The world's unsolved problems
993 open questions across 14 fields, gathered from Wikipedia. Pick one and start thinking.
488 results in Mathematics · clear · surprise me
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Novikov conjecture on the homotopy invariance of certain polynomials in the Pontryagin classes of a manifold, arising from the fundamental…
Novikov conjecture on the homotopy invariance of certain polynomials in the Pontryagin classes of a manifold, arising from the fundamental group.
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Quadrisecants of wild knots
it has been conjectured that wild knots always have infinitely many quadrisecants.
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Telescope conjecture
the last of Ravenel's conjectures in stable homotopy theory to be resolved.
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Unknotting problem
can unknots be recognized in polynomial time?
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Volume conjecture relating quantum invariants of knots to the hyperbolic geometry of their knot complements.
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Whitehead conjecture
every connected subcomplex of a two-dimensional aspherical CW complex is aspherical.
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Zeeman conjecture
given a finite contractible two-dimensional CW complex K, is the space K \times [0, 1] collapsible?
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Nearby Lagrangian conjecture
prove or find a counter-example to the statement: Any closed exact Lagrangian submanifold of the cotangent bundle of a closed manifold is Hamiltonian isotopic to the zero section.
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Data last refreshed 2026-10-20 03:01 UTC.