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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

$3,969 Vol.

Polymarket

October 31, 2026

$908 Vol.

6%

December 31, 2026

$3,061 Vol.

11%

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 advances in artificial intelligence have accelerated progress on the Riemann Hypothesis and related questions about the distribution of zeros of the Riemann zeta function. In August 2026, an unreleased research version of Anthropic’s Claude model autonomously coordinated dozens of subagents to raise the proven lower bound on the share of nontrivial zeros lying on the critical line from 41.6 percent to 67.2 percent, a leap verified by human mathematicians at Anthropic and external experts before formalization in Lean. A University of Lorraine researcher then published a simpler, AI-independent proof of the same result in early September. Complementary work from physicists has tied the hypothesis to dynamical phase transitions observable on quantum processors. These developments, alongside ongoing large-language-model experiments in number theory, represent the primary recent catalysts shaping trader views on near-term substantive breakthroughs.

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.
Volume
$3,969
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.Recent advances in artificial intelligence have accelerated progress on the Riemann Hypothesis and related questions about the distribution of zeros of the Riemann zeta function. In August 2026, an unreleased research version of Anthropic’s Claude model autonomously coordinated dozens of subagents to raise the proven lower bound on the share of nontrivial zeros lying on the critical line from 41.6 percent to 67.2 percent, a leap verified by human mathematicians at Anthropic and external experts before formalization in Lean. A University of Lorraine researcher then published a simpler, AI-independent proof of the same result in early September. Complementary work from physicists has tied the hypothesis to dynamical phase transitions observable on quantum processors. These developments, alongside ongoing large-language-model experiments in number theory, represent the primary recent catalysts shaping trader views on near-term substantive breakthroughs.

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.
Volume
$3,969
End Date
Jan 1, 2027
Market Opened
Aug 13, 2026, 5:09 PM ET

Resolver

0x65070BE91...

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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 11%, followed by "October 31, 2026" at 6%. Prices reflect real-time crowd-sourced probabilities. For example, a share priced at 11¢ implies that the market collectively assigns a 11% 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.

The current frontrunner for "Further substantive progress on the Riemann Hypothesis by ___?" is "December 31, 2026" at 11%, meaning the market assigns a 11% chance to that outcome. The next closest outcome is "October 31, 2026" at 6%. These odds update in real-time as traders buy and sell shares, so they reflect the latest collective view of what's most likely to happen. Check back frequently or bookmark this page to follow how the odds shift as new information emerges.

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.