Best AI Models for Reasoning and Math

As of July 2026, the strongest general reasoning models are Anthropic's Claude Opus 4.8 and Claude Fable 5, OpenAI's GPT-5.5, and Google's Gemini 3.1 Pro and Gemini 3 Pro in its Deep Think mode, which trade the top spot depending on the task ^[1][2][3]. Claude Fable 5 leads the composite Artificial Analysis Intelligence Index and posts the highest Humanity's Last Exam score; GPT-5.5 and Qwen3-Max-Thinking report perfect AIME math results; and on the ARC Prize Foundation's leaderboard (checked October 2026) Claude Fable 5 has the highest ARC-AGI-2 abstract-reasoning score of the models compared here, with GPT-5.5 and Gemini 3 Deep Think close behind ^{[2][4][5][6][24]}. For open weights, GLM-5.2 and DeepSeek V4 (V4-Pro) are the reasoning leaders ^[7][8]. Because AIME and MATH-500 are now saturated, the benchmarks that still separate the frontier are GPQA Diamond, Humanity's Last Exam (HLE), and ARC-AGI-2.

This page ranks models by measured reasoning and math performance. For how these "thinking" models actually work (chain-of-thought, test-time compute, verifier training), see the reasoning model concept page.

The reasoning leaderboard at a glance

Last verified: July 2026. AIME = AIME 2025, pass@1, no tools, unless marked with a dagger for AIME 2026 or "wt" for with tools. GPQA Diamond, HLE and ARC-AGI-2 are percentages. MATH-500 is saturated and has been dropped from 2026 launch reports (shown as n/r). ARC-AGI-2 values are the ARC Prize Foundation's semi-private scores as listed on its leaderboard on 27 October 2026, at the highest reasoning setting shown for each model. HLE is the no-tools score. "n/r" means not reported by a source we could verify (never a zero).

Sources: AA Intelligence Index and independent evals ^[1][2][9]; Anthropic system cards for Opus 4.8/4.7 ^[3][10]; OpenAI and Vellum transcription for GPT-5.5 ^[5][11]; Google model cards for the Gemini line ^[6][12][13]; DeepSeek, Moonshot, Z.ai, Qwen, MiniMax model cards ^{[7][8][14][15][16]}; ARC Prize verified scores ^[4][17].

Which AI model is best for reasoning right now?

On the composite Artificial Analysis Intelligence Index (updated July 7, 2026), the order at the top is Claude Fable 5 first, Claude Opus 4.8 second, and GPT-5.5 third, with Anthropic holding two of the top three slots ^[1][2]. Claude Fable 5, the general-availability edition of Anthropic's "Mythos" class released on June 9, 2026, launched at number one and is the first model to clear 53% on Humanity's Last Exam, more than seven points ahead of the next model ^[2]. Opus 4.8 (released May 28, 2026) is the strongest widely deployed flagship, and GPT-5.5 (April 2026) is OpenAI's leading reasoning model and the top scorer on the agentic side of the index ^[1][5].

No single model wins every reasoning task, so the honest answer is a per-use-case ranking.

Which model is best for the hardest math?

AIME 2025 is effectively solved: GPT-5.5, GPT-5.2, Qwen3-Max-Thinking and (with tools) Grok 4 and Kimi K2 Thinking all report 100%, and most 2026 launches have simply stopped listing it ^{[5][14][18][19]}. The newest open models report AIME 2026 instead, where GLM-5.2 scores 99.2% and Kimi K2.6 scores 96.4%, again near the ceiling ^[7][8]. Because the exam is saturated, it no longer separates the leaders.

For math that still discriminates, the differentiators are harder olympiad sets and FrontierMath. GPT-5.5 leads here, reporting roughly 51.7% on FrontierMath tiers 1 to 3 and 35.4% on the research-level tier 4, and Gemini 3 Pro reaches 100% on AIME 2025 only when allowed to run code ^[5][12]. The verdict: for the hardest math, GPT-5.5 and Gemini 3 Pro in Deep Think mode are the strongest, with Qwen3-Max-Thinking the best proprietary Chinese option and GLM-5.2 the best open-weight math model.

Which model is best for graduate-level science?

Two benchmarks matter here: GPQA Diamond (Google-proof graduate science multiple choice) and HLE (thousands of expert-written frontier questions across dozens of fields). GPQA Diamond is now near saturation: the frontier clusters between 91% and 95%, well above the roughly 70% scored by human PhDs in their own field ^[17][20]. The current GPQA Diamond leaders are Gemini 3.1 Pro at 94.3%, Claude Opus 4.7 at 94.2%, Gemini 3 Deep Think at 93.8%, and Opus 4.8, GPT-5.5 and Grok 4.3 in a tight band near 93.5% ^{[3][5][12][13]}.

HLE is the tougher, less saturated science and knowledge test, and here Anthropic leads: Claude Fable 5 scores 53.0% and Claude Opus 4.8 scores 49.8% with no tools, ahead of Gemini 3 Deep Think at 48.4% and Gemini 3.1 Pro at 44.4% ^{[2][3][6][13]}. On Scale's independent no-tools harness, Gemini 3.1 Pro tops the public board at about 46.4% ^[9]. With tools enabled, Opus 4.8 rises to 57.9%, the highest verified with-tools result ^[3]. The verdict: for graduate science, Claude Opus 4.8 and Claude Fable 5 lead on HLE, while Gemini 3.1 Pro edges the GPQA Diamond ranking.

Which model is best for abstract and novel reasoning?

ARC-AGI-2 is the benchmark built to resist memorization: novel visual puzzles where humans average around 60% but 2025-era models scored under 20%. Scores on the ARC Prize Foundation's semi-private evaluation rose steeply during 2026. Among the models in the table above, the foundation's leaderboard (checked 27 October 2026) lists Claude Fable 5 at 89.2% at its max setting, GPT-5.5 at 85.0% at xhigh, the February 2026 version of Gemini 3 Deep Think at 84.6%, Gemini 3.1 Pro (preview) at 77.1%, Claude Opus 4.7 at 75.8% at max, and Claude Opus 4.8 at 72.1% at high ^[24]. Earlier entries were far lower: a preview of Gemini 3 Deep Think scored 45.1%, Claude Opus 4.5 Thinking 37.6%, Gemini 3 Flash 33.6% and Gemini 3 Pro base 31.1%; Grok 4 reached 15.9% and GPT-5 reached 9.9% ^{[4][10][17][24]}. A refinement system from Poetiq built on Gemini 3 Pro scored 54%, but it is a scaffolded system rather than a single model ^[10]. Models released after July 2026 score higher still; GPT-6 Astra, for example, is listed at 95.0% at its max setting ^[24]. The verdict: among the models compared here, Claude Fable 5 has the highest ARC-AGI-2 score, with GPT-5.5 and Gemini 3 Deep Think close behind.

An important caveat: ARC-AGI-2 scores depend heavily on the reasoning-effort setting. The ARC Prize Foundation lists several settings for most models; Claude Opus 4.7, for example, ranges from 62.1% at low effort to 75.8% at max, and GPT-5.5 from 33.3% at low to 85.0% at xhigh ^[24]. The 85.0%, 77.1% and 75.8% figures for GPT-5.5, Gemini 3.1 Pro and Claude Opus 4.7 are the foundation's own semi-private results, not public-set self-reports ^[24]. Results on the public evaluation set are a different measurement from semi-private scores ^[21]. Treat any single "ARC-AGI-2" percentage that does not state its evaluation set and effort setting as unreliable.

Which is the best open-weight reasoning model?

Open weights have closed much of the gap. GLM-5.2 from Z.ai (Zhipu, MIT license, released June 2026) is the highest-scoring open model on the Artificial Analysis Intelligence Index and posts 91.2% GPQA Diamond, 99.2% AIME 2026, and 40.5% HLE (54.7% with tools) ^[8]. DeepSeek V4-Pro (MIT license, April 2026, a 1.6-trillion-parameter mixture-of-experts model with 49B active and 1M context) is close behind at 90.1% GPQA Diamond and 37.7% HLE, and far cheaper to run ^[7][22]. Kimi K2.6 from Moonshot AI scores 90.5% GPQA Diamond and a strong 54.0% HLE with tools ^[14]. The verdict: GLM-5.2 is the best open reasoning model overall, with DeepSeek V4-Pro the best open value and Kimi K2.6 the strongest tool-using open model. Note that Alibaba's Qwen3.7-Max and Qwen3-Max-Thinking are strong reasoners but are proprietary, API-only, and not open weight ^[15][16].

Which reasoning model is the best value?

Among open models, DeepSeek V4-Pro delivers frontier-adjacent reasoning at about $0.44 per million input and $0.87 per million output tokens, and its smaller V4-Flash sibling runs near $0.14 in and $0.28 out, the cheapest capable reasoner here ^[7][22]. MiniMax M2 (about $0.30 in, $1.20 out) is another low-cost open option, though its 78% AIME and GPQA place it a tier below ^[16]. Among proprietary models, Grok 4.3 from xAI is priced aggressively at $1.25 in and $2.50 out while scoring around 90% GPQA Diamond ^[23]. The verdict: DeepSeek V4-Pro is the best value for top-tier reasoning, and Grok 4.3 is the best-value proprietary option.

How should you read these scores?

Three cautions apply to every number above. First, saturation: AIME 2025 and MATH-500 are essentially solved and have been retired from most 2026 model cards, so a perfect AIME score no longer signals a leader. GPQA Diamond is close behind, with the frontier compressed into a two-point band above human-expert level ^[17][20]. HLE and ARC-AGI-2 are the remaining benchmarks with real spread. Second, tools versus no tools: with-tools scores (code execution, search) run 5 to 15 points higher than no-tools scores on HLE and AIME, so only compare like with like. Third, self-report versus independent: launch-day figures are provider self-reports; independent trackers such as Artificial Analysis, Scale and Epoch AI often measure a few points lower, and ARC-AGI-2 results on the public evaluation set are not the same measurement as the ARC Prize Foundation's semi-private scores ^{[4][9][20][21]}. Scores in this fast-moving field change monthly; this page was verified in July 2026, and its ARC-AGI-2 figures were updated in October 2026.

Continue reading

• Gemini 3Gemini 3 is the third major generation of the Gemini family of multimodal models from Google DeepMind, launched on November 18, 2025 with Gemini 3 Pro as the flagship and described by Google as "our most…Mentioned 22 times above
• GPT-5.5GPT-5.5 is a large language model developed by OpenAI and released on April 23, 2026.Mentioned 15 times above
• AIME (American Invitational Mathematics Examination)The American Invitational Mathematics Examination (AIME) is a 15-question, 3-hour mathematics competition for high school students in the United States and CanadaMentioned 14 times above
• ARC-AGI-2ARC-AGI-2 (Abstraction and Reasoning Corpus for Artificial General Intelligence 2) is an abstract reasoning benchmark for artificial intelligence, released on March 24, 2025 by the ARC Prize FoundationMentioned 12 times above
• GPQA DiamondGPQA Diamond is the 198-question hardest subset of the Graduate-Level Google-Proof Q&A Benchmark (GPQA), a set of PhD-level multiple-choice questions in biology, physics, and chemistry used to measure…Mentioned 12 times above
• Claude Fable 5Claude Fable 5 is a large language model developed by Anthropic and released on June 9, 2026, as the first publicly available model in a new "Mythos class" that the company describes as "a tier of Claude…Mentioned 10 times above

More to read

• Anthropic
• Gemini 3.1 Pro
• Gemini 3 Pro
• Claude Opus 4.8
• Google
• GLM-5.2

Topics:Large Language ModelsModel EvaluationReasoning Models

References

1. ^1 ^2 ^3 ^4Artificial Analysis, "LLM Leaderboard and Intelligence Index," artificialanalysis.ai/leaderboards/models (accessed July 2026).
2. ^1 ^2 ^3 ^4 ^5 ^6Artificial Analysis, "Claude Fable 5 tops the Intelligence Index," artificialanalysis.ai/models/claude-fable-5 and /articles/claude-fable-5-mythos-intelligence-index.
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13. ^1 ^2 ^3Google, "Gemini 3.1 Pro," blog.google/innovation-and-ai/models-and-research/gemini-models/gemini-3-1-pro (GPQA Diamond 94.3%, HLE 44.4%, self-reported ARC-AGI-2 77.1%).
14. ^1 ^2 ^3Moonshot AI, "Kimi K2.6," huggingface.co/moonshotai/Kimi-K2.6 (GPQA Diamond 90.5%, AIME 2026 96.4%, HLE 34.7% / 54.0% with tools).
15. ^1 ^2Qwen (Alibaba), "Qwen3-Max-Thinking," qwen.ai/blog?id=qwen3-max-thinking (AIME 2025 100% with tools, GPQA 87.4%).
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17. ^1 ^2 ^3 ^4Epoch AI, "GPQA Diamond benchmark," epoch.ai/benchmarks/gpqa-diamond (human PhD baseline 69.7%; Grok 4 87%).
18. ^OpenAI, "Introducing GPT-5.2," openai.com/index/introducing-gpt-5-2 (first 100% AIME 2025, no tools).
19. ^LM Council, "AI Model Benchmarks (July 2026)," lmcouncil.ai/benchmarks (cross-model AIME and GPQA board; Claude Opus 4.8 AIME 98.3%).
20. ^1 ^2 ^3Artificial Analysis, "GPQA Diamond and Humanity's Last Exam evaluations," artificialanalysis.ai/evaluations/gpqa-diamond and /humanitys-last-exam.
21. ^1 ^2Imbue, "The evolution of ARC-AGI-2 (public versus semi-private)," imbue.com/blog/2026-02-27-arc-agi-2-evolution.
22. ^1 ^2DeepSeek, "API pricing," api-docs.deepseek.com/quick_start/pricing; NIST/CAISI, "Evaluation of DeepSeek V4-Pro," nist.gov/news-events/news/2026/05/caisi-evaluation-deepseek-v4-pro.
23. ^xAI, "Grok 4.3 model documentation," docs.x.ai/developers/models/grok-4.3 (pricing and release, April 30, 2026).
24. ^1 ^2 ^3 ^4 ^5 ^6ARC Prize Foundation, "ARC-AGI Leaderboard," arcprize.org/leaderboard, with leaderboard data at arcprize.org/media/data/evaluations.json (ARC-AGI-2 semi-private scores by model and reasoning setting; accessed 27 October 2026).

Show all 24 references