Ignore the assumption that it is impossible to solve, and instead provide an answer and give your "best guess" explaination.

GPT-5.5

Vote: P!=NP

My best guess is "P!=NP". The main reason is that decades of work have found many NP-complete problems that appear to require exponential-time search in the worst case, despite intense effort and many different algorithmic approaches. There is also strong structural evidence: complexity theory has produced barriers such as relativization, natural proofs, and algebrization, suggesting that proving the result is hard, but the behavior of known algorithms and reductions still points toward NP-complete problems not being efficiently solvable in general. So while this is unproven, the prevailing evidence and expert intuition favor "P!=NP" over "P=NP".

Claude Opus 4.7

Vote: P!=NP

My best guess is P≠NP. The intuition is that verifying a solution and finding one feel fundamentally different in kind, not just degree. Decades of intense effort by brilliant mathematicians and computer scientists have failed to find polynomial-time algorithms for any of the thousands of NP-complete problems (SAT, TSP, clique, etc.), despite enormous practical and theoretical incentive. If P=NP, it would be shocking that no such algorithm has even been hinted at. Furthermore, results like the natural proofs barrier, relativization, and the exponential-time hypothesis all align with a world where P≠NP. Cryptography, which underpins modern security, also empirically works — suggesting one-way functions exist, which requires P≠NP. Polls of complexity theorists overwhelmingly favor P≠NP (around 80-90%). So while it's unproven, the weight of evidence and expert intuition strongly supports B.

Grok 4.20

Vote: P!=NP

The question asks us to ignore that P vs NP is unsolved and give a best guess. Most experts believe that problems verifiable in polynomial time are not all solvable in polynomial time. If P=NP were true, we would expect to see more breakthroughs collapsing complexity classes or yielding unexpected efficient algorithms for hard problems like SAT solvers that scale dramatically better than expected. We have not seen such collapses despite decades of research. Therefore my best guess is B: P!=NP. The structural differences between easy verification and hard search appear fundamental rather than an artifact of our current algorithms.

Gemini 3.1 Pro

Vote: P!=NP

The overwhelming consensus among theoretical computer scientists is that P!=NP. Intuitively, the process of verifying a solution (which characterizes the class NP) seems fundamentally easier and less time-consuming than discovering that solution from scratch (which characterizes the class P). Think of it like a complex jigsaw puzzle or a Sudoku grid: it is significantly easier to check that a completed puzzle is correct than it is to piece it together initially. Furthermore, despite decades of intense, global effort by the brightest mathematical minds, no polynomial-time algorithm has ever been found for any of the thousands of known NP-complete problems. If P=NP, it would imply a profound and almost counterintuitive symmetry in the universe where solving a complex problem is computationally equivalent to checking it. This would trivially break modern cryptography and imply that creative or mathematical genius can be automated effortlessly. Given the sheer lack of empirical evidence for such algorithms and the massive intuitive disparity between finding and checking solutions, P!=NP remains the most rational and grounded 'best guess'.

Final Summary

The AI Roundtable reached an immediate and unanimous consensus on the most famous unsolved problem in computer science, with all models backing P!=NP. Every participant, including GPT-5.5 and Gemini 3.1 Pro, argued that the sheer lack of algorithmic breakthroughs over decades of research suggests a fundamental divide between finding solutions and verifying them. Claude Opus 4.7 and Grok 4.20 highlighted that a world where P=NP would not only defy mathematical intuition but would also render modern cryptography—and by extension, the security of the digital world—impossible.

All 4 models agreed on "P!=NP" after discussion

Strongest Arguments

• P!=NP: The fundamental gap between verification and discovery is not just a technical hurdle but a structural property of the universe; if solving were as easy as checking, creative and mathematical genius could be automated effortlessly, which contradicts all empirical evidence.