Consciousness
You can recognize a strawberry’s color and say “red.” How does that processing relate to the way red appears to you?
Explore all problems.
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?
Riemann hypothesis
There are 25 primes up to 100 and 168 up to 1,000. Their uneven counts follow a broad trend; a conjecture about the zeta function predicts how far they can stray from a refined estimate.
Biological aging
Cells change, tissues lose resilience and organs age at different rates. Which changes drive the others, and how do they become a whole-body process?
Dark energy
The universe's expansion is accelerating. “Dark energy” names the gap in our explanation, while several different physical accounts remain possible.
Quantum gravity
Gravity describes a changing spacetime. Quantum physics describes matter and its possibilities. How should they work together in a single physical account?
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.
Room-temperature superconductivity
The goal is a material that conducts electricity without resistance at room temperature and normal atmospheric pressure. Achieving both conditions together remains a research target.
Birch and Swinnerton-Dyer conjecture
An elliptic curve has both rational solutions and an analytic function. The conjecture predicts that these two ways of studying it encode the same rank.
Matter–antimatter asymmetry
Matter and antimatter can annihilate each other. Yet the observable universe contains enough leftover matter to make stars, planets, and people. What produced that imbalance?
Eukaryogenesis
Complex cells with nuclei descended from simpler ancestors. How did their internal compartments, mitochondria, and distinctive cellular organization come together?
Functions of sleep
Sleep is essential, but why do its benefits require a state in which an animal becomes less responsive to its surroundings?
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?
Fusion power
Producing fusion energy is a milestone. Can a complete plant deliver more electricity to the grid than it consumes, repeatedly and with components that survive operation?
Hodge conjecture
Some topological features of a complex algebraic shape look as though they should come from smaller algebraic shapes inside it. Must they?
Strong CP problem
The theory of the strong nuclear force permits a kind of asymmetry that experiments find to be extraordinarily small. Why is nature so close to the symmetric case?
Evolution of multicellularity
Cells have repeatedly evolved into organisms that live and reproduce together. What turns a group of cells into a coherent evolutionary individual?
Memory engrams
Experiences leave lasting changes in the brain. How do those changes form a memory that can be preserved, revised, and retrieved later?
Unique Games conjecture
A special kind of constraint puzzle is predicted to remain hard even when almost all its rules can be satisfied.