Mathematics · Benchmark profile

FrontierMath v2 Tiers 1-3

Epoch AI's corrected v2 core FrontierMath suite of private advanced mathematics problems. Models can reason iteratively and use Python; scores are pass rates on the private set.

Reference2026Active51 models

Data verified 21 Jul 2026 · Methodology 1.6.0

Benchmark score on FrontierMath v2 Tiers 1-3

Leaderboard · 51 models

GPT-5.6 Sol leads at 89%, followed by GPT-5.6 Terra (84.9%) and GPT-5.6 Luna (78.6%).

Display onlyMathematics2026

#1Closed

GPT-5.6 Sol

OpenAI

gpt-5.6-sol

89%

Overall #3 · Context 1.05M tokens

#2Closed

GPT-5.6 Terra

OpenAI

gpt-5.6-terra

84.9%

Overall #10 · Context 1.05M tokens

#3Closed

GPT-5.6 Luna

OpenAI

gpt-5.6-luna

78.6%

Overall #14 · Context 1.05M tokens

Visual analysis

See the field.

Switch between model placement, score distribution and descriptive provider averages. Every view uses the same sourced leaderboard.

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OpenAIAnthropicMetaGoogleMoonshot AIZ.AI

FrontierMath v2 Tiers 1-3 leaderboard

20 ranked models · higher is better

View accessible chart data

Accessible data for FrontierMath v2 Tiers 1-3 leaderboard
Model	Rank	Provider	Score
GPT-5.6 Sol	#1	OpenAI	89%
GPT-5.6 Terra	#2	OpenAI	84.9%
GPT-5.6 Luna	#3	OpenAI	78.6%
GPT-5.5	#4	OpenAI	51.7%
GPT-5.5 Pro	#5	OpenAI	51%
GPT-5.4 Pro	#6	OpenAI	50%
GPT-5.4	#7	OpenAI	47.6%
Claude Opus 4.8	#8	Anthropic	47.2%
Claude Opus 4.7	#9	Anthropic	43.8%
Claude Opus 4.6	#10	Anthropic	40.7%
GPT-5.2	#11	OpenAI	40.7%
Muse Spark	#12	Meta	39%
Gemini 3.5 Flash	#13	Google	39.0%
Kimi K2.6	#14	Moonshot AI	39.0%
Gemini 3 Pro	#15	Google	37.6%
Gemini 3.1 Pro	#16	Google	36.9%
Gemini 3 Flash	#17	Google	35.6%
GLM-5.1	#18	Z.AI	33.4%
Claude Sonnet 4.6	#19	Anthropic	32.4%
GPT-5.1	#20	OpenAI	31.0%

Benchmark score table (51 models)

One best score per model · higher is better

FrontierMath v2 Tiers 1-3 leaderboard ranked by score
Rank	Model	Provider	License	Evidence use	Score
#1	GPT-5.6 Sol gpt-5.6-sol	OpenAI	closed	Reference only	89%
#2	GPT-5.6 Terra gpt-5.6-terra	OpenAI	closed	Estimated reference	84.9%
#3	GPT-5.6 Luna gpt-5.6-luna	OpenAI	closed	Estimated reference	78.6%
#4	GPT-5.5 gpt-5.5	OpenAI	closed	Estimated reference	51.7%
#5	GPT-5.5 Pro gpt.5.5.pro	OpenAI	closed	Estimated reference	51%
#6	GPT-5.4 Pro gpt-5-4-pro	OpenAI	closed	Estimated reference	50%
#7	GPT-5.4 gpt-5.4	OpenAI	closed	Reference only	47.6%
#8	Claude Opus 4.8 claude-opus-4-8	Anthropic	closed	Reference only	47.2%
#9	Claude Opus 4.7 claude-opus-4-7	Anthropic	closed	Reference only	43.8%
#10	Claude Opus 4.6 claude-opus-4-6	Anthropic	closed	Reference only	40.7%
#11	GPT-5.2 gpt-5.2	OpenAI	closed	Estimated reference	40.7%
#12	Muse Spark muse-spark	Meta	closed	Reference only	39%
#13	Gemini 3.5 Flash gemini-3.5-flash	Google	closed	Estimated reference	39.0%
#14	Kimi K2.6 kimi-k2.6	Moonshot AI	open	Estimated reference	39.0%
#15	Gemini 3 Pro gemini-3-pro	Google	closed	Reference only	37.6%
#16	Gemini 3.1 Pro gemini-3-1-pro	Google	closed	Estimated reference	36.9%
#17	Gemini 3 Flash gemini-3-flash	Google	closed	Reference only	35.6%
#18	GLM-5.1 glm-5-1	Z.AI	open	Reference only	33.4%
#19	Claude Sonnet 4.6 claude-sonnet-4-6	Anthropic	closed	Reference only	32.4%
#20	GPT-5.1 gpt.5.1	OpenAI	closed	Estimated reference	31.0%
#21	GPT-5.4 mini gpt-5.4-mini	OpenAI	closed	Estimated reference	28.3%
#22	Kimi K2.5 kimi-k2.5	Moonshot AI	—	Reference only	27.9%
#23	Qwen3.6 Plus qwen3-6-plus	Alibaba Cloud	closed	Reference only	26.2%
#24	GPT-5.4 nano gpt.5.4.nano	OpenAI	closed	Reference only	25.9%
#25	o4-mini (high) o4-mini-high	OpenAI	closed	Estimated reference	24.8%
#26	Qwen 3.6 Max (preview) qwen3-6-max-preview	Alibaba Cloud	closed	Reference only	23.1%
#27	DeepSeek V3.2 deepseek-v3.2	DeepSeek	open	Reference only	22.1%
#28	Kimi K2 kimi-k2	Moonshot AI	closed	Reference only	21.4%
#29	Qwen3.5 Plus qwen3-5-plus	Alibaba Cloud	closed	Estimated reference	21.0%
#30	Claude Opus 4.5 claude-opus-4-5	Anthropic	closed	Reference only	20.7%
#31	Grok 4 grok-4	xAI	closed	Reference only	19.7%
#32	o3 o3	OpenAI	closed	Reference only	18.7%
#33	GLM-5 glm-5	Z.AI	open	Reference only	16.4%
#34	Gemini 2.5 Pro gemini-2.5-pro	Google	closed	Reference only	14.1%
#35	Claude Sonnet 4.5 claude-sonnet-4-5	Anthropic	closed	Estimated reference	13.5%
#36	o1 o1	OpenAI	closed	Estimated reference	9.3%
#37	Qwen3 235B 2507 (Reasoning) qwen3-235b-2507-reasoning	Alibaba Cloud	open	Estimated reference	8.5%
#38	Qwen3.5 Flash qwen3-5-flash	Alibaba Cloud	closed	Reference only	6.2%
#39	Claude Haiku 4.5 claude-haiku-4-5-20251001	Anthropic	closed	Estimated reference	5.9%
#40	GPT-4.1 gpt-4-1	OpenAI	closed	Reference only	5.5%
#41	Gemini 2.5 Flash gemini-2.5-flash	Google	closed	Reference only	4.8%
#42	GPT-4.1 mini gpt-4-1-mini	OpenAI	closed	Estimated reference	4.5%
#43	GLM-4.6 glm-4.6	Z.AI	open	Reference only	3.8%
#44	Grok 3 [Beta] grok-3-beta	xAI	closed	Reference only	3.8%
#45	GLM-4.7 glm-4.7	Z.AI	open	Reference only	2.4%
#46	Claude 3.5 Sonnet claude-3-5-sonnet	Anthropic	closed	Estimated reference	2.1%
#47	DeepSeek V3 deepseek-v3	DeepSeek	open	Reference only	1.7%
#48	GPT-4.1 nano gpt-4-1-nano	OpenAI	closed	Estimated reference	1.0%
#49	Llama 4 Maverick llama-4-maverick	Meta	open	Reference only	0.7%
#50	GPT-4o gpt-4o	OpenAI	closed	Reference only	0.3%
#51	Llama 4 Scout llama-4-scout	Meta	open	Reference only	0%

The top of this snapshot is led by GPT-5.6 Sol at 89%; third place is 10.4 points behind. The top-10 spread is 48.3 points.

Compare top models

GPT-5.6 Sol vs GPT-5.6 Terra GPT-5.6 Terra vs GPT-5.6 Luna GPT-5.6 Luna vs GPT-5.5 GPT-5.5 vs GPT-5.5 Pro

About FrontierMath v2 Tiers 1-3

Definition and scoring

Organisation: Epoch AI
Category: Mathematics
Version: 2026
Direction: higher is better
Ranking use: Reference
Contamination risk: Unknown

Epoch AI's corrected v2 core FrontierMath suite of private advanced mathematics problems. Models can reason iteratively and use Python; scores are pass rates on the private set. Results stay tied to the exact model variant and evaluation system. Multiple systems for the same model use the best published score on this page; overall Lumina scoring uses the median of ranking-eligible rows.

Open benchmark source ↗

FAQ

Quick answers

What does FrontierMath v2 Tiers 1-3 measure?

Epoch AI's corrected v2 core FrontierMath suite of private advanced mathematics problems. Models can reason iteratively and use Python; scores are pass rates on the private set.

Which model scores highest on FrontierMath v2 Tiers 1-3?

GPT-5.6 Sol by OpenAI currently leads with 89%.

How many models are evaluated on FrontierMath v2 Tiers 1-3?

51 models in the LuminaBench cohort have a qualifying score on this benchmark.

Does this affect overall Lumina rank?

No. This benchmark is display-only and does not enter the overall Lumina composite.

FrontierMath

Rolling · 30 results · Weighted 2.3%

BenchLM Math prior

bench-align-v5.1 · 26 results · Reference

AIME 2025

Rolling · 38 results · Not Weighted

AIME 2026

Rolling · 23 results · Weighted 2.3%

USAMO 2026

Rolling · 6 results · Weighted 2.3%

HMMT Feb 2026

Rolling · 10 results · Weighted 2.3%

Mathematics · Benchmark profile

FrontierMath v2 Tiers 1-3

Epoch AI's corrected v2 core FrontierMath suite of private advanced mathematics problems. Models can reason iteratively and use Python; scores are pass rates on the private set.

Reference2026Active51 models

Data verified 21 Jul 2026 · Methodology 1.6.0

Benchmark score on FrontierMath v2 Tiers 1-3

Leaderboard · 51 models

GPT-5.6 Sol leads at 89%, followed by GPT-5.6 Terra (84.9%) and GPT-5.6 Luna (78.6%).

Display onlyMathematics2026

#1Closed

GPT-5.6 Sol

OpenAI

gpt-5.6-sol

89%

Overall #3 · Context 1.05M tokens

#2Closed

GPT-5.6 Terra

OpenAI

gpt-5.6-terra

84.9%

Overall #10 · Context 1.05M tokens

#3Closed

GPT-5.6 Luna

OpenAI

gpt-5.6-luna

78.6%

Overall #14 · Context 1.05M tokens

Visual analysis

See the field.

Switch between model placement, score distribution and descriptive provider averages. Every view uses the same sourced leaderboard.

ViewModelsColours

OpenAIAnthropicMetaGoogleMoonshot AIZ.AI

FrontierMath v2 Tiers 1-3 leaderboard

20 ranked models · higher is better

View accessible chart data

Accessible data for FrontierMath v2 Tiers 1-3 leaderboard
Model	Rank	Provider	Score
GPT-5.6 Sol	#1	OpenAI	89%
GPT-5.6 Terra	#2	OpenAI	84.9%
GPT-5.6 Luna	#3	OpenAI	78.6%
GPT-5.5	#4	OpenAI	51.7%
GPT-5.5 Pro	#5	OpenAI	51%
GPT-5.4 Pro	#6	OpenAI	50%
GPT-5.4	#7	OpenAI	47.6%
Claude Opus 4.8	#8	Anthropic	47.2%
Claude Opus 4.7	#9	Anthropic	43.8%
Claude Opus 4.6	#10	Anthropic	40.7%
GPT-5.2	#11	OpenAI	40.7%
Muse Spark	#12	Meta	39%
Gemini 3.5 Flash	#13	Google	39.0%
Kimi K2.6	#14	Moonshot AI	39.0%
Gemini 3 Pro	#15	Google	37.6%
Gemini 3.1 Pro	#16	Google	36.9%
Gemini 3 Flash	#17	Google	35.6%
GLM-5.1	#18	Z.AI	33.4%
Claude Sonnet 4.6	#19	Anthropic	32.4%
GPT-5.1	#20	OpenAI	31.0%

Benchmark score table (51 models)

One best score per model · higher is better

FrontierMath v2 Tiers 1-3 leaderboard ranked by score
Rank	Model	Provider	License	Evidence use	Score
#1	GPT-5.6 Sol gpt-5.6-sol	OpenAI	closed	Reference only	89%
#2	GPT-5.6 Terra gpt-5.6-terra	OpenAI	closed	Estimated reference	84.9%
#3	GPT-5.6 Luna gpt-5.6-luna	OpenAI	closed	Estimated reference	78.6%
#4	GPT-5.5 gpt-5.5	OpenAI	closed	Estimated reference	51.7%
#5	GPT-5.5 Pro gpt.5.5.pro	OpenAI	closed	Estimated reference	51%
#6	GPT-5.4 Pro gpt-5-4-pro	OpenAI	closed	Estimated reference	50%
#7	GPT-5.4 gpt-5.4	OpenAI	closed	Reference only	47.6%
#8	Claude Opus 4.8 claude-opus-4-8	Anthropic	closed	Reference only	47.2%
#9	Claude Opus 4.7 claude-opus-4-7	Anthropic	closed	Reference only	43.8%
#10	Claude Opus 4.6 claude-opus-4-6	Anthropic	closed	Reference only	40.7%
#11	GPT-5.2 gpt-5.2	OpenAI	closed	Estimated reference	40.7%
#12	Muse Spark muse-spark	Meta	closed	Reference only	39%
#13	Gemini 3.5 Flash gemini-3.5-flash	Google	closed	Estimated reference	39.0%
#14	Kimi K2.6 kimi-k2.6	Moonshot AI	open	Estimated reference	39.0%
#15	Gemini 3 Pro gemini-3-pro	Google	closed	Reference only	37.6%
#16	Gemini 3.1 Pro gemini-3-1-pro	Google	closed	Estimated reference	36.9%
#17	Gemini 3 Flash gemini-3-flash	Google	closed	Reference only	35.6%
#18	GLM-5.1 glm-5-1	Z.AI	open	Reference only	33.4%
#19	Claude Sonnet 4.6 claude-sonnet-4-6	Anthropic	closed	Reference only	32.4%
#20	GPT-5.1 gpt.5.1	OpenAI	closed	Estimated reference	31.0%
#21	GPT-5.4 mini gpt-5.4-mini	OpenAI	closed	Estimated reference	28.3%
#22	Kimi K2.5 kimi-k2.5	Moonshot AI	—	Reference only	27.9%
#23	Qwen3.6 Plus qwen3-6-plus	Alibaba Cloud	closed	Reference only	26.2%
#24	GPT-5.4 nano gpt.5.4.nano	OpenAI	closed	Reference only	25.9%
#25	o4-mini (high) o4-mini-high	OpenAI	closed	Estimated reference	24.8%
#26	Qwen 3.6 Max (preview) qwen3-6-max-preview	Alibaba Cloud	closed	Reference only	23.1%
#27	DeepSeek V3.2 deepseek-v3.2	DeepSeek	open	Reference only	22.1%
#28	Kimi K2 kimi-k2	Moonshot AI	closed	Reference only	21.4%
#29	Qwen3.5 Plus qwen3-5-plus	Alibaba Cloud	closed	Estimated reference	21.0%
#30	Claude Opus 4.5 claude-opus-4-5	Anthropic	closed	Reference only	20.7%
#31	Grok 4 grok-4	xAI	closed	Reference only	19.7%
#32	o3 o3	OpenAI	closed	Reference only	18.7%
#33	GLM-5 glm-5	Z.AI	open	Reference only	16.4%
#34	Gemini 2.5 Pro gemini-2.5-pro	Google	closed	Reference only	14.1%
#35	Claude Sonnet 4.5 claude-sonnet-4-5	Anthropic	closed	Estimated reference	13.5%
#36	o1 o1	OpenAI	closed	Estimated reference	9.3%
#37	Qwen3 235B 2507 (Reasoning) qwen3-235b-2507-reasoning	Alibaba Cloud	open	Estimated reference	8.5%
#38	Qwen3.5 Flash qwen3-5-flash	Alibaba Cloud	closed	Reference only	6.2%
#39	Claude Haiku 4.5 claude-haiku-4-5-20251001	Anthropic	closed	Estimated reference	5.9%
#40	GPT-4.1 gpt-4-1	OpenAI	closed	Reference only	5.5%
#41	Gemini 2.5 Flash gemini-2.5-flash	Google	closed	Reference only	4.8%
#42	GPT-4.1 mini gpt-4-1-mini	OpenAI	closed	Estimated reference	4.5%
#43	GLM-4.6 glm-4.6	Z.AI	open	Reference only	3.8%
#44	Grok 3 [Beta] grok-3-beta	xAI	closed	Reference only	3.8%
#45	GLM-4.7 glm-4.7	Z.AI	open	Reference only	2.4%
#46	Claude 3.5 Sonnet claude-3-5-sonnet	Anthropic	closed	Estimated reference	2.1%
#47	DeepSeek V3 deepseek-v3	DeepSeek	open	Reference only	1.7%
#48	GPT-4.1 nano gpt-4-1-nano	OpenAI	closed	Estimated reference	1.0%
#49	Llama 4 Maverick llama-4-maverick	Meta	open	Reference only	0.7%
#50	GPT-4o gpt-4o	OpenAI	closed	Reference only	0.3%
#51	Llama 4 Scout llama-4-scout	Meta	open	Reference only	0%

The top of this snapshot is led by GPT-5.6 Sol at 89%; third place is 10.4 points behind. The top-10 spread is 48.3 points.

Compare top models

GPT-5.6 Sol vs GPT-5.6 Terra GPT-5.6 Terra vs GPT-5.6 Luna GPT-5.6 Luna vs GPT-5.5 GPT-5.5 vs GPT-5.5 Pro

About FrontierMath v2 Tiers 1-3

Definition and scoring

Organisation: Epoch AI
Category: Mathematics
Version: 2026
Direction: higher is better
Ranking use: Reference
Contamination risk: Unknown

Open benchmark source ↗

FAQ

Quick answers

What does FrontierMath v2 Tiers 1-3 measure?

Epoch AI's corrected v2 core FrontierMath suite of private advanced mathematics problems. Models can reason iteratively and use Python; scores are pass rates on the private set.

Which model scores highest on FrontierMath v2 Tiers 1-3?

GPT-5.6 Sol by OpenAI currently leads with 89%.

How many models are evaluated on FrontierMath v2 Tiers 1-3?

51 models in the LuminaBench cohort have a qualifying score on this benchmark.

Does this affect overall Lumina rank?

No. This benchmark is display-only and does not enter the overall Lumina composite.

FrontierMath

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bench-align-v5.1 · 26 results · Reference

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AIME 2026

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USAMO 2026

Rolling · 6 results · Weighted 2.3%

HMMT Feb 2026

Rolling · 10 results · Weighted 2.3%

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FrontierMath v2 Tiers 1-3

Leaderboard · 51 models

GPT-5.6 Sol

GPT-5.6 Terra

GPT-5.6 Luna

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FrontierMath v2 Tiers 1-3 leaderboard

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Benchmark score table (51 models)

Crop FrontierMath v2 Tiers 1-3 benchmark table

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Definition and scoring

Quick answers

What does FrontierMath v2 Tiers 1-3 measure?

Which model scores highest on FrontierMath v2 Tiers 1-3?

How many models are evaluated on FrontierMath v2 Tiers 1-3?

Does this affect overall Lumina rank?

FrontierMath v2 Tiers 1-3

Leaderboard · 51 models

GPT-5.6 Sol

GPT-5.6 Terra

GPT-5.6 Luna

See the field.

FrontierMath v2 Tiers 1-3 leaderboard

Crop FrontierMath v2 Tiers 1-3 leaderboard

Benchmark score table (51 models)

Crop FrontierMath v2 Tiers 1-3 benchmark table

Compare top models

Definition and scoring

Quick answers

What does FrontierMath v2 Tiers 1-3 measure?

Which model scores highest on FrontierMath v2 Tiers 1-3?

How many models are evaluated on FrontierMath v2 Tiers 1-3?

Does this affect overall Lumina rank?

Leaderboard · 51 models

GPT-5.6 Sol

GPT-5.6 Terra

GPT-5.6 Luna

See the field.

Benchmark score table (51 models)

Compare top models

Definition and scoring

Quick answers

What does FrontierMath v2 Tiers 1-3 measure?

Which model scores highest on FrontierMath v2 Tiers 1-3?

How many models are evaluated on FrontierMath v2 Tiers 1-3?

Does this affect overall Lumina rank?

More Mathematics benchmarks

Leaderboard · 51 models

GPT-5.6 Sol

GPT-5.6 Terra

GPT-5.6 Luna

See the field.

Benchmark score table (51 models)

Compare top models

Definition and scoring

Quick answers

What does FrontierMath v2 Tiers 1-3 measure?

Which model scores highest on FrontierMath v2 Tiers 1-3?

How many models are evaluated on FrontierMath v2 Tiers 1-3?

Does this affect overall Lumina rank?

More Mathematics benchmarks