Mathematics
Mathematical structures, relationships, and proofs.
146 problemsWhat’s still
not solved?
Explore open problems in science, mathematics, and engineering. Understand what’s known, what’s missing, and where to read more.
Find a subject.
Physics
Matter, energy, physical phenomena, and the universe.
106 problemsBiology
Living systems, their origins, and their mechanisms.
88 problemsCognitive science
Experience, cognition, and behavior.
58 problemsComputer science
Computation, algorithms, and learned AI systems.
68 problemsEngineering
Devices and processes with defined performance goals.
58 problemsCollections
Browse all collectionsMillennium Prize Problems
Five open problems from Clay’s famous prize program, linking mathematics with computation and mathematical physics.
5 problemsThe observed universe
Unseen matter, cosmic expansion, energetic particles, and brief radio flashes.
40 problemsOrigins and complexity
From the first living systems to complex cells and multicellular organisms, explore several transitions in life’s history.
10 problemsA few open problems.
Consciousness
You can recognize a strawberry’s color and say “red.” How does that processing relate to the way red appears to you?
Collatz conjecture
Choose a positive whole number. Halve it if it is even; otherwise triple it and add one. Repeat. Does every starting number reach one?
Dark matter
Bent light and galaxy motions reveal gravity that known stars and gas cannot fully explain. What supplies the additional mass?
Origin of life
Before there were cells, there were molecules. How did chemical systems begin passing useful abilities to descendants and sustaining their own reproduction?
P 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?
Dreaming
A sleeping mind can build vivid worlds. Do those experiences perform a function, reflect other useful processes, or do both?