Best AI for Math: Which Model Actually Solves It

The best AI for math right now is Claude Opus 5, which sits at the top of MathArena‘s cross-competition ranking with an expected score of 84.4%. That is the short answer, and it comes with a longer one. Ask a different question, like who writes the best proof or who reads handwriting most accurately, and a different model wins every time.

This guide covers which model to use for which kind of maths, what the scores actually mean, and why almost every “perfect” maths score you will see quoted carries a warning label. We also cover the free options that get you within a few points of the flagships for a fraction of the cost. Then there is OpenAI’s Astra announcement in August 2026, and what it actually changed.

The Key Takeaways

• Claude Opus 5 leads MathArena’s overall ranking at 84.4% ±2.8%, ahead of GPT-5.6 Sol at 79.7% and GPT-5.5 at 77.8%.
• Every model scoring 100% on AIME 2026 carries a contamination warning, meaning it was released after the exam. The best score without that flag is GPT-5.2 at 98.33%.
• Getting the answer and proving it are different skills. Claude Opus 4.6 scores 96.67% on AIME final answers but only 47.02% on USAMO proofs.
• For homework you do not need a flagship. Step 3.5 Flash hits 96.67% on AIME 2026 at $0.013 per problem, around 40x cheaper than the top model for 3.3 points less.
• Research maths is still mostly unsolved. The best model manages 37.5% on formal Lean proofs, and only 3 of 50 open problems in Epoch AI’s set have fallen to AI.

What Is the Best AI for Math Right Now?

Most articles answering this question rank models on benchmarks that stopped being useful years ago. The common one is GSM8K, a set of grade-school word problems that modern models finish with near-perfect scores, so it cannot separate a frontier model from a mid-tier one. Ranking 2026 models on it is like timing Olympic sprinters with a sundial.

The board worth reading is MathArena, which runs models on maths competitions after the competitions happen, then publishes accuracy, cost and token counts for each one. Here is its overall recommendation table as of 5 August 2026.

One detail matters before you take those numbers anywhere. That “expected score” is a statistical estimate across many competitions, not a mark from a single exam. The ± figures are confidence intervals, and the gap between Opus 5 and GPT-5.6 Sol is close enough that treating them as clearly separated would be overreading the data.

MathArena also lists no cost for GPT-5.6 Sol, because it flagged the usage data OpenAI returned as erroneous. We have left it out rather than repeat a figure the board itself does not stand behind.

Best AI for Math by Task

“Maths” is not one skill, and the boards make that obvious the moment you split them apart. A model that aces competition answers can fall apart when asked to justify them. Here is who actually wins each category.

The pattern is hard to miss. GPT-5.5 wins three of the seven categories outright, while Claude Opus 5 takes the aggregate crown and GPT-5.6 Sol leads only on the hardest formal work.

Choosing one model and one only? GPT-5.5 covers the widest range of real maths.

Why Every 100% Math Score Comes With a Warning

This is the part almost nobody covers, and it changes how you should read every maths benchmark you see. On MathArena’s AIME 2026 board, several models score a flawless 100%. Each of those scores sits next to a warning icon.

“Model was released after competition release.”

That is MathArena’s contamination flag, and it means the model shipped after the exam was already public. The problems, and often full worked solutions, could have been sitting in its training data. A perfect score under those conditions might show brilliant reasoning, or it might show good recall, and the board is honest that it cannot tell you which.

Read the clean rows and the picture gets more interesting. GPT-5.2 scores 98.33% at $0.12 per problem with no contamination flag at all.

It predates the exam, so it could not have memorised anything. That arguably makes it the most trustworthy number on the board.

None of this means the flagged models are cheating. It means a benchmark score is evidence, not proof, and anyone quoting “100% on AIME” without the asterisk is selling you more certainty than exists.

Getting the Answer and Proving It Are Different Skills

AIME asks for a number. USAMO asks you to prove your reasoning holds. Models that look identical on the first task separate dramatically on the second, and this is the single most useful thing to understand before picking a model for serious maths.

Look at Claude Opus 4.6. On AIME 2026 final answers it scores 96.67%. On USAMO proofs it scores 47.02%, a collapse of almost fifty points on the same subject, and it is the most expensive model in the table while doing it.

The practical lesson is simple. If you need working you can check, a rigorous argument, or anything a marker grades on method rather than the final number, test the model on proofs specifically.

A leaderboard built on final-answer accuracy tells you almost nothing about that.

The Best Free AI for Math

Here is the finding that should save most readers money. On AIME 2026, Step 3.5 Flash scores 96.67% at $0.013 per problem. Claude Opus 4.8 scores 100% at $0.54.

That is roughly 40 times the cost for 3.3 percentage points.

For competition training where every mark counts, the flagship earns its price. For homework, it plainly does not.

The same logic applies to the free tiers of the major chatbots. ChatGPT, Claude and Gemini all handle GCSE, A-level and first-year undergraduate maths comfortably on their free plans, because that difficulty band was saturated long ago. Paid reasoning modes only start to matter at competition and proof level, which is a much smaller slice of what people actually need.

Cheap models also tend to think longer to get there, burning more tokens on the same problem. That is invisible if you are using a chat app on a flat subscription, and it only shows up on an API bill.

Best AI Math Tools That Are Not Chatbots

Language models compute answers by reasoning in text, which is why they go confidently wrong in ways a calculator never is. Dedicated maths tools work differently, and for some jobs they remain the better choice.

Wolfram Alpha

Wolfram Alpha computes symbolically rather than predicting text, so for integrals, differential equations and exact symbolic manipulation it is still the most reliable answer you can get. The free tier returns results, but the step-by-step working sits behind the paid plan, which is the main reason students bounce off it.

Symbolab

Symbolab has the most generous free tier in this group, showing step-by-step algebra and calculus solutions without asking for payment first. It covers trigonometry, statistics and linear algebra too, and a paid premium tier adds practice sets and guided learning paths on top.

Photomath

Photomath remains the easiest entry point for younger students, since you point a phone camera at a textbook problem and get a solution back. The app is free, with Photomath Plus at $9.99 per month or $69.99 per year adding animated tutorials and textbook-specific solutions.

GeoGebra

GeoGebra is completely free, runs in any browser, and pairs its solver with a strong interactive graphing suite. If the thing you actually need is to see a function rather than solve it, this is the one to open.

Handwriting, Photos and Diagrams

Plenty of maths never arrives as typed text. It is scrawled in a notebook, printed in a textbook, or drawn as a geometry diagram, and reading that correctly is a separate capability from solving it.

MathArena tests this with the Kangaroo competition papers, which mix diagrams and visual reasoning. GPT-5.5 leads at 94.93%, followed by GPT-5.4 at 92.47% and Kimi K3 at 91.25%. Gemini’s Flash models sit just behind at meaningfully lower cost, with Gemini 3.6 Flash at 87.85% for $0.042 per problem.

For photographing homework and getting a usable answer, that spread barely matters. Any of these will read clear handwriting well. The gap only opens up on messy notation, dense diagrams and multi-part geometry, where the stronger vision models pull ahead.

What Astra’s Ten Proofs Actually Mean

On 1 August 2026, OpenAI announced Astra, its next major model, by publishing solutions to ten open problems in mathematics and theoretical computer science. The problems spanned group theory, high-dimensional geometry, quantum complexity, lattice cryptography and extremal combinatorics, and each had been open for at least a decade.

The headline result was the first explicit construction of a non-sofic group, a question left open since 1999. Every solution shipped with a machine-checkable Lean 4 certificate published on GitHub, which matters because it answers the standard objection to AI-generated proofs, namely that nobody can independently verify them. The total compute bill came to roughly $2,000.

Thomas Bloom, a mathematician at the University of Manchester, called the results “big news” in coverage of the announcement. OpenAI’s Noam Brown added a caveat worth keeping in view, noting the team “didn’t spend a lot on each problem” and that test-time compute could be pushed considerably further.

Two things temper this. Astra is not publicly available, has no release date, no pricing and no model card, and it is expected to require federal sign-off before any public release. Our full write-up on what OpenAI Astra is and what it proved goes through the ten results one by one.

Researchers also tried other major problems and failed. That does not appear in the headline number.

The wider picture supports caution. Epoch AI’s FrontierMath Open Problems set expanded to 50 unsolved research problems on 31 July 2026, and AI has solved three of them. On MathArena’s formal Lean board, the best model manages 37.5%. Research mathematics has started to fall, but slowly.

Which AI Should You Use for Math?

If you want one answer, use GPT-5.5. It wins competition answers, olympiad proofs and visual maths, which covers most of what students and working professionals actually throw at a model.

If you want the strongest general maths model and cost is not the deciding factor, Claude Opus 5 tops the aggregate ranking. In case you are working through homework or revision, a cheap fast model gets you within a few points for pennies, and the free tiers of the major chatbots are enough. And if you need an exact symbolic result, open Wolfram Alpha instead of any chatbot.

The awkward part is that no single subscription covers those cases well, which is why serious maths users end up switching between models depending on the problem in front of them. Fello AI puts Claude, ChatGPT, Gemini, Grok and DeepSeek in one native Mac and iOS app at $9.99 per month. You can send a proof to one model and a diagram to another without juggling subscriptions.

Whichever you pick, check the working. A model that produces the right number through faulty reasoning will produce the wrong number the moment the problem shifts, and on proofs the leaderboards show that happening constantly.

For broader study tools beyond maths, see our guides to the best AI tools for students and researchers and the top 12 AI tools for studying smarter. Teachers marking maths work will find more in our guide to AI for teachers, and a full model-by-model breakdown lives in our best AI models comparison. If you are heading for the job market rather than an exam, the same head-to-head approach decides the best AI for a resume.

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