The Prediction Markets

Which math problems will AI solve in 2026?

Closes
Jan 1, 2027, in 2 months
Traded
$62K
Venues
Polymarket
Prices updated
2 min ago
Share

What the markets expect

Hodge Conjecture 24%

Next is Ramsey Number R(5,5) at 18%. Only Polymarket lists this market, so there is no second price to compare.

Odds by venue

Consensus blends each venue’s last price, weighted by how much has traded there. Best Yes price is the cheapest ask across venues, and the payout is what a winning $100 stake returns before fees. Open a row for each venue’s contract name, bid and ask, and how closely their rules match.

Prices come from our regular polls of each venue, the oldest 2 min ago. Ages are as of when this page was built.

  • Polymarket
Hodge Conjecture
24%
Polymarket 24%polled, 2 min agoBest Yes 26¢ on Polymarket, $100 pays $385 (3.85x)
Polymarket
Contract
Hodge Conjecture
Last price
24%
As of
Polled 2 min ago
Buy Yes
26¢
Sell Yes
22¢
$100 on Yes pays
$385 (3.85x)
Volume
$18K
Trade this on Polymarket
Ramsey Number R(5,5)
18%
Polymarket 18%polled, 2 min agoBest Yes 19¢ on Polymarket, $100 pays $526 (5.26x)
Polymarket
Contract
Ramsey Number R(5,5)
Last price
18%
As of
Polled 2 min ago
Buy Yes
19¢
Sell Yes
17¢
$100 on Yes pays
$526 (5.26x)
Volume
$1K
Trade this on Polymarket
Hadwiger-Nelson Problem
16%
Polymarket 16%polled, 2 min agoBest Yes 17¢ on Polymarket, $100 pays $588 (5.88x)
Polymarket
Contract
Hadwiger-Nelson Problem
Last price
16%
As of
Polled 2 min ago
Buy Yes
17¢
Sell Yes
15¢
$100 on Yes pays
$588 (5.88x)
Volume
$3K
Trade this on Polymarket
Hodge Conjecture
14%
Polymarket 14%polled, 2 min agoBest Yes 16¢ on Polymarket, $100 pays $625 (6.25x)
Polymarket
Contract
Hadamard Matrix Conjecture
Last price
14%
As of
Polled 2 min ago
Buy Yes
16¢
Sell Yes
12¢
$100 on Yes pays
$625 (6.25x)
Volume
$5K
Trade this on Polymarket
Birch and Swinnerton-Dyer
13.5%
Polymarket 13.5%polled, 2 min agoBest Yes 15¢ on Polymarket, $100 pays $667 (6.67x)
Polymarket
Contract
Birch and Swinnerton-Dyer
Last price
13.5%
As of
Polled 2 min ago
Buy Yes
15¢
Sell Yes
12¢
$100 on Yes pays
$667 (6.67x)
Volume
$13K
Trade this on Polymarket
Beal's Conjecture
13%
Polymarket 13%polled, 2 min agoBest Yes 14¢ on Polymarket, $100 pays $714 (7.14x)
Polymarket
Contract
Beal's Conjecture
Last price
13%
As of
Polled 2 min ago
Buy Yes
14¢
Sell Yes
12¢
$100 on Yes pays
$714 (7.14x)
Volume
$3K
Trade this on Polymarket
Twin Prime Conjecture
8.5%
Polymarket 8.5%polled, 2 min agoBest Yes 9¢ on Polymarket, $100 pays $1,111 (11.1x)
Polymarket
Contract
Twin Prime Conjecture
Last price
8.5%
As of
Polled 2 min ago
Buy Yes
9¢
Sell Yes
8¢
$100 on Yes pays
$1,111 (11.1x)
Volume
$971
Trade this on Polymarket
Odd Perfect Number
8%
Polymarket 8%polled, 2 min agoBest Yes 9¢ on Polymarket, $100 pays $1,111 (11.1x)
Polymarket
Contract
Odd Perfect Number
Last price
8%
As of
Polled 2 min ago
Buy Yes
9¢
Sell Yes
7¢
$100 on Yes pays
$1,111 (11.1x)
Volume
$2K
Trade this on Polymarket
Strong Goldbach Conjecture
8%
Polymarket 8%polled, 2 min agoBest Yes 9¢ on Polymarket, $100 pays $1,111 (11.1x)
Polymarket
Contract
Strong Goldbach Conjecture
Last price
8%
As of
Polled 2 min ago
Buy Yes
9¢
Sell Yes
7¢
$100 on Yes pays
$1,111 (11.1x)
Volume
$3K
Trade this on Polymarket
Collatz Conjecture
7.5%
Polymarket 7.5%polled, 2 min agoBest Yes 8¢ on Polymarket, $100 pays $1,250 (12.5x)
Polymarket
Contract
Collatz Conjecture
Last price
7.5%
As of
Polled 2 min ago
Buy Yes
8¢
Sell Yes
7¢
$100 on Yes pays
$1,250 (12.5x)
Volume
$2K
Trade this on Polymarket
Show 4 more outcomes
Yang-Mills
7.5%
Polymarket 7.5%polled, 2 min agoBest Yes 9¢ on Polymarket, $100 pays $1,111 (11.1x)
Polymarket
Contract
Yang-Mills
Last price
7.5%
As of
Polled 2 min ago
Buy Yes
9¢
Sell Yes
6¢
$100 on Yes pays
$1,111 (11.1x)
Volume
$1K
Trade this on Polymarket
Riemann Hypothesis
7%
Polymarket 7%polled, 2 min agoBest Yes 8¢ on Polymarket, $100 pays $1,250 (12.5x)
Polymarket
Contract
Riemann Hypothesis
Last price
7%
As of
Polled 2 min ago
Buy Yes
8¢
Sell Yes
6¢
$100 on Yes pays
$1,250 (12.5x)
Volume
$6K
Trade this on Polymarket
P versus NP
4.1%
Polymarket 4.1%polled, 2 min agoBest Yes 5.7¢ on Polymarket, $100 pays $1,754 (17.5x)
Polymarket
Contract
P versus NP
Last price
4.1%
As of
Polled 2 min ago
Buy Yes
5.7¢
Sell Yes
2.4¢
$100 on Yes pays
$1,754 (17.5x)
Volume
$2K
Trade this on Polymarket
Legendre's Conjecture
4%
Polymarket 4%polled, 2 min agoBest Yes 5.9¢ on Polymarket, $100 pays $1,695 (16.9x)
Polymarket
Contract
Legendre's Conjecture
Last price
4%
As of
Polled 2 min ago
Buy Yes
5.9¢
Sell Yes
2.1¢
$100 on Yes pays
$1,695 (16.9x)
Volume
$1K
Trade this on Polymarket

Who resolves this market

Polymarket
Polymarket resolves via:
UMA optimistic oracle, source: huggingface.co

How the odds have moved

The top 3 outcomes on both venues, with the consensus between them. Hover for exact values.

  • Hodge Conjecture
  • Ramsey Number R(5,5)
  • Hadwiger-Nelson Problem

Order books

Each venue’s resting orders for the selected outcome’s Yes contract, side by side. Top of book streams live; depth refreshes every 15 seconds.

Polymarket

Open on Polymarket ↗

Top of book

Connecting
Best bid
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Spread
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Best ask
—

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Depth · top 8 levels

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Recent trades

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What your stake buys

Enter a stake to see where it buys the most after fees, using each venue’s live order book.

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Buy

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Buys at the asks resting now (taker orders), cheapest after fees first, from order-book snapshots up to 15 seconds old. Fees: Kalshi 0.07 × price × (1 − price) per share, rounded up to the cent; Polymarket 0.05 × price × (1 − price) per share (other / general rate). Fee calculator. Estimates only, not advice.

About this market

Live prediction market odds for "Which math problems will AI solve in 2026?". Hodge Conjecture leads at 24%. Next is Ramsey Number R(5,5) at 18%. $62K has traded across 14 outcomes on Polymarket. The market is expected to resolve by Jan 1, 2027.

This market will resolve to "Yes" if an eligible AI lab announces a solution to the problem specified in the title by December 31, 2026, 11:59 PM ET. Otherwise, this market will resolve to "No". A qualifying announcement must be made by an eligible AI lab or an official representative of the lab, and must express that the problem specified in the title 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 the Clay Mathematics 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.

Questions

What does the consensus price mean?

It is the price of a Yes contract that pays $1 if the outcome happens. A 14¢ price means traders put the chance near 14%. Where two venues list the same outcome, we blend their last prices, weighting the venue with more trading volume more heavily (neither counts for less than a quarter). When only one outcome can win, each venue’s prices add up to a little over 100% (its margin); the fair chance removes that margin so the outcomes add up to exactly 100%.

How is the payout worked out?

A Yes contract pays $1 if it wins, so at the best ask a $100 stake buys 100 ÷ ask contracts. At 18¢ that is about 555 contracts, paying $556 (5.56x) if Yes happens. Venue fees and price slippage on larger orders are not included.

Why do the venues show different prices?

Each venue has its own traders, fees and order book. Contracts can also settle on slightly different terms, which is why each row lists how closely the rules match.

Is a price gap an arbitrage?

Only when you can buy Yes on one venue below what someone pays for Yes on the other, after fees, and both contracts settle the same way. We show the executable bid and ask so you can check.

How fresh are these prices?

Venue prices refresh every few minutes, and the order book and live quotes stream continuously. Each venue’s card shows when we last observed it.

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