Unsolved Problems
Showing 1-7 of 7 problems
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Problem Set
Status
The Mathematics of the Brain
Create a mathematically consistent, predictive model of brain function that goes beyond biological inspiration....
The Invariant Subspace Problem
Does every bounded linear operator on an infinite-dimensional separable Hilbert space have a non-trivial closed invariant subspace?...
The Schanuel Conjecture
If $z_1, \ldots, z_n$ are complex numbers that are linearly independent over the rationals, then the transcendence degree of $\mathbb{Q}(z_1, \ldots, ...
The Birkhoff Conjecture
If a billiard table is strictly convex and integrable, is it necessarily an ellipse?...
Invariant Subspace Problem
Does every bounded operator on an infinite-dimensional complex Banach space have a nontrivial closed invariant subspace?...
Mandelbrot Set Local Connectivity
Is the Mandelbrot set locally connected?...
Weinstein Conjecture
Does every regular compact contact-type level set of a Hamiltonian carry a periodic orbit?...