The world's unsolved problems
993 open questions across 14 fields, gathered from Wikipedia. Pick one and start thinking.
Showing all 993 problems · surprise me
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Baum–Connes conjecture
the assembly map is an isomorphism.
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Berge conjecture that the only knots in the 3-sphere which admit lens space surgeries are Berge knots.
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Bing–Borsuk conjecture
every n-dimensional homogeneous absolute neighborhood retract is a topological manifold.
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Borel conjecture
aspherical and closed manifolds are determined up to homeomorphism by their fundamental groups.
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Halperin conjecture on rational Serre spectral sequences of certain fibrations.
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Hilbert–Smith conjecture
if a locally compact topological group has a continuous, faithful group action on a topological manifold, then the group must be a Lie group.
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Mazur's conjectures
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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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Definition of "disease"
There is no overarching, clear definition of what a disease is. On one hand, there is a scientific definition which is tied to a physiological process, and on the other hand, there is the subjective suffering of a patient and the loss of their life...
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Evidence-based medicine
Evidence-based medicine (EBM) has become the central paradigm in medical practice and research. However, debate continues around EBM and about how results obtained from large samples of patients can be applied to the individual.
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Lack of reliable diagnoses in some disorders
Though manuals like the Diagnostic and Statistical Manual of Mental Disorders (DSM) have covered a lot of ground when it comes to defining mental illnesses, in some disorders the reliability of diagnosis is still very poor. For example, inter-rater...
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Cultural issues in defining mental disorders
Some mental illnesses like paraphilias, compulsive sexual behavior, personality disorders, etc., are still at least partially defined by societal and cultural norms, rather than a threat to an individual's well-being.
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Still no causal classification of mental disorders
A patient with a paralysis is referred to an oncologist if the condition is caused by a cancer metastasis in the spinal cord; a treatment by a neurologist is a secondary consideration. Likewise, renal insufficiency is sometimes caused by heart problems,...
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Diseases with unknown cause
There are numerous diseases for which causes are not known. There are others for which the etiology is fully or partially understood, but for which effective treatments are not yet available.
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Mechanisms of action
It is sometimes unknown how drugs work. Often it is possible to study gene expression in a model organism, and determine the genes that are inhibited by a certain substance, and make further inferences from this data. A classical example of an unknown...
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Consciousness
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Problem of representation
How exactly does the mind function (or how does the brain interpret and represent information about the world)?
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Perception
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Learning and memory
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Neuroplasticity
How plastic is the mature brain?
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Cognition and decisions
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Language
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Language acquisition
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Data last refreshed 2026-10-20 03:01 UTC.