Scalable fault-tolerant quantum computing
Error correction can protect small quantum computations. Can those ingredients become a machine that runs large, useful calculations with controlled errors and manageable resources?
Explore all problems.
Yang–Mills existence and mass gap
A successful framework for particle physics still needs a rigorous four-dimensional construction with a positive gap above its vacuum energy.
Hierarchy problem
The Higgs field sets an important scale in particle physics. Why is that scale so much smaller than other scales that may enter the underlying theory?
Sex chromosome evolution
Some lineages keep the same sex chromosomes for vast spans of time; others replace them repeatedly. Why do their evolutionary paths differ so much?
Neural coding
Neural activity carries information, but which aspects of that activity does the brain actually use? A pattern readable by an analyst need not be the pattern used for behavior.
Derandomization
Random choices help many algorithms run quickly. Can every efficient algorithm with a bounded error probability be replaced by an efficient deterministic one?
Solid-state batteries
Solid electrolytes promise new battery designs. Can a lithium-metal cell combine high energy, repeated cycling, safe operation, and manufacturability without impractical mechanical pressure?
Goldbach conjecture
Every even whole number greater than two appears to be the sum of two primes. A proof covering all of them is still missing.
Absolute neutrino mass
Neutrino oscillations show that neutrinos have mass differences, but they do not tell us the absolute masses. How light are these elusive particles?
Latitudinal diversity gradient
Many groups contain more species near the equator than near the poles. Which ecological and evolutionary processes generate this large-scale pattern?
Perceptual binding
Vision assigns colors, shapes, and movements to objects. How do distributed neural representations support those assignments without mixing features from different objects?
Matrix multiplication exponent
Multiplying two square matrices seems to require more work than writing their answer. Is the best possible asymptotic exponent actually two?
Lithium–sulfur batteries
Sulfur offers attractive battery capacity, but a practical cell must keep that capacity through many cycles without hiding its weaknesses behind excess electrolyte or lithium.
Twin prime conjecture
Prime pairs such as 11 and 13 are separated by two. Do such pairs keep appearing without end?
Majorana nature of neutrinos
A neutrino might be its own antiparticle. Establishing whether that is true would change how we understand neutrino mass and a basic particle-number symmetry.
Species coexistence
Many species persist together despite competing for resources. Which mechanisms keep any one competitor from excluding the others in real, changing ecosystems?
Language acquisition
Children build language abilities from experience while their brains are developing. How do learning, prior capacities, and interaction produce that transformation?
Classical integer factorization
77 = 7 × 11 is easy to check. Can a classical computer find the complete prime factorization of every integer efficiently as its written length grows?
Artificial photosynthesis
Devices can use sunlight to make fuels. Can direct solar-fuel systems remain efficient, selective, safe, and durable as they grow beyond carefully controlled demonstrations?
Odd perfect numbers
A perfect number equals the sum of its positive proper divisors. All known examples are even; the existence of an odd one remains unsettled.
Cosmic inflation
A short period of rapid expansion could explain several features of the early universe. What physical process, if any, produced it?
Genetic architecture of complex traits
Thousands of genetic variants can contribute to a trait, yet finding an association does not reveal how those variants work together to produce it.
Human general intelligence
Performance across different cognitive tasks is often related. Which brain mechanisms help explain that shared variation and the many abilities that do not reduce to it?
One-way functions
Can a function be easy to compute but hard to reverse on typical inputs? A rigorous unconditional example is still missing.