GPT-5.6 Sol has had a rocky run. On P2, it completed four rounds over 106 minutes, interrupted twice by network issues. However, its compute control is astonishing—it generated only 230,000 tokens, the most efficient of the three perfect scores.

Kimi K3 is like an endless behemoth. This MoE model with 2.8 trillion parameters spewed out 1.54 million tokens in one go—6.5 times that of Sol. Just for problem P3, it launched six assaults, battling for 491 minutes.

P1 is the gentlest appetizer on the entire stage, with all models completing it in just a few minutes, and human players almost never miss it.

The problem states: There are 2026 positive integers greater than 1 written on a blackboard. In each step, select two numbers m and n, erase them, and replace them with gcd(m, n) and lcm(m, n)/gcd(m, n). Repeat this process until no further operations are possible. Prove that: (a) the process must terminate, leaving exactly one number M greater than 1; (b) the value of M is independent of the order of operations.

To better understand this question, let’s conduct a miniature experiment.

The board initially shows only 12 and 18. 12 = 2² × 3, 18 = 2 × 3². Step 1: gcd(12,18) = 6, lcm(12,18)/6 = 6, the board becomes [6, 6]. Step 2: gcd(6,6) = 6, lcm(6,6)/6 = 1, the board becomes [6, 1]. Only one number greater than 1 remains; the game ends. M = 6.

No matter how you rearrange the order of operations, M is always 6. Why?

The answer lies in the factors.

For each prime p, take the GCD of the number of times each number is divisible by p, then multiply these prime powers together—this value remains unchanged from the first step to the last.

Claude Fable 5: Directly created a counter that shrinks with every step.

For this problem, Fable 5 defines a quantity Φ = T + N, where T is the sum of the number of prime factors of all numbers on the board (counting repetitions), and N is the count of numbers greater than 1. For example, with the board [12, 18], the prime factors of 12 are 2, 2, 3 (totaling 3), and those of 18 are 2, 3, 3 (also totaling 3), so T = 6 and N = 2, giving Φ = 8.

Then it proves that with each operation, Φ decreases by at least 1. There are two cases—if gcd(m, n) > 1, the total number of prime factors T decreases; if gcd(m, n) = 1, T remains unchanged but the count of numbers greater than 1 decreases by one, so N decreases by 1. Since Φ is a positive integer and decreases by at least 1 at each step, the process must terminate in a finite number of steps. A single counter,一刀斩断.

GPT-5.6 Sol: Track the product, lexicographically reduce dimensions.

Sol focuses on two quantities: P = the product of all numbers, and K = the count of numbers greater than 1. In each operation, if gcd(m, n) = d > 1, the product of the two new numbers is mn/d, which is smaller than the original, causing the global product P to strictly decrease. If d = 1, P remains unchanged, but K decreases by 1.

The pair (P, K) strictly decreases in lexicographical order: either P decreases, or P remains the same while K decreases. The lexicographical order of positive integers cannot decrease infinitely. Termination.

Two entirely different approaches solved part (a) of the same problem.

In part (b), all three models converge: each proves that, for every prime p, the greatest common divisor of the maximum number of times each number on the board is divisible by p remains unchanged throughout the operations. The final formula is identical—

Returning to the example with 12 and 18: For p = 2, v₂(12) = 2, v₂(18) = 1, gcd = 1, contribution is 2¹. For p = 3, v₃(12) = 1, v₃(18) = 2, gcd = 1, contribution is 3¹. M = 2 × 3 = 6, exactly matching the manual calculation.

The cheapest blank ticket on the market

Problem P6, the final problem of Day 2, asks you to prove that a recursive sequence eventually becomes periodic.

Last year, only six humans worldwide solved P6 at IMO 2025.

Claude Fable 5: 26 minutes, two rounds, perfect score. GPT-5.6 Sol: 60 minutes, two rounds, perfect score. Kimi K3: 381 minutes, four rounds, perfect score.

Grok 4.5 produced only 7,053 tokens on P6, ranking last among all entries. The submission file clearly states: "Full proof: (Not yet complete.)"

$0.18, the cheapest blank ticket on the platform.

Grok's issues go beyond this. Throughout the entire test, it repeatedly fell into a strange hallucination: confidently claiming that "the proof has been written to the file," while in the background, it never even touched the writing tool.

This is not a matter of mathematical ability, but of agent capability. The model knows it should write a file and claims to have done so, but it did not actually perform the action at the tool invocation level.

In 2024, DeepMind's AlphaProof first reached the silver medal threshold at the IMO level.

In 2025, OpenAI and DeepMind both made moves. OpenAI secured a gold medal with 35 points by solving five problems without disclosing its model, while Gemini Deep Think reached the same level.

In 2026, three general-purpose large models achieved perfect scores. This time, none of them underwent any specialized mathematical training, and all are accessible to everyone—even one is open-source.

The person who wrote the challenge letter

The starting point of the entire test is a company called Axiom Math.

They translated all six problems from IMO 2026 word-for-word into formalized Lean 4 statements that machines can understand.

With this machine-readable set of questions, AI can directly output Lean proofs and be automatically graded by compilers, eliminating the need for human graders.

After receiving the problem statement, Deedy Das quickly built an automated testing framework. Various models raced through the course, completing all six challenges. AxiomProver independently achieved a perfect score.

Notably, the founder of Axiom Math, Hong Letong, is only 25 years old. Born in Guangzhou, she earned dual degrees in mathematics and physics from MIT in just three years and is also a recipient of the Morgan Prize.

At the end of last year, she led AxiomProver to achieve a perfect score on the Putnam Mathematical Competition—the sixth perfect score in the competition’s 98-year history.

In March this year, the company completed a $200 million Series A funding round, reaching a valuation of $1.6 billion.

A model capable of writing 4,229 lines of strictly proven code holds more than just the ability to solve math problems.

What it truly governs is a long chain of logical reasoning, where each step cannot be skipped, cannot be wrong, and cannot be ambiguous.

Whether it's contract loopholes, eligibility for insurance claims, or tax compliance, beneath the surface, these are all the same type of issue: the answer cannot be "close enough."

In the past, this item-by-item verification could only be done by professionals and was charged by the hour.

Today, as this capability is integrated into consumer products, you can simply open your phone to solve tricky problems.

Reference materials:

https://x.com/deedydas/status/2079409461874332066

This article is from the WeChat public account "New Intelligence Yuan," authored by ASI Revelation, edited by Moses.