Recent OpenAI success solving the Navier-Stokes Millennium problem in early September 2026 via thousands of coordinated AI agents and Lean formalization has sharply raised trader expectations that large language models and multi-agent systems will resolve another problem before the 2027 deadline. With Hodge Conjecture and Birch and Swinnerton-Dyer Conjecture trading within five points of each other, sentiment reflects their relative accessibility: Hodge benefits from recent AI gains in algebraic geometry and related benchmarks, while Birch draws from ongoing LLM-assisted number theory work. The low 13.5% probability assigned to no further solutions underscores confidence in current scaling trends, tempered by verification timelines and the technical barriers still separating demonstrated capabilities from fully accepted proofs.
Experimental AI-generated summary referencing Polymarket data. This is not trading advice and plays no role in how this market resolves. · UpdatedHodge Conjecture 43%
Birch and Swinnerton-Dyer 37%
No solution by Dec 31, 2027 14%
Yang-Mills 3.0%
$93,063 Vol.
$93,063 Vol.
Dec 31, 2027
Hodge Conjecture
43%
Birch and Swinnerton-Dyer
37%
No solution by Dec 31, 2027
14%
Yang-Mills
3%
Riemann Hypothesis
2%
P versus NP
1%
Hodge Conjecture 43%
Birch and Swinnerton-Dyer 37%
No solution by Dec 31, 2027 14%
Yang-Mills 3.0%
$93,063 Vol.
$93,063 Vol.
Dec 31, 2027
Hodge Conjecture
$32,418 Vol.
43%
Birch and Swinnerton-Dyer
$13,309 Vol.
37%
No solution by Dec 31, 2027
$23,304 Vol.
14%
Yang-Mills
$6,627 Vol.
3%
Riemann Hypothesis
$12,531 Vol.
2%
P versus NP
$4,873 Vol.
1%
This market will resolve according to the first qualifying Millennium Prize Problem for which an eligible AI lab announces a solution by December 31, 2027, 11:59 PM ET.
If no eligible AI lab announces a solution to a qualifying problem by December 31, 2027, 11:59 PM ET, this market will resolve to "No solution by Dec 31, 2027". If solutions to two or more qualifying problems are announced on the same calendar day (ET), this market will resolve to the problem whose name, as listed below, comes first in alphabetical order.
The qualifying problems are, in alphabetical order, the Birch and Swinnerton-Dyer Conjecture, the Hodge Conjecture, P versus NP, the Riemann Hypothesis, and the Yang-Mills existence and mass gap problem (https://www.claymath.org/millennium-problems/). Announcements concerning the Navier-Stokes existence and smoothness problem will not qualify.
A qualifying announcement must be made by an eligible AI lab or an official representative of the lab, and must express that the problem has been solved; announcements of partial results or progress toward a solution will not qualify. The announcement must present the solution as the work of the lab, its researchers, or its models, alone or jointly with outside researchers. An announcement that only credits or congratulates outside researchers, including researchers who used the lab's models, compute, or research credits, will not qualify. No further confirmation from Clay Math Institute or any other organization is required.
The eligible AI labs are Anthropic, Google, SpaceXAI, Alibaba, OpenAI, Baidu, Z.ai, Xiaomi, Moonshot, Meta, Nvidia, DeepSeek, MiniMax, Meituan, Amazon, ByteDance, Mistral, Tencent, StepFun, Microsoft, Harmonic, Axiom Math, Math Inc, Safe Superintelligence, Thinking Machines Lab, Reflection AI, Periodic Labs, Apple, IBM, Huawei, Samsung, Oracle, Salesforce, Cohere, AI21 Labs, Reka, Sakana AI, Poolside, Magic, Perplexity, Anysphere, Kuaishou, SenseTime, iFlytek, Baichuan, and 01.AI, together with their subsidiaries and research divisions, and any other company with a model listed on the MMLU-pro leaderboard (https://huggingface.co/spaces/TIGER-Lab/MMLU-Pro) at the time of the announcement. Announcements by any other company, organization, or individual will not qualify.
The primary resolution source for this market will be official information from the eligible AI labs and/or their official representatives; however, a consensus of credible reporting may also be used.Recent OpenAI success solving the Navier-Stokes Millennium problem in early September 2026 via thousands of coordinated AI agents and Lean formalization has sharply raised trader expectations that large language models and multi-agent systems will resolve another problem before the 2027 deadline. With Hodge Conjecture and Birch and Swinnerton-Dyer Conjecture trading within five points of each other, sentiment reflects their relative accessibility: Hodge benefits from recent AI gains in algebraic geometry and related benchmarks, while Birch draws from ongoing LLM-assisted number theory work. The low 13.5% probability assigned to no further solutions underscores confidence in current scaling trends, tempered by verification timelines and the technical barriers still separating demonstrated capabilities from fully accepted proofs.
This market will resolve according to the first qualifying Millennium Prize Problem for which an eligible AI lab announces a solution by December 31, 2027, 11:59 PM ET.
If no eligible AI lab announces a solution to a qualifying problem by December 31, 2027, 11:59 PM ET, this market will resolve to "No solution by Dec 31, 2027". If solutions to two or more qualifying problems are announced on the same calendar day (ET), this market will resolve to the problem whose name, as listed below, comes first in alphabetical order.
The qualifying problems are, in alphabetical order, the Birch and Swinnerton-Dyer Conjecture, the Hodge Conjecture, P versus NP, the Riemann Hypothesis, and the Yang-Mills existence and mass gap problem (https://www.claymath.org/millennium-problems/). Announcements concerning the Navier-Stokes existence and smoothness problem will not qualify.
A qualifying announcement must be made by an eligible AI lab or an official representative of the lab, and must express that the problem has been solved; announcements of partial results or progress toward a solution will not qualify. The announcement must present the solution as the work of the lab, its researchers, or its models, alone or jointly with outside researchers. An announcement that only credits or congratulates outside researchers, including researchers who used the lab's models, compute, or research credits, will not qualify. No further confirmation from Clay Math Institute or any other organization is required.
The eligible AI labs are Anthropic, Google, SpaceXAI, Alibaba, OpenAI, Baidu, Z.ai, Xiaomi, Moonshot, Meta, Nvidia, DeepSeek, MiniMax, Meituan, Amazon, ByteDance, Mistral, Tencent, StepFun, Microsoft, Harmonic, Axiom Math, Math Inc, Safe Superintelligence, Thinking Machines Lab, Reflection AI, Periodic Labs, Apple, IBM, Huawei, Samsung, Oracle, Salesforce, Cohere, AI21 Labs, Reka, Sakana AI, Poolside, Magic, Perplexity, Anysphere, Kuaishou, SenseTime, iFlytek, Baichuan, and 01.AI, together with their subsidiaries and research divisions, and any other company with a model listed on the MMLU-pro leaderboard (https://huggingface.co/spaces/TIGER-Lab/MMLU-Pro) at the time of the announcement. Announcements by any other company, organization, or individual will not qualify.
The primary resolution source for this market will be official information from the eligible AI labs and/or their official representatives; however, a consensus of credible reporting may also be used.
If no eligible AI lab announces a solution to a qualifying problem by December 31, 2027, 11:59 PM ET, this market will resolve to "No solution by Dec 31, 2027". If solutions to two or more qualifying problems are announced on the same calendar day (ET), this market will resolve to the problem whose name, as listed below, comes first in alphabetical order.
The qualifying problems are, in alphabetical order, the Birch and Swinnerton-Dyer Conjecture, the Hodge Conjecture, P versus NP, the Riemann Hypothesis, and the Yang-Mills existence and mass gap problem (https://www.claymath.org/millennium-problems/). Announcements concerning the Navier-Stokes existence and smoothness problem will not qualify.
A qualifying announcement must be made by an eligible AI lab or an official representative of the lab, and must express that the problem has been solved; announcements of partial results or progress toward a solution will not qualify. The announcement must present the solution as the work of the lab, its researchers, or its models, alone or jointly with outside researchers. An announcement that only credits or congratulates outside researchers, including researchers who used the lab's models, compute, or research credits, will not qualify. No further confirmation from Clay Math Institute or any other organization is required.
The eligible AI labs are Anthropic, Google, SpaceXAI, Alibaba, OpenAI, Baidu, Z.ai, Xiaomi, Moonshot, Meta, Nvidia, DeepSeek, MiniMax, Meituan, Amazon, ByteDance, Mistral, Tencent, StepFun, Microsoft, Harmonic, Axiom Math, Math Inc, Safe Superintelligence, Thinking Machines Lab, Reflection AI, Periodic Labs, Apple, IBM, Huawei, Samsung, Oracle, Salesforce, Cohere, AI21 Labs, Reka, Sakana AI, Poolside, Magic, Perplexity, Anysphere, Kuaishou, SenseTime, iFlytek, Baichuan, and 01.AI, together with their subsidiaries and research divisions, and any other company with a model listed on the MMLU-pro leaderboard (https://huggingface.co/spaces/TIGER-Lab/MMLU-Pro) at the time of the announcement. Announcements by any other company, organization, or individual will not qualify.
The primary resolution source for this market will be official information from the eligible AI labs and/or their official representatives; however, a consensus of credible reporting may also be used.
Market Opened: Sep 9, 2026, 3:43 PM ET
Volume
$93,063End Date
Jan 1, 2028Market Opened
Sep 9, 2026, 3:43 PM ETResolver
0x69c47De9D...This market will resolve according to the first qualifying Millennium Prize Problem for which an eligible AI lab announces a solution by December 31, 2027, 11:59 PM ET.
If no eligible AI lab announces a solution to a qualifying problem by December 31, 2027, 11:59 PM ET, this market will resolve to "No solution by Dec 31, 2027". If solutions to two or more qualifying problems are announced on the same calendar day (ET), this market will resolve to the problem whose name, as listed below, comes first in alphabetical order.
The qualifying problems are, in alphabetical order, the Birch and Swinnerton-Dyer Conjecture, the Hodge Conjecture, P versus NP, the Riemann Hypothesis, and the Yang-Mills existence and mass gap problem (https://www.claymath.org/millennium-problems/). Announcements concerning the Navier-Stokes existence and smoothness problem will not qualify.
A qualifying announcement must be made by an eligible AI lab or an official representative of the lab, and must express that the problem has been solved; announcements of partial results or progress toward a solution will not qualify. The announcement must present the solution as the work of the lab, its researchers, or its models, alone or jointly with outside researchers. An announcement that only credits or congratulates outside researchers, including researchers who used the lab's models, compute, or research credits, will not qualify. No further confirmation from Clay Math Institute or any other organization is required.
The eligible AI labs are Anthropic, Google, SpaceXAI, Alibaba, OpenAI, Baidu, Z.ai, Xiaomi, Moonshot, Meta, Nvidia, DeepSeek, MiniMax, Meituan, Amazon, ByteDance, Mistral, Tencent, StepFun, Microsoft, Harmonic, Axiom Math, Math Inc, Safe Superintelligence, Thinking Machines Lab, Reflection AI, Periodic Labs, Apple, IBM, Huawei, Samsung, Oracle, Salesforce, Cohere, AI21 Labs, Reka, Sakana AI, Poolside, Magic, Perplexity, Anysphere, Kuaishou, SenseTime, iFlytek, Baichuan, and 01.AI, together with their subsidiaries and research divisions, and any other company with a model listed on the MMLU-pro leaderboard (https://huggingface.co/spaces/TIGER-Lab/MMLU-Pro) at the time of the announcement. Announcements by any other company, organization, or individual will not qualify.
The primary resolution source for this market will be official information from the eligible AI labs and/or their official representatives; however, a consensus of credible reporting may also be used.Recent OpenAI success solving the Navier-Stokes Millennium problem in early September 2026 via thousands of coordinated AI agents and Lean formalization has sharply raised trader expectations that large language models and multi-agent systems will resolve another problem before the 2027 deadline. With Hodge Conjecture and Birch and Swinnerton-Dyer Conjecture trading within five points of each other, sentiment reflects their relative accessibility: Hodge benefits from recent AI gains in algebraic geometry and related benchmarks, while Birch draws from ongoing LLM-assisted number theory work. The low 13.5% probability assigned to no further solutions underscores confidence in current scaling trends, tempered by verification timelines and the technical barriers still separating demonstrated capabilities from fully accepted proofs.
This market will resolve according to the first qualifying Millennium Prize Problem for which an eligible AI lab announces a solution by December 31, 2027, 11:59 PM ET.
If no eligible AI lab announces a solution to a qualifying problem by December 31, 2027, 11:59 PM ET, this market will resolve to "No solution by Dec 31, 2027". If solutions to two or more qualifying problems are announced on the same calendar day (ET), this market will resolve to the problem whose name, as listed below, comes first in alphabetical order.
The qualifying problems are, in alphabetical order, the Birch and Swinnerton-Dyer Conjecture, the Hodge Conjecture, P versus NP, the Riemann Hypothesis, and the Yang-Mills existence and mass gap problem (https://www.claymath.org/millennium-problems/). Announcements concerning the Navier-Stokes existence and smoothness problem will not qualify.
A qualifying announcement must be made by an eligible AI lab or an official representative of the lab, and must express that the problem has been solved; announcements of partial results or progress toward a solution will not qualify. The announcement must present the solution as the work of the lab, its researchers, or its models, alone or jointly with outside researchers. An announcement that only credits or congratulates outside researchers, including researchers who used the lab's models, compute, or research credits, will not qualify. No further confirmation from Clay Math Institute or any other organization is required.
The eligible AI labs are Anthropic, Google, SpaceXAI, Alibaba, OpenAI, Baidu, Z.ai, Xiaomi, Moonshot, Meta, Nvidia, DeepSeek, MiniMax, Meituan, Amazon, ByteDance, Mistral, Tencent, StepFun, Microsoft, Harmonic, Axiom Math, Math Inc, Safe Superintelligence, Thinking Machines Lab, Reflection AI, Periodic Labs, Apple, IBM, Huawei, Samsung, Oracle, Salesforce, Cohere, AI21 Labs, Reka, Sakana AI, Poolside, Magic, Perplexity, Anysphere, Kuaishou, SenseTime, iFlytek, Baichuan, and 01.AI, together with their subsidiaries and research divisions, and any other company with a model listed on the MMLU-pro leaderboard (https://huggingface.co/spaces/TIGER-Lab/MMLU-Pro) at the time of the announcement. Announcements by any other company, organization, or individual will not qualify.
The primary resolution source for this market will be official information from the eligible AI labs and/or their official representatives; however, a consensus of credible reporting may also be used.
If no eligible AI lab announces a solution to a qualifying problem by December 31, 2027, 11:59 PM ET, this market will resolve to "No solution by Dec 31, 2027". If solutions to two or more qualifying problems are announced on the same calendar day (ET), this market will resolve to the problem whose name, as listed below, comes first in alphabetical order.
The qualifying problems are, in alphabetical order, the Birch and Swinnerton-Dyer Conjecture, the Hodge Conjecture, P versus NP, the Riemann Hypothesis, and the Yang-Mills existence and mass gap problem (https://www.claymath.org/millennium-problems/). Announcements concerning the Navier-Stokes existence and smoothness problem will not qualify.
A qualifying announcement must be made by an eligible AI lab or an official representative of the lab, and must express that the problem has been solved; announcements of partial results or progress toward a solution will not qualify. The announcement must present the solution as the work of the lab, its researchers, or its models, alone or jointly with outside researchers. An announcement that only credits or congratulates outside researchers, including researchers who used the lab's models, compute, or research credits, will not qualify. No further confirmation from Clay Math Institute or any other organization is required.
The eligible AI labs are Anthropic, Google, SpaceXAI, Alibaba, OpenAI, Baidu, Z.ai, Xiaomi, Moonshot, Meta, Nvidia, DeepSeek, MiniMax, Meituan, Amazon, ByteDance, Mistral, Tencent, StepFun, Microsoft, Harmonic, Axiom Math, Math Inc, Safe Superintelligence, Thinking Machines Lab, Reflection AI, Periodic Labs, Apple, IBM, Huawei, Samsung, Oracle, Salesforce, Cohere, AI21 Labs, Reka, Sakana AI, Poolside, Magic, Perplexity, Anysphere, Kuaishou, SenseTime, iFlytek, Baichuan, and 01.AI, together with their subsidiaries and research divisions, and any other company with a model listed on the MMLU-pro leaderboard (https://huggingface.co/spaces/TIGER-Lab/MMLU-Pro) at the time of the announcement. Announcements by any other company, organization, or individual will not qualify.
The primary resolution source for this market will be official information from the eligible AI labs and/or their official representatives; however, a consensus of credible reporting may also be used.
Volume
$93,063End Date
Jan 1, 2028Market Opened
Sep 9, 2026, 3:43 PM ETResolver
0x69c47De9D...Recent OpenAI success solving the Navier-Stokes Millennium problem in early September 2026 via thousands of coordinated AI agents and Lean formalization has sharply raised trader expectations that large language models and multi-agent systems will resolve another problem before the 2027 deadline. With Hodge Conjecture and Birch and Swinnerton-Dyer Conjecture trading within five points of each other, sentiment reflects their relative accessibility: Hodge benefits from recent AI gains in algebraic geometry and related benchmarks, while Birch draws from ongoing LLM-assisted number theory work. The low 13.5% probability assigned to no further solutions underscores confidence in current scaling trends, tempered by verification timelines and the technical barriers still separating demonstrated capabilities from fully accepted proofs.
Experimental AI-generated summary referencing Polymarket data. This is not trading advice and plays no role in how this market resolves. · Updated
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