By an engineer who solves integrals on restaurant napkins and refuses to surrender his slide rule
A Friendly Warning to the Over confident
If you believe AI Math is solved because your favorite chatbot can factor a quadratic, grab a coffee and settle in. Real mathematics is a wilderness of hidden valleys, false summits, and the occasional dragon shaped counterexample. In that wilderness, an AI Math solver is more than a calculator, it is an explorer that must prove each claim under a harsh sun. This two part journey explains why Gemini 2.5 Pro remains the strongest explorer on the toughest trail, the International Mathematical Olympiad, while newer rivals still slide on loose gravel.
Table of Contents
1. Two Very Different Arenas
Press releases love to trumpet benchmark records, yet the phrase AI Math benchmark hides two distinct species. Mixing them muddles the conversation, so let us place them side by side.
| Arena | Judge | Problem Style | Success Metric | Real world Analogy |
|---|---|---|---|---|
| Vals AI Benchmarks | Automated script | Single answer, deterministic | Return the boxed integer quickly and cheaply | Timed multiple choice quiz |
| MathArena IMO | Human mathematicians | Open ended proofs across six Olympiad problems | Present a rigorous chain of reasoning that earns partial credit | Jury graded thesis defense |
Vals asks “Did you hit the bullseye?” MathArena asks “Do you understand why the bullseye exists and can you teach it back to us?” Those are radically different games inside the same stadium named AI Math.
2. Anatomy of a True Olympiad Test
The International Mathematical Olympiad, or IMO, stretches six problems across two days. Each receives a score from zero to seven. Solving just one in full is a heroic feat. MathArena cloned that format for the 2025 leaderboard. Judges graded model outputs hours after the problems went public, eliminating any hope of training contamination. The top five results look like this:
| Model | Overall Accuracy | Cost (USD) | P1 | P2 | P3 | P4 | P5 | P6 |
|---|---|---|---|---|---|---|---|---|
| Gemini 2.5 Pro | 31.55 % | 431.97 | 14 % | 0 % | 71 % | 46 % | 57 % | 0 % |
| o3 (high) | 16.67 % | 223.33 | 0 % | 0 % | 7 % | 36 % | 57 % | 0 % |
| o4 Mini (high) | 14.29 % | 103.34 | 16 % | 0 % | 5 % | 46 % | 18 % | 0 % |
| Grok 4 | 11.90 % | 527.85 | 13 % | 4 % | 18 % | 13 % | 25 % | 0 % |
| DeepSeek R1 | 6.85 % | 59.50 | 4 % | 0 % | 5 % | 0 % | 32 % | 0 % |
Source: MathArena.ai
Percentages under P1–P6 show how often each model earned non zero credit on the six problems. Gemini dominated Problem 3, a geometry haymaker, with a seventy one percent partial credit rate. It floundered on Problems 2 and 6, both number theory minefields, yet still doubled its closest rival’s overall score.
Thirty one percent may sound modest, but perspective matters. The median human contestant scores zero on at least three IMO questions. A model that assembles fragmentary proofs on half the set has crossed a frontier in AI Math problem solving.
3. Inside the MathArena IMO Prompt: How the Test Really Works and Why Gemini 2.5 Pro Wins
The MathArena team wanted a benchmark that no AI Math solver could simply memorize, so they grabbed the freshest questions on the planet, the six problem set from the 2025 International Mathematical Olympiad. Then they did something clever. Instead of relying on a script to check boxed integers, they asked four human judges with Olympiad experience to grade every attempt. Each model received the exact same prompt template:
That prompt demands more than symbolic manipulation. It forces the model to produce a logical story, which aligns with what teachers call AI Math problem solving, not just mechanical output. To give every engine a fair shot, MathArena allowed best of 32 sampling. Each model generated thirty two drafts, then used an internal judge to pick the strongest. This strategy cost money.
Gemini 2.5 Pro’s final batch rang up about four hundred thirty dollars, while Grok 4’s deeper context length pushed past five hundred. Yet the spending bought quality. Gemini’s chosen proofs looked like they were written by a disciplined graduate student: definitions first, lemmas tagged, diagrams described in words, and each claim anchored to a textbook theorem.
When the judges finished, Gemini stood alone at 31.55 percent, or 13 of 42 available points. That’s miles below a human bronze, yet miles above every other large language model. Grok 4 posted 11.90 percent. o3’s high precision mode landed at 16.67 percent. DeepSeek R1 struggled at 6.85 percent. The spread shows why MathArena matters. On a saturated quiz like MATH 500 the same models bunch within a few points. Here the gap is wide enough to drive research agendas.
Gemini crushed Problem 3, a geometry construction, with a seventy one percent success rate. It also earned partial credit on the combinatorics grind of Problem 5. Its weak spots were Problem 2 and Problem 6. Judges noticed a pattern. Where Gemini failed, it usually failed honestly, dropping a “Cannot complete the proof” note instead of hallucinating a shortcut. That humility protected it from zero point penalties for bogus theorems, a common pitfall in LLM Math.
Grok 4 tells the opposite story. On deterministic sets it reigns. Inside this proof arena, its minimalist style collapses. Many Grok outputs skip giant reasoning steps, a fatal move because MathArena’s rubric rewards transparency over brevity. Even the o4 Mini model, which charges a fraction per run, scored higher than Grok on Problem 1 by simply writing complete explanations.
4. Inside Gemini’s Tool Kit
Why does Gemini out reason fresher engines? Three traits stand out when you trace its proof logs.
- Proof Grammar
Gemini keeps a neat ledger of claims and dependencies. Definitions arrive before use. Lemmas carry names. Equations reference earlier lines. That narrative discipline turns raw computation into readable mathematics, a core demand in any LLM Math contest. - Spatial Instincts
In geometry challenges, the model picks coordinate frames that simplify symmetry, then rotates axes to expose equal angles. Judges praised the elegance, not just the outcome. That move mirrors seasoned Olympiad craft. - Sampling Patience
MathArena lets each model spawn thirty two drafts, then picks the best. Gemini’s drafts wander, yet its self judge reliably promotes the coherent one. The extra tokens cost money but purchase depth: an investment evident in its problem three dominance.
These skills convert partial attempts into real points, a currency automated quizzes never notice.
5. Where Gemini Trips
A champion still trips. Judges flagged two recurring faults.
Imaginary Citations
When stuck, Gemini invents theorems with scholarly names that never appeared in a textbook. The habit is less common than early 2025 builds, yet each ghost citation taxes trust.
Context Collapse
Proofs running past two thousand tokens sometimes lose track of an earlier assumption, breaking later logic. Modern AI Math benchmarks will soon stretch contexts to forty thousand tokens or more. Gemini must stretch with them.
These flaws remind us that AI Math help remains a work in progress, not a finished product.
6. Grok 4, Monarch of Numbers, Peasant of Proofs
Shift environments and the scoreboard flips. Vals AI’s automated trials crown Grok 4 monarch. Look at the top slice:
| Model | MGSM Accuracy | AIME Accuracy | MATH 500 Accuracy | Input Cost | Output Cost | Latency |
|---|---|---|---|---|---|---|
| Grok 4 (xAI) | 90.9% | 90.6% | 96.2% | $3.00 | $15.00 | 116.62 s |
| Gemini 2.5 Pro Exp | 92.2% | 85.8% | 95.2% | $1.25 | $10.00 | 9.39 s |
| Claude Opus 4 (Nonthink) | 93.8% | 41.3% | 90.4% | $15.00 | $75.00 | 14.81 s |
| Claude Sonnet 4 (Think) | 92.8% | 76.3% | 93.8% | $3.00 | $15.00 | 63.47 s |
| o4 Mini (OpenAI) | 93.4% | 83.7% | 94.2% | $1.10 | $4.40 | 12.54 s |
| Qwen 3 (235B) (Alibaba) | 92.7% | 84.0% | 94.6% | $0.22 | $0.88 | 142.75 s |
| DeepSeek R1 | 92.4% | 74.0% | 92.2% | $8.00 | $8.00 | 156.47 s |
Source: vals.ai/benchmarks, July 2025
In deterministic arenas Grok crushes the leaderboard, especially on MATH 500 where its ninety six percent stands as an AI benchmark ranking headline. Why this split personality? Grok’s policy prunes explanation to save tokens. That wins timed quizzes but forfeits partial credit in proof scoring. The very minimalism that fuels victory in one game becomes a liability in the other.
7. MGSM: The Language Wild Card
Another battlefield matters: MGSM, the Multilingual Grade School Math benchmark. It translates GSM8K problems into ten languages from Telugu to Swahili. It measures whether an AI Math problem solver can stay logical across scripts.
- Gemini posts 92.2 percent at nine second latency.
- Grok posts 90.9 percent at over one hundred seconds.
- Claude Opus 4 tops the chart with 93.8 percent but charges a wallet draining seventy five dollars in output tokens.
Even here, one subtlety surfaces. All models dip lowest in Bengali. Training data scarcity leaves a dent in multilingual reasoning. A universal AI Math solver online free must fix that gap.
8. Contamination: The Silent Inflator
Public datasets float through GitHub mirrors, Kaggle repos, and class websites. When a model later “solves” those exact questions, we confuse memorization for reasoning. The risk is glaring in AIME and MATH 500, which have circulated online for years. MathArena dodges that bullet by scoring puzzles published mere days earlier. A fair future for LLM Math benchmarks hinges on secrecy windows, random sampling, and forensic audits of pre training corpora.
9. Shopping List for the Ideal AI Math Solver
The next leap will need concrete upgrades.
- Proof Discipline: Track every variable, inequality, and hidden assumption across pages of tokens.
- Citation Integrity: Reference only theorems that live on Wikipedia or in a standard text, never thin air.
- Multilingual Reach: Lift Bengali, Swahili, and Marathi from afterthoughts to first class citizens.
- Economic Footprint: Shrink the price tag. Gemini’s $432 per Olympiad run is research money, not classroom money.
- Explainable Computation: Show work. Promote partial credit. Teachers need an AI Math problem solving partner, not a black box.
10. Practical Advice for Different Users
- Teachers: For daily worksheets, Grok or o4 Mini provides instant correct integers. For Olympiad coaching, Gemini’s partial proofs expose hidden holes in student reasoning.
- Researchers: Use MathArena to validate chain of thought upgrades, Vals to benchmark speed tuning.
- Start ups: Compare AI benchmark ranking tables before embedding a model. Latency and cost can swing profit margins.
- Students: Treat every AI Math solver as a study buddy, never an answer vending machine. You learn by thinking, not by copying output.
11. Benchmark Saturation and the Next Frontier
A funny thing happens when every model clears ninety percent on a test. The test dies. Engineers stop bragging, investors stop caring, and researchers hunt fresh prey. AI Math benchmarks feel this squeeze right now.
- MATH 500 once separated rookies from champions. Today seven models sit above ninety four percent.
- AIME looks heroic at first, yet Grok’s ninety point run suggests the ceiling is near.
- MGSM squeezes ten languages into 250 questions, and the top ten models are bunched so tight that statisticians argue the differences are noise.
When a benchmark flatlines, innovation shifts. Teams either increase problem difficulty or change the scoring lens. MathArena chose difficulty. Its proof based approach injects brand new variance. The score spread from thirty one percent at the top to under seven percent at the bottom proves the move worked.
Table – Benchmarks at Risk of Saturation
| Benchmark | Top Accuracy | Low Accuracy | Spread | Status |
|---|---|---|---|---|
| MATH 500 | 96 % | 92 % | 4 % | Nearly saturated |
| MGSM | 94 % | 90 % | 4 % | Nearly saturated |
| AIME | 90 % | 71 % | 19 % | Some headroom |
| MathArena IMO | 32 % | 7 % | 25 % | Healthy variance |
AI Math research needs stressful tests. Without those tests, progress slows because every gradient looks good. Expect a new wave of datasets that force models to create proofs, explain diagrams, or teach a novice. Explanation rubrics raise the bar because you cannot memorize creativity.
12. Teaching Silicon to Think Aloud
The strongest insight from MathArena is not Gemini’s win. It is the proof logs. Each attempt shows the model trying, failing, pivoting, and finally writing something coherent. That iterative grind means the model internalizes steps, not just answers.
When you watch Gemini tackle geometry, you see it declare the circumcenter, set a coordinate frame, chase angle bisectors, then deploy a rotation. Those moves follow the same blueprint a human coach would recommend. The difference sits in speed. A human might stare at paper for thirty minutes. Gemini iterates thirty two drafts in ten minutes. Its raw velocity, combined with partial credit scoring, blurs the line between human and engine.
This think aloud style is the future of every AI Math solver. A classroom tool that hides its reasoning cannot win trust. A research partner that hides its chain of thought leaves errors invisible. Transparency is not a garnish. It is the main ingredient.
13. The Multilingual Gap
MGSM exposes a linguistic fault. All current leaders drop hardest in Bengali. Swahili also drags scores. The cause is simple. English dominates pre training corpora. So do European languages. Low resource scripts appear in fragments, which hampers tokenization.
Fixing this gap is not charity, it is growth. Half the globe speaks languages under represented in public datasets. A universal AI Math helper must parse Urdu boards, Gujarati textbooks, Amharic PDFs. Expect the next generation of LLM Math benchmarks to arrive bilingual or trilingual by default. That change forces model builders to widen data crawls, redesign tokenizers, and double down on character level reasoning.
14. Economic Reality Check
Training a frontier model costs millions, but inference cost shapes real adoption. The MathArena table gives a shock. Grok’s partial proofs cost five hundred dollars per Olympiad run. Gemini’s full set costs over four hundred. Claude’s multilingual lead costs seventy five just in output tokens. That bill is fine for research labs, impossible for classrooms.
Engineers will answer in two ways. Some will compress weights and quantize activations. Others will build hybrid stacks: a cheap retrieval model finds relevant lemmas, then a heavyweight core handles the final proof. Either path lowers marginal cost, which turns an academic trophy into a mass market tutor.
15. Ethical Potholes on the Proof Highway
High voltage AI Math problem solvers bring new risks.
- Ghost References: Gemini occasionally invents theorems. A lazy reader might accept the lie and teach it forward.
- Plagiarized Proofs: If a model copies an Olympiad winner’s archived solution, that is hidden theft. Data contamination checks fight this, yet perfect policing is hard.
- Proof by Intimidation: A model may write overlong formalism, bury a fallacy mid paragraph, and feed it to a trusting user. Clear explain as you go rules shrink that risk.
As engines grow, so must pedagogy. Teachers need rubrics to test not just outcomes but the structural integrity of an AI Math problem solver.
16. The Road Ahead: A Vision in Three Steps
- Transparent Reasoning Engines
Every next gen AI Math solver will expose its chain of thought, allow step through debugging, and cite canonical sources. That upgrade turns partial credit into a teaching asset. - Global Language Equity
Research leaders will train dedicated sub models on under represented scripts until MGSM’s Bengali gap disappears. A fair math tutor speaks the student’s language. - Proofs at Penny Scale
Cloud providers will bundle low precision inference, chunked attention, and retrieval augmented generation. Expect MathArena level proofs for under a dollar within two years.
17. Closing Reflections: The Hum of Infinite Ascent
Thirty one percent is not a medal. It is a milestone. A decade ago, no machine wrote a coherent Olympiad proof. Today Gemini does it thirty percent of the time, and Grok races past ninety percent on deterministic tests. The arc is clear. Each fresh benchmark sparks a leap in model design. Each leap retires an old ceiling and unveils a taller one.
Mathematics stays a human conversation. AI Math models are the newest voices at the whiteboard. Sometimes they mumble, sometimes they misquote, yet they often illuminate. Our charge is to challenge them with real problems, audit their logic, and fold their strengths into human learning.
Keep the dialogue open. Keep the benchmarks sharp. Keep ambition sky high. Knowledge itself is the prize.
Call to Action
- Researchers: design stealth benchmarks that stay uncontaminated long enough to measure real reasoning gains.
- Engineers: bake proof engines into your AI Math solvers to capture partial credit and user trust.
- Educators: treat LLM outputs as starting points, not gospel.
- Students: keep solving by hand. The moment you let the model think for you, you stop learning.
In the end, mathematics remains a human conversation. AI Math models are the newest voices in the room. Their ideas are sometimes brilliant, sometimes half baked, but always illuminating. Let’s keep the dialogue open, the benchmarks fair, and the ambition sky high.
Azmat — Founder of Binary Verse AI | Tech Explorer and Observer of the Machine Mind Revolution. Looking for the smartest AI models ranked by real benchmarks? Explore our AI IQ Test 2025 results to see how top models. For questions or feedback, feel free to contact us or explore our website.
1. Which AI is best for math in 2025?
There is no single “best” AI for math; it depends entirely on the task. For fast, accurate answers to standard problems found in benchmarks like MATH 500, models like Grok 4 are leaders. However, for complex, proof-based reasoning required in competitions like the International Mathematical Olympiad (IMO), our analysis shows that Gemini 2.5 Pro is the clear winner, as it excels at building logical arguments from scratch, not just finding a final answer.
2. Why does Grok 4 perform so well on some AI Math benchmarks?
Grok 4’s architecture is highly optimized for speed and finding correct, single-integer answers. This makes it a monarch in automated, multiple-choice style benchmarks like MATH 500 and AIME, where its ability to prune explanations and return a result quickly is a major advantage. However, as this article’s analysis shows, this same minimalist approach becomes a liability in proof-based arenas where explaining your work is crucial for earning points.
3. What makes Gemini 2.5 Pro better at solving difficult math proofs?
Gemini 2.5 Pro’s strength lies in its ability to mimic human-like reasoning. Our deep dive reveals three key traits:
Proof Grammar: It structures its answers like a mathematician, with clear definitions, named lemmas, and logical steps.
Spatial Instincts: In geometry problems, it demonstrates an intuitive grasp of the best coordinate frames to use, simplifying complex problems.
Sampling Patience: It generates many potential proof paths and has a strong internal judge to select the most coherent one, a strategy that earns high partial credit on Olympiad-level problems.
4. What is the MathArena IMO benchmark, and why does it matter?
The MathArena IMO is a newer, more challenging AI Math benchmark that uses the fresh problem set from the most recent International Mathematical Olympiad. Unlike automated tests that just check a final answer, every submission to MathArena is graded by human mathematicians who score the AI’s reasoning, clarity, and logical rigor. It matters because it avoids training data contamination and measures true problem-solving ability, not just memorization.
5. Can AI solve International Mathematical Olympiad (IMO) problems?
Yes, but not perfectly. As of mid-2025, no AI can consistently win medals. However, Gemini 2.5 Pro achieved a groundbreaking score of 31.55% on the 2025 IMO problem set in the MathArena benchmark. This is far below a human champion but significantly ahead of all other models and marks the first time an AI has demonstrated the ability to earn substantial partial credit on multiple, brand-new Olympiad problems.
6. Are AI math solvers expensive to use?
The cost varies dramatically. For standard homework problems, models like Grok 4 or o4 Mini are efficient. However, for generating high-quality proofs on Olympiad-level problems, the cost can be substantial. Our analysis shows that a single successful Olympiad run using the “best of 32” sampling method cost
7. Do AI models have weaknesses in math?
Yes. Even the best models, like Gemini 2.5 Pro, have flaws. Our research identified two main issues:
Imaginary Citations: Sometimes, when stuck, the model will invent plausible-sounding theorems to support its claims.
Context Collapse: In very long proofs, it can occasionally lose track of an early assumption, leading to logical errors.
This proves that all AI outputs should be treated as a study aid to be verified, not an unquestionable answer key.
8. For practical use, should I use Grok 4 or Gemini 2.5 Pro for math?
This article suggests a “horses for courses” approach:
For Teachers & Students on standard assignments: Grok 4 or o4 Mini provide fast, correct answers for verification.
For Olympiad coaching or deep understanding of proofs: Gemini 2.5 Pro is superior, as its partial proofs are excellent tools for learning and identifying reasoning gaps.
For Researchers: Use automated benchmarks like Vals to test for speed, and proof-based benchmarks like MathArena to test for reasoning.