Unverified50% confidenceFactExact time
The true Millennium Prize Problem refers to a universal proof of whether smooth solutions always exist for three-dimensional incompressible fluids under general conditions — a question that has neither been proven nor disproven to this day.
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9/22/2026
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Partially VerifiedThe core question of the Navier-Stokes Millennium Prize Problem is: given smooth initial conditions in three-dimensional space, does the equation always have a global smooth solution?74% similarVerifiedThe existence of smooth solutions to the Navier–Stokes equations in three-dimensional space has not yet been mathematically proven, and is one of the Millennium Prize Problems offered by the Clay Mathematics Institute.73% similarUnverifiedTerence Tao suggests that if a similar self-replicating fluid machine could be constructed in the true three-dimensional Navier-Stokes equation, the answer to the Millennium Prize Problem would most likely be that blowup exists.71% similarUnverified三体问题对任意初始条件都不存在通用的闭式解，庞加莱在19世纪末通过数学证明揭示了其不可积性70% similarUnverifiedSince the Navier–Stokes equations were proposed in the 19th century, the existence and smoothness of their solutions has remained unproven.69% similar
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