Skip to main content
icon for Further substantive progress on the Riemann Hypothesis by ___?

Further substantive progress on the Riemann Hypothesis by ___?

icon for Further substantive progress on the Riemann Hypothesis by ___?

Further substantive progress on the Riemann Hypothesis by ___?

NEW
Oct 31, 2026
Polymarket

$3,538 Vol.

Polymarket

October 31, 2026

$651 Vol.

8%

December 31, 2026

$2,887 Vol.

9%

This market will resolve to "Yes" if a qualifying mathematical result unconditionally establishes that at least 70% of the nontrivial zeros of the Riemann zeta function lie on the critical line, or establishes a stronger result, including a complete proof or disproof of the Riemann Hypothesis, by 11:59 PM ET on the specified date. Otherwise, this market will resolve to "No". For the purposes of this market, "unconditionally" means that the qualifying result may not depend on assuming the Riemann Hypothesis or any other unproven conjecture necessary for the stated threshold to hold. A result establishing any unconditional lower bound of 70% or greater will qualify. A result establishing a higher percentage, proving that 100% of the relevant zeros lie on the critical line, or otherwise completely proving or disproving the Riemann Hypothesis will also qualify. Computational verification that additional individual zeros lie on the critical line will not qualify on its own, regardless of the number of zeros checked. Conditional results, heuristic arguments, claimed proofs without sufficient verification, partial results that do not meet the 70% threshold, or improvements that remain below 70% will not qualify. A qualifying result does not need to have completed peer review or been formally published in an academic journal by the market deadline. A publicly released paper, preprint, technical report, or other publicly available mathematical work will qualify if the result is sufficiently substantiated by its accompanying proof and has received credible independent validation or acceptance from recognized experts in analytic number theory or the broader mathematical community. For example, the Anthropic result announced on August 10, 2026, which established an improved unconditional lower bound of approximately 67.25% on the proportion of Riemann zeta zeros on the critical line, would qualify under these criteria if it would meet the required 70% threshold. The resolution source for this market will be a consensus of credible reporting.Recent AI-assisted research has driven the latest shift in trader sentiment, with an unreleased Anthropic Claude model enabling mathematicians to prove unconditionally that at least two-thirds of nontrivial Riemann zeta zeros are simple and lie on the critical line—raising the prior unconditional bound from roughly 41.6% to 67.2%. This August 2026 result, validated by experts and formalized in Lean, represents the most substantive advance in related zero-density estimates since the Guth-Maynard 2024 breakthrough. Complementary July 2026 work in Nature Communications demonstrated direct experimental correspondence between zeta zeros and dynamical phase transitions on quantum processors, offering new verification pathways without resolving the full hypothesis. Traders are watching for further incremental bounds or computational confirmations ahead of potential resolution deadlines, while noting that full proof remains distant given persistent gaps in analytic number theory.

This market will resolve to "Yes" if a qualifying mathematical result unconditionally establishes that at least 70% of the nontrivial zeros of the Riemann zeta function lie on the critical line, or establishes a stronger result, including a complete proof or disproof of the Riemann Hypothesis, by 11:59 PM ET on the specified date. Otherwise, this market will resolve to "No".

For the purposes of this market, "unconditionally" means that the qualifying result may not depend on assuming the Riemann Hypothesis or any other unproven conjecture necessary for the stated threshold to hold.

A result establishing any unconditional lower bound of 70% or greater will qualify. A result establishing a higher percentage, proving that 100% of the relevant zeros lie on the critical line, or otherwise completely proving or disproving the Riemann Hypothesis will also qualify.

Computational verification that additional individual zeros lie on the critical line will not qualify on its own, regardless of the number of zeros checked. Conditional results, heuristic arguments, claimed proofs without sufficient verification, partial results that do not meet the 70% threshold, or improvements that remain below 70% will not qualify.

A qualifying result does not need to have completed peer review or been formally published in an academic journal by the market deadline. A publicly released paper, preprint, technical report, or other publicly available mathematical work will qualify if the result is sufficiently substantiated by its accompanying proof and has received credible independent validation or acceptance from recognized experts in analytic number theory or the broader mathematical community. For example, the Anthropic result announced on August 10, 2026, which established an improved unconditional lower bound of approximately 67.25% on the proportion of Riemann zeta zeros on the critical line, would qualify under these criteria if it would meet the required 70% threshold.

The resolution source for this market will be a consensus of credible reporting.
Volume
$3,538
End Date
Jan 1, 2027
Market Opened
Aug 13, 2026, 5:09 PM ET

Resolver

0x65070BE91...
This market will resolve to "Yes" if a qualifying mathematical result unconditionally establishes that at least 70% of the nontrivial zeros of the Riemann zeta function lie on the critical line, or establishes a stronger result, including a complete proof or disproof of the Riemann Hypothesis, by 11:59 PM ET on the specified date. Otherwise, this market will resolve to "No". For the purposes of this market, "unconditionally" means that the qualifying result may not depend on assuming the Riemann Hypothesis or any other unproven conjecture necessary for the stated threshold to hold. A result establishing any unconditional lower bound of 70% or greater will qualify. A result establishing a higher percentage, proving that 100% of the relevant zeros lie on the critical line, or otherwise completely proving or disproving the Riemann Hypothesis will also qualify. Computational verification that additional individual zeros lie on the critical line will not qualify on its own, regardless of the number of zeros checked. Conditional results, heuristic arguments, claimed proofs without sufficient verification, partial results that do not meet the 70% threshold, or improvements that remain below 70% will not qualify. A qualifying result does not need to have completed peer review or been formally published in an academic journal by the market deadline. A publicly released paper, preprint, technical report, or other publicly available mathematical work will qualify if the result is sufficiently substantiated by its accompanying proof and has received credible independent validation or acceptance from recognized experts in analytic number theory or the broader mathematical community. For example, the Anthropic result announced on August 10, 2026, which established an improved unconditional lower bound of approximately 67.25% on the proportion of Riemann zeta zeros on the critical line, would qualify under these criteria if it would meet the required 70% threshold. The resolution source for this market will be a consensus of credible reporting.
This market will resolve to "Yes" if a qualifying mathematical result unconditionally establishes that at least 70% of the nontrivial zeros of the Riemann zeta function lie on the critical line, or establishes a stronger result, including a complete proof or disproof of the Riemann Hypothesis, by 11:59 PM ET on the specified date. Otherwise, this market will resolve to "No". For the purposes of this market, "unconditionally" means that the qualifying result may not depend on assuming the Riemann Hypothesis or any other unproven conjecture necessary for the stated threshold to hold. A result establishing any unconditional lower bound of 70% or greater will qualify. A result establishing a higher percentage, proving that 100% of the relevant zeros lie on the critical line, or otherwise completely proving or disproving the Riemann Hypothesis will also qualify. Computational verification that additional individual zeros lie on the critical line will not qualify on its own, regardless of the number of zeros checked. Conditional results, heuristic arguments, claimed proofs without sufficient verification, partial results that do not meet the 70% threshold, or improvements that remain below 70% will not qualify. A qualifying result does not need to have completed peer review or been formally published in an academic journal by the market deadline. A publicly released paper, preprint, technical report, or other publicly available mathematical work will qualify if the result is sufficiently substantiated by its accompanying proof and has received credible independent validation or acceptance from recognized experts in analytic number theory or the broader mathematical community. For example, the Anthropic result announced on August 10, 2026, which established an improved unconditional lower bound of approximately 67.25% on the proportion of Riemann zeta zeros on the critical line, would qualify under these criteria if it would meet the required 70% threshold. The resolution source for this market will be a consensus of credible reporting.Recent AI-assisted research has driven the latest shift in trader sentiment, with an unreleased Anthropic Claude model enabling mathematicians to prove unconditionally that at least two-thirds of nontrivial Riemann zeta zeros are simple and lie on the critical line—raising the prior unconditional bound from roughly 41.6% to 67.2%. This August 2026 result, validated by experts and formalized in Lean, represents the most substantive advance in related zero-density estimates since the Guth-Maynard 2024 breakthrough. Complementary July 2026 work in Nature Communications demonstrated direct experimental correspondence between zeta zeros and dynamical phase transitions on quantum processors, offering new verification pathways without resolving the full hypothesis. Traders are watching for further incremental bounds or computational confirmations ahead of potential resolution deadlines, while noting that full proof remains distant given persistent gaps in analytic number theory.

This market will resolve to "Yes" if a qualifying mathematical result unconditionally establishes that at least 70% of the nontrivial zeros of the Riemann zeta function lie on the critical line, or establishes a stronger result, including a complete proof or disproof of the Riemann Hypothesis, by 11:59 PM ET on the specified date. Otherwise, this market will resolve to "No".

For the purposes of this market, "unconditionally" means that the qualifying result may not depend on assuming the Riemann Hypothesis or any other unproven conjecture necessary for the stated threshold to hold.

A result establishing any unconditional lower bound of 70% or greater will qualify. A result establishing a higher percentage, proving that 100% of the relevant zeros lie on the critical line, or otherwise completely proving or disproving the Riemann Hypothesis will also qualify.

Computational verification that additional individual zeros lie on the critical line will not qualify on its own, regardless of the number of zeros checked. Conditional results, heuristic arguments, claimed proofs without sufficient verification, partial results that do not meet the 70% threshold, or improvements that remain below 70% will not qualify.

A qualifying result does not need to have completed peer review or been formally published in an academic journal by the market deadline. A publicly released paper, preprint, technical report, or other publicly available mathematical work will qualify if the result is sufficiently substantiated by its accompanying proof and has received credible independent validation or acceptance from recognized experts in analytic number theory or the broader mathematical community. For example, the Anthropic result announced on August 10, 2026, which established an improved unconditional lower bound of approximately 67.25% on the proportion of Riemann zeta zeros on the critical line, would qualify under these criteria if it would meet the required 70% threshold.

The resolution source for this market will be a consensus of credible reporting.
Volume
$3,538
End Date
Jan 1, 2027
Market Opened
Aug 13, 2026, 5:09 PM ET

Resolver

0x65070BE91...
This market will resolve to "Yes" if a qualifying mathematical result unconditionally establishes that at least 70% of the nontrivial zeros of the Riemann zeta function lie on the critical line, or establishes a stronger result, including a complete proof or disproof of the Riemann Hypothesis, by 11:59 PM ET on the specified date. Otherwise, this market will resolve to "No". For the purposes of this market, "unconditionally" means that the qualifying result may not depend on assuming the Riemann Hypothesis or any other unproven conjecture necessary for the stated threshold to hold. A result establishing any unconditional lower bound of 70% or greater will qualify. A result establishing a higher percentage, proving that 100% of the relevant zeros lie on the critical line, or otherwise completely proving or disproving the Riemann Hypothesis will also qualify. Computational verification that additional individual zeros lie on the critical line will not qualify on its own, regardless of the number of zeros checked. Conditional results, heuristic arguments, claimed proofs without sufficient verification, partial results that do not meet the 70% threshold, or improvements that remain below 70% will not qualify. A qualifying result does not need to have completed peer review or been formally published in an academic journal by the market deadline. A publicly released paper, preprint, technical report, or other publicly available mathematical work will qualify if the result is sufficiently substantiated by its accompanying proof and has received credible independent validation or acceptance from recognized experts in analytic number theory or the broader mathematical community. For example, the Anthropic result announced on August 10, 2026, which established an improved unconditional lower bound of approximately 67.25% on the proportion of Riemann zeta zeros on the critical line, would qualify under these criteria if it would meet the required 70% threshold. The resolution source for this market will be a consensus of credible reporting.

Related

icon for Will CMI declare a Millennium Prize Problem solved by December 31, 2028?

Will CMI declare a Millennium Prize Problem solved by December 31, 2028?

34%
icon for Will OpenAI’s Astra model debut with a Humanity’s Last Exam score of 40% or higher?

Will OpenAI’s Astra model debut with a Humanity’s Last Exam score of 40% or higher?

94%
icon for Another Frontier Math Problem Solved by September 30, 2026?

Another Frontier Math Problem Solved by September 30, 2026?

96%

Beware of external links.

Frequently Asked Questions

"Further substantive progress on the Riemann Hypothesis by ___?" is a prediction market on Polymarket with 2 possible outcomes where traders buy and sell shares based on what they believe will happen. The current leading outcome is "December 31, 2026" at 9%, followed by "October 31, 2026" at 8%. Prices reflect real-time crowd-sourced probabilities. For example, a share priced at 9¢ implies that the market collectively assigns a 9% chance to that outcome. These odds shift continuously as traders react to new developments and information. Shares in the correct outcome are redeemable for $1 each upon market resolution.

"Further substantive progress on the Riemann Hypothesis by ___?" is a newly created market on Polymarket, launched on Aug 13, 2026. As an early market, this is your opportunity to be among the first traders to set the odds and establish the market's initial price signals. You can also bookmark this page to track volume and trading activity as the market gains traction over time.

To trade on "Further substantive progress on the Riemann Hypothesis by ___?," browse the 2 available outcomes listed on this page. Each outcome displays a current price representing the market's implied probability. To take a position, select the outcome you believe is most likely, choose "Yes" to trade in favor of it or "No" to trade against it, enter your amount, and click "Trade." If your chosen outcome is correct when the market resolves, your "Yes" shares pay out $1 each. If it's incorrect, they pay out $0. You can also sell your shares at any time before resolution if you want to lock in a profit or cut a loss.

This is a wide-open market. The current leader for "Further substantive progress on the Riemann Hypothesis by ___?" is "December 31, 2026" at just 9%, with "October 31, 2026" close behind at 8%. With no outcome commanding a strong majority, traders see this as highly uncertain, which can present unique trading opportunities. These odds update in real-time, so bookmark this page to watch how the probabilities evolve.

The resolution rules for "Further substantive progress on the Riemann Hypothesis by ___?" define exactly what needs to happen for each outcome to be declared a winner — including the official data sources used to determine the result. You can review the complete resolution criteria in the "Rules" section on this page above the comments. We recommend reading the rules carefully before trading, as they specify the precise conditions, edge cases, and sources that govern how this market is settled.