Every summit worth climbing
58 of the great open problems in human knowledge — the questions where the textbook runs out and the research begins. Pick one and Cordelet builds the climb from your altitude up to the frontier, ending at the real open problem and the honest lines of attack on it.
Mathematics
Riemann Hypothesis
A 160-year-old pattern in the primes that no one can prove — math's most famous open problem.
P vs NP
If a solution is easy to check, is it always easy to find? A million-dollar question at the heart of computing.
Navier–Stokes existence and smoothness
We use the equations of fluid flow daily — yet can't prove their solutions never blow up.
Birch and Swinnerton-Dyer conjecture
A startling claim that a curve's whole-number solutions are encoded in a single function.
The Collatz conjecture
A rule a child can follow, an answer no mathematician can prove. Start anywhere — do you always reach 1?
The twin prime conjecture
Primes keep turning up in pairs just two apart — forever? Simple to ask, brutally hard to prove.
Goldbach's conjecture
Every even number is the sum of two primes — checked into the quintillions, proven for none.
Physics
Quantum gravity
Our two best theories of reality contradict each other. Uniting them is physics' deepest quest.
The nature of dark matter
85% of the universe's matter is invisible and unidentified. What is it?
The nature of dark energy
Something is pushing the universe apart, faster and faster. We have no idea what.
The quantum measurement problem
Why does a particle's haze of possibilities snap into one outcome when we look?
High-temperature superconductivity
Some materials carry current with zero loss — and we still can't explain why.
The black hole information paradox
Throw a book into a black hole. Is its information gone forever — or would that break physics itself?
Why is there more matter than antimatter?
The Big Bang should have made equal parts that annihilated to nothing. The tiny imbalance is why anything exists.
Biology & Medicine
The origin of life
How did lifeless chemistry on the early Earth cross the line into living, replicating cells?
The basis of consciousness
How does three pounds of brain tissue produce the felt experience of being you?
The protein folding problem
A chain of amino acids folds into a precise machine in milliseconds. How does it know the shape?
The molecular basis of aging
Is aging an inevitable wearing-down, or a program we could one day slow or reverse?
A universal cancer cure
Why do our own cells turn against us — and could one strategy defeat them all?
How one cell builds a whole body
A single fertilized egg becomes trillions of precisely arranged cells. What reads the blueprint?
Computer Science
Artificial general intelligence
Can a machine match the full, flexible breadth of human thought — and how would we know?
The foundations of cryptography
All modern security rests on a bet: that some problems are truly hard. Can we ever prove it?
Quantum computing's true power
Which problems can quantum machines crack that ordinary computers never will?
AI interpretability
We build neural networks we can't read. Can we ever truly understand what they learn inside?
Provably correct software
Can we ever write software proven, mathematically, to be free of bugs and exploits?
Chemistry
Artificial photosynthesis
Plants turn sunlight, water and air into fuel. Can we engineer it to power the world cleanly?
Room-temperature catalysis of nitrogen fixation
Feeding humanity depends on a brutally energy-hungry reaction. Nature does it gently — can we?
Predicting a molecule's properties from first principles
Can we compute what a new material or drug will do before ever making it?
The origin of homochirality
Life uses only left-handed amino acids. Why did nature pick a hand — and why that one?
Designing a catalyst from scratch
Could we design an enzyme atom by atom, on a computer, for any reaction we want?
Earth & Cosmos
Are we alone in the universe?
Is life a cosmic fluke or a near-inevitability? The answer reshapes our place in everything.
Predicting earthquakes
Can the moment a fault will slip ever be forecast — or is the Earth fundamentally unpredictable?
Tipping points in the climate system
Where are the thresholds past which change becomes abrupt and irreversible?
Earth's magnetic field
A churning ocean of molten iron shields all life from space. How does it work — and why does it flip?
The origin of the Moon
A Mars-sized world struck the young Earth — maybe. We still can't fully explain our own Moon.
Neuroscience & Mind
The neural code
Thoughts and memories are patterns of firing neurons. What's the language they're written in?
How memories are stored and retrieved
A lifetime of experience lives in your brain. Where exactly, and how do you call it back?
Why we sleep and dream
We spend a third of our lives unconscious. Biology still can't fully say why.
The binding problem
Color, motion, and sound are handled by different brain regions. How do they fuse into one seamless experience?
How anesthesia switches off the mind
A simple gas can erase awareness entirely, then bring it back. What exactly does it switch off?
Language & Linguistics
The origin of language
No other species has it. How did human language begin — and why only us?
How children learn language
Toddlers master grammar no one teaches them, from a sliver of data. How?
Undeciphered scripts
Ancient writing no one can read, like Linear A. Are these lost voices gone for good?
Could we talk to animals?
From whale song to bee dances — is any of it truly language, and could AI translate it?
Economics & Society
What causes economic recessions
Whole economies lurch and crash. Can the booms and busts ever be truly understood — or predicted?
Aggregating preferences fairly
Can any voting system turn individual wishes into a fair collective choice? A theorem says: not perfectly.
Cooperation in the prisoner's dilemma
Self-interest predicts we should betray each other. Why does cooperation flourish anyway?
Why some nations are rich and others poor
Institutions, geography, luck? The single biggest question in economics.
Can markets be beaten?
If prices already reflect every known fact, no one should win. So how do some investors keep doing it?
Engineering & Energy
Practical nuclear fusion power
The reaction that powers the stars, in a box on Earth — clean, limitless energy, if we can tame it.
Grid-scale energy storage
Sun and wind are free but fickle. Storing their energy cheaply at scale would remake civilization.
Scalable carbon capture
Can we pull CO₂ back out of the air fast and cheaply enough to matter?
Cheap fresh water at scale
Two-thirds of the planet is water we can't drink. Can we make the ocean drinkable for everyone?
General-purpose robots
Machines beat us at chess but can't fold laundry. Why is the physical world so hard for robots?
Foundations & Philosophy
Do we have free will?
Are your choices truly yours, or the inevitable output of physics and neurons firing?
Why is there something rather than nothing?
The deepest question of all — why does a universe exist at all, instead of nothing?
The limits of proof
Gödel showed some true statements can never be proven. What does that mean for certainty itself?
Are we living in a simulation?
Could reality be something computed — and could we ever tell from the inside?