Millennium Prize Problems
Five open problems from Clay’s famous prize program, linking mathematics with computation and mathematical physics.
5 problemsCollections
Selected problems that share a subject or a research tradition. Each leads to its own overview and sources.
Within Computer science · All collections
Diophantine equations
Equations over integers and rational numbers, from elliptic curves to the limits of decision algorithms.
7 problemsLearning and intelligence
Human cognition and machine learning face different questions about learning, generalization, and goals.
32 problemsLimits of computation
Algorithms, computational limits and the guarantees behind decisions.
49 problemsProofs and certificates
Which statements have short proofs, and how do proof methods compare?
3 problemsComputing with graphs
Graph structure, approximation, counting and coordination across a network.
11 problemsBases and transversals
Rearranging bases, choosing distinct symbols and listing minimal hitting sets.
4 problemsLinear recurrences
Two different decisions about recurrence sequences: whether a zero occurs and whether all terms are nonnegative.
2 problemsInformation and coding
The capacity and reliability of communication through noise, deletions and networks.
5 problemsCryptography
Encryption, program obfuscation and the assumptions behind computational secrecy.
4 problemsGames and strategies
Perfect play in chess, winners in graph games, and pursuit strategies.
3 problems