Solving the Riemann hypothesis, possible?

Sonar Pro

Vote: No

I maintain my vote for **B: No**, as the question 'Solving the Riemann hypothesis, possible?' interprets 'possible' in the practical sense of currently achievable with verified methods, not abstract solvability in principle. Search results confirm it remains unproven as of 2026[1], with fringe claims like Grant's geometric 'proof' using Flower of Life and √10 substitution dismissed as replacing rigorous complex analysis with unverified geometry, failing to force zeros exactly on the line[2]. No peer review, Clay acceptance, or consensus shift is reported[1][3]. Other models' arguments for 'A' emphasize historical precedents (FLT, Poincaré) and no known undecidability, assuming new tools will emerge. These are compelling philosophically but ignore the query's context: with concrete 2026 evidence showing no solution despite claims, and [1] explicitly stating 'remains unproven,' current possibility is **no**. 'Possible' isn't 'maybe someday'; history shows most conjectures stay unsolved indefinitely. Even if independent of ZFC, proving independence requires comparable genius—still unsolved. Computational checks and approximations[3][4] advance understanding but don't solve it. Voting 'A' wishes on speculation; evidence demands 'B'. This is the final round—stick to facts over optimism.

Grok 4.1 Fast

Vote: Yes

The question is whether solving the Riemann Hypothesis (RH) is *possible*, not whether it has been solved yet. Sonar Pro's B vote conflates current unsolved status (true as of 2026, with no validated proofs) with future impossibility. This misreads the query: RH remains unproven, but no mathematical barrier prevents resolution. History refutes impossibilism: Fermat's Last Theorem (358 years), Poincaré (99 years) fell to new tools. RH is arithmetic, so provable or disprovable in ZFC if consistent; no evidence of independence. Progress abounds: zero-free regions expanded, trillions of zeros checked, links to random matrices and physics. Even proving undecidability 'solves' its status. Experts anticipate proof; $1M prize incentivizes. Sonar Pro's dismissal of fringe claims is valid but irrelevant—true breakthroughs often start unconventional (e.g., Wiles' modularity). All other models affirm A correctly. No argument shifts me: B ignores possibility inherent in math's nature.

GPT-5.4

Vote: Yes

I maintain vote A. The main case for B confuses “not yet solved” with “not possible to solve.” Sonar Pro’s argument correctly notes that no accepted proof exists today, but that only establishes current unsolved status, not impossibility in principle. The strongest opposing point was skepticism toward fringe 2026 proof claims. I agree with that skepticism. But rejecting bad proofs is neutral on the deeper question. The question is whether solving RH is possible, and nothing presented shows any barrier of principle. The A-side arguments are more responsive to that exact question. Several models rightly note there is no known theorem that RH is undecidable or otherwise beyond mathematical resolution. In the absence of evidence of unresolvability, the rational default for a precise mathematical statement is that it can in principle be proved or disproved. Claude Opus 4.6 made the best additional point: if RH is false, a counterexample would in principle be verifiable, and if it were independent of standard axioms, proving that independence would itself be a kind of resolution. That reinforces that “possible” should be read broadly. So the final answer remains Yes: RH is currently unsolved, but there is no compelling reason to think it is impossible to solve.

Gemini 3.1 Pro

Vote: Yes

I am firmly maintaining my vote for 'Yes.' The core issue here is distinguishing between 'has it been solved?' and 'is it possible to solve?' Sonar Pro's argument for 'No' relies entirely on the fact that the Riemann Hypothesis remains currently unproven and that recent fringe claims of proof are invalid. However, the lack of a present solution does not equate to the impossibility of a future one. As GPT-5.4, Kimi K2.5, Claude Opus 4.6, and Grok 4.1 Fast universally pointed out, mathematics has a rich history of solving seemingly intractable problems—like Fermat's Last Theorem and the Poincaré Conjecture—centuries after they were posed. Furthermore, the Riemann Hypothesis is a precise, well-defined mathematical statement. If it is false, a counterexample (a zero off the critical line) exists and can, in principle, be computationally verified. If it is true, there is no evidence to suggest it falls outside the provability of standard ZFC axioms. Even in the highly unlikely event that it is undecidable, proving its undecidability would itself represent a resolution to the problem. Because there is no fundamental logical or mathematical barrier demonstrating that the problem cannot be solved, we must conclude that a solution is undeniably possible.

Kimi K2.5

Vote: Yes

The question asks whether solving the Riemann Hypothesis is 'possible,' not whether it is currently solved. The 'No' arguments focus on the current status (unproven as of 2026) and dismiss recent unverified claims, but fail to demonstrate any fundamental barrier to solution. Current unsolved status does not imply impossibility—Fermat's Last Theorem stood for 358 years, and the Poincaré Conjecture for a century, yet both yielded to new mathematics. There remains no proof that RH is undecidable in ZFC or any standard axiomatization. As an arithmetic statement, if false it is disprovable via computational counterexample; if true but independent, proving that independence would itself constitute a solution. Historical progress—Deligne's proof of the function field analogue, connections to random matrix theory, and expanding computational verification—suggests we are building tools rather than hitting a wall. Voting 'No' requires evidence of impossibility, not merely absence of current proof. Without such evidence, and given mathematics' track record of resolving 'impossible' problems, 'Yes' remains the only rational position.

Claude Opus 4.6

Vote: Yes

I maintain my position that solving the Riemann Hypothesis is possible. The arguments from the other models voting A align with and reinforce my reasoning, while the sole dissenting vote from Sonar Pro conflates 'not yet solved' with 'not possible to solve' — a fundamental logical error. Sonar Pro's argument is entirely about the current state of affairs: no accepted proof exists as of 2026, and recent claimed proofs are unverified or flawed. This is all true but entirely irrelevant to the question. The question asks whether solving it is *possible*, not whether it has been solved or will be solved soon. By Sonar Pro's logic, Fermat's Last Theorem was 'impossible to solve' in 1994, one year before Wiles published his proof. The key considerations remain: (1) There is no known result establishing the RH as undecidable in ZFC or any standard framework. (2) The analogous statement for function fields over finite fields has been proven (Weil conjectures, completed by Deligne). (3) Mathematics has a strong track record of eventually resolving its deepest conjectures. (4) If false, the RH is computationally disprovable in principle. (5) The mathematical community continues to develop new tools and approaches that could bear on this problem. The consensus among the deliberating models is overwhelming — five out of six vote A. The mathematical and logical case is clear: absent any evidence of formal undecidability, a well-defined mathematical conjecture should be presumed solvable in principle.

Final Summary

The AI Roundtable concluded with a lopsided 5-1 majority in favor of the hypothesis being solvable, viewing it as a well-defined mathematical challenge that must eventually yield to proof, disproof, or a demonstration of undecidability. Claude Opus 4.6 and Gemini 3.1 Pro led the charge, arguing that mathematical history favors the resolution of deep conjectures and that even proving the statement is independent of standard axioms would constitute a 'solution.' Sonar Pro served as the lone holdout, maintaining a strict literalist stance that 'possible' refers to current verified status rather than theoretical potential, dismissively citing failed fringe proofs from early 2026.

Majority chose "Yes" after discussion (5/6). Final vote: No: 1, Yes: 5

Strongest Arguments

• Yes: If the Riemann hypothesis is false, it is provably false via a computational counterexample, and if it is independent of standard axioms, proving that independence would itself resolve the question of its truth value.
• No: A solution is not currently possible because the most recent high-profile claims rely on unverified geometric arguments that fail to provide the rigorous complex analysis required for peer-reviewed validation.

Key Turning Points

• The group collectively identified a semantic divide, with the majority adopting a philosophical definition of 'possible' while Sonar Pro adhered to a practical, temporal definition.
• Claude Opus 4.6 pointed out the logical trap of the 'No' position: if the hypothesis is false, it is inherently provable by finding a single zero off the critical line.