Unverified50% confidenceFactExact time
Pólya proved in 1921 that simple random walks in one and two dimensions return to the origin almost surely, whereas in three dimensions and higher they leave the origin permanently with positive probability.
1
Sources
50%
Confidence
Long-term
Relevance
9/11/2026
First Seen
Sources
Related Entities
Related Claims
UnverifiedThe 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?59% similarUnverifiedThe 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.58% similarUnverifiedCharikar 于 2002 年提出的 SimHash 指出随机超平面划分后两向量符号一致的概率等于 1 减去夹角除以 π57% similarUnverifiedThe AI's proof used tools from algebraic number theory such as infinite class field towers and Golod–Shafarevich theory, introducing algebraic number theory ideas into the unit distance problem in planar geometry.54% similarUnverified在纽结理论中，AI发现了双曲体积与代数不变量之间此前未知的函数关系52% similar
Cite This Claim
Stable URI
https://kongchang.com/claim/894628API
curl https://kongchang.com/api/v1/knowledge/claims/894628MCP
get_claim(id=894628)