On July 21, 2025, Google DeepMind announced that an advanced version of its Gemini model had scored 35 out of 42 points at the International Mathematical Olympiad, a gold-medal score certified by the competition's official graders. One year later, at the 2026 Olympiad in Shanghai, two Chinese companies, Huawei and Xiaohongshu, announced perfect scores of 42 out of 42, something only 7 of the 666 human contestants managed that year.
So is learning math now pointless? It's the exact opposite. These machines are built out of math, they still make mistakes with total confidence, and only someone who understands what they are reading can use them without getting fooled. Here's why.
Under the hood, AI is math
There is no magic and no mysterious thinking behind chatbots. There are a few big ideas from math, and you meet the first versions of them in middle school and high school.
Linear algebra: everything becomes a list of numbers
To an AI, a word, an image or a sound becomes a list of numbers, called a vector. The model transforms those lists by multiplying them by huge grids of numbers, called matrices. The basic operation is a weighted sum, which you already know how to compute: with inputs 2, 3 and 1 and weights 0.5, −1 and 4, you get 0.5 × 2 + (−1) × 3 + 4 × 1 = 2.
A language model chains together billions of operations like that one. GPT-3, released by OpenAI in 2020, already had 175 billion weights, called parameters. Everything the model "knows" is stored in those numbers.
Probability: predicting what comes next
A language model is not looking for the truth. At each step, it computes a probability for every possible continuation of the text, then picks one. After "two plus two equals," the continuation "four" gets a very high probability because it shows up constantly in the text the model was trained on. That explains both how fluent these tools sound and why they get things wrong: an answer can be highly probable without being correct.
For a machine, learning means walking downhill
How do you tune 175 billion parameters? Nobody does it by hand. You measure the model's error on examples with a function called the loss function, then nudge every parameter in the direction that makes the error smaller. To know which direction that is, you use the derivative.
Here is a miniature version with a single parameter x and an error f(x) = (x − 3)², which is smallest when x = 3. Its derivative is f′(x) = 2(x − 3): the slope of the curve at x. The rule of gradient descent fits on one line: new value = old value − step size × slope. With a step size of 0.1 and a starting point of x = 0:
- the slope is 2 × (0 − 3) = −6, so x becomes 0 − 0.1 × (−6) = 0.6;
- the slope is now −4.8, so x becomes 0.6 + 0.48 = 1.08;
- then 1.464, then 1.7712, and so on: at each step, the distance to 3 is multiplied by 0.8. After 20 steps, x is about 2.965.
If the step is too big, say 1.1, x jumps back and forth across the minimum and moves farther away each time: 6.6, then −1.32, then 8.184. Choosing that step size is part of an engineer's job. With billions of parameters, the slope becomes a gradient, the list of derivatives with respect to each one, but the idea is exactly the same. It isn't new either: the French mathematician Augustin-Louis Cauchy presented it to the Paris Academy of Sciences in October 1847, to compute the orbits of celestial bodies.
All of this is standard high school content. Derivatives, slopes and the shape of a graph are the core of Calculus: on a curve that is concave up everywhere, like (x − 3)², walking downhill leads to the minimum. The error functions of real neural networks are far less tidy, which is what makes training them so delicate.
What AI can already do in math
The progress of the last two years is real. It just needs to be described without hype.
- Olympiad problems. In 2024, Google DeepMind's AlphaProof and AlphaGeometry 2 scored 28 out of 42, silver-medal level, but humans had to translate the problems by hand into a formal proof language, and the computation took two to three days. In 2025, Gemini Deep Think scored 35 out of 42 while writing its proofs in plain language, within the four and a half hours of the exam. OpenAI announced the same score for an experimental model, graded by three former medalists rather than by the Olympiad itself. In 2026, Huawei and Xiaohongshu announced 42 out of 42, with Xiaohongshu stating that its solutions had been graded by the organizers.
- New results. In May 2025, Google DeepMind's AlphaEvolve found a way to multiply two 4 × 4 matrices with complex entries using 48 multiplications, down from the 49 of Volker Strassen's 1969 method. In May 2026, an internal OpenAI model produced a counterexample to a 1946 conjecture by Paul Erdős about how many pairs of points in the plane can sit exactly 1 unit apart. Nine mathematicians, including Fields Medalist Timothy Gowers, published a checked and annotated version.
- Searching the literature. Finding, among millions of papers, the one that already solves a problem is a genuine service to researchers.
What AI still can't do
That last point led to an instructive episode. In mid-October 2025, an OpenAI executive claimed that GPT-5 had found solutions to ten Erdős problems listed as open. In fact, the model had located papers that had already solved them. Thomas Bloom, who runs the reference website for these problems, called the claim "a dramatic misrepresentation": on his site, "open" only meant that he personally didn't know of a paper settling the question. The post was deleted.
The current limits are better measured by a project called First Proof. In June 2026, ten researchers each contributed a problem they had solved in their own work but not yet published, so it could not be in any training data. Four AI systems took part, and a group of 30 mathematicians reviewed their answers. The best one solved 6 problems out of 10. According to Nature, the models fell short of top mathematicians, produced false statements even when told to check their references, and sometimes copied passages line by line from an earlier paper without ever citing it.
Those made-up outputs aren't a fluke. A September 2025 study by researchers at OpenAI and Georgia Tech, led by Adam Tauman Kalai, shows that the way these models are trained and scored rewards a confident guess over an honest "I don't know": a wrong answer costs no more than admitting uncertainty.
Finally, keep things in proportion. An Olympiad problem is very hard, but it has a known solution that fits in a few hours of writing. Research often means not knowing whether the question is well posed, or whether an answer even exists.
Why understanding still matters
To check the answer
An AI can give a wrong answer with the same confidence as a right one. To catch it, you need to know what to expect. If you're told that a price rising 3% a year doubles in 10 years, one calculation proves it wrong: 1.03¹⁰ ≈ 1.34, an increase of only 34%. Doubling actually takes about 24 years, since 1.03²⁴ ≈ 2.03. Plugging a solution back into the equation, estimating the order of magnitude, trying a simple case, checking the units: you only build those habits by doing math yourself.
To build the model
Before computing anything, you have to decide what to compute. Turning a situation into equations, choosing assumptions, judging whether a result makes sense: that is the heart of math. An AI can suggest a model, but if you can't judge that choice, you can't judge the answer either.
To think critically about numbers
Picture a disease that affects 1 person in 1,000 and a test that catches 99% of sick people but also comes back positive for 1% of healthy people. Your test is positive. What is the probability that you are sick? The instinctive answer is 99%. Out of 100,000 people, there are 100 sick people, 99 of whom test positive, and 99,900 healthy people, 999 of whom test positive by mistake. So the probability is 99 ÷ (99 + 999) = 99 ÷ 1,098, about 9%. That reasoning is conditional probability, a unit of high school Geometry, and it protects you far better than any ready-made answer.
Learning with AI: coach or answer machine?
An experiment with nearly 1,000 high school students in Turkey, published in 2025 in the journal PNAS by Hamsa Bastani and colleagues, gives a clear answer. Some students practiced with an assistant similar to ChatGPT, some with an assistant designed to give hints instead of solutions, and some with no AI at all.
- During practice sessions, grades went up 48% with the standard assistant and 127% with the hint-based one.
- On the exam, taken without AI, students who had used the standard assistant scored 17% lower than students who never had access.
- Students who had used the hint-based assistant scored about the same as the group without AI.
The authors' explanation is simple: without guardrails, students used the AI as a crutch during practice, then did worse on their own. The tool isn't good or bad in itself. What matters is who does the thinking. A few rules to make sure it's you:
- Try it yourself first, for at least a few minutes, and write down what you tried.
- Ask for a hint, not the solution: what's the first step, where is my mistake.
- Explain your reasoning to the AI and ask it to find the flaw.
- Check the final answer yourself, by plugging it back in or estimating its size.
- Redo the problem the next day with no help. If you can't, you watched; you didn't learn.
That's the whole idea behind an AI math tutor that walks you through a problem one hint at a time instead of handing you an answer to copy.
Understanding is the real edge
AI computes faster than we do and now solves Olympiad problems. But it is built from derivatives, matrices and probabilities, it makes mistakes with a straight face, and it can't decide for you what is worth computing. The more answers machines produce, the more value shifts to people who can ask the right question and check the result. That is exactly what math trains.
It's also how Mathflow works. The app, built with Inria and used by more than 50,000 students, takes every topic through three levels, Explore, Explain and Solve, and Alphi, the AI coach, guides you with questions and hints rather than ready-made answers. It's free to start.
Sources
- Google DeepMind (Thang Luong and Edward Lockhart), Advanced version of Gemini with Deep Think officially achieves gold-medal standard at the International Mathematical Olympiad, 2025
- AFP (France 24), AI catches up with humans to score 100% at top maths contest, 2026
- Davide Castelvecchi (Nature), Humans outperform AI at this highly rigorous mathematics test, 2026
- Noga Alon, Thomas Bloom, Timothy Gowers et al., Remarks on the disproof of the unit distance conjecture, 2026
- TechCrunch, OpenAI's 'embarrassing' math, 2025
- Adam Tauman Kalai, Ofir Nachum, Santosh Vempala and Edwin Zhang, Why Language Models Hallucinate, 2025
- Hamsa Bastani et al., Generative AI without guardrails can harm learning: Evidence from high school mathematics, PNAS, 2025
- Claude Lemaréchal, Cauchy and the gradient method, Documenta Mathematica, 2012
