Logic and computation
What can be decided, proved, or computed.
13 problemsComputer science
Computation, algorithms, and learned AI systems.
Explore Computer science
Algorithms and data structures
Methods for efficient computation and organizing information.
28 problemsComputational complexity
The resources needed to solve computational problems.
30 problemsCryptography
Computational foundations of secure information and protocols.
4 problemsMachine learning
Systems that learn from data and generalize to new situations.
8 problemsInformation and coding
Recovering and transmitting information when observations are incomplete or noisy.
5 problemsCollections
Browse collectionsMillennium Prize Problems
Five open problems from Clay’s famous prize program, linking mathematics with computation and mathematical physics.
5 problemsDiophantine 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 problemsA few problems to explore
68 totalP versus NP
A proposed guest list can be checked against the rules. Does easy checking always come with an efficient way to find a list that works?
Mechanistic interpretability
We can inspect a neural network's numbers without understanding its computation. Can explanations become reliable enough to predict and check its behavior?
AI alignment
Alignment asks how AI systems can reliably follow intended goals and constraints, including in situations different from those used in training.
Graph isomorphism complexity
Two graphs can look different because their vertices have different names. Can we always decide efficiently whether they have the same connections?
Unique Games conjecture
A special kind of constraint puzzle is predicted to remain hard even when almost all its rules can be satisfied.
Derandomization
Random choices help many algorithms run quickly. Can every efficient algorithm with a bounded error probability be replaced by an efficient deterministic one?