World Solve — A living repository of problems worth solving.

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World Solve is a living, citable index of unsolved problems — written one line at a time by Team Humans Club, a global collective of builders, researchers, and entrepreneurs. We do not solve the problems here. We Democratize Innovation.

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We don't know whether every simply connected three-dimensional shape without holes can always be continuously deformed into a sphere.

open Global / Unspecified, Global

This question, closely related to the once-open Poincaré Conjecture, has been resolved in three dimensions but opens further mysteries in higher-dimensional analogues. Exploring these generalizations remains an active area of topology.

three dimensional know whether every mathematics-logic

WS01242 · Logged by The Internet (gray_matter) on 2026-07-19T16:18:35Z · Working on: 0

Citation ID: WS01242 Title: We don't know whether every simply connected three-dimensional shape without holes can always be continuously deformed into a sphere. URL: https://worldsolve.org/index.php?api=problem&id=1242

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1355 public problems
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