a public catalog of open problems
Goldbach's Conjecture has been open for
284 yearsCan every even whole number greater than 2 be written as the sum of two prime numbers? It shares this board with 22 more of the hardest open problems in mathematics, physics, chemistry, and engineering — how long each has resisted, why, and what falls with it.
Mathematics 6 open
-
In 284 years no one has found an even number that isn't two primes added together — or proved that none exists
-
Primes thin out forever, yet we can't prove whether pairs separated by just 2 ever stop appearing
-
We can't prove the primes hide no secret pattern
-
Nobody knows whether the equations describing every breath of wind and splash of water can suddenly break down
-
A rule a child can follow — halve it, or triple it and add one — has trapped every number ever tested, and no one can prove it always will
-
We don't know whether every problem whose answer is easy to check is also easy to solve
Physics 6 open
-
Physics' two great theories contradict each other, and no one can unite them
-
Nobody knows what 85% of the matter in the universe actually is
-
No one can explain how quantum 'maybes' become the definite world we see
-
The Big Bang should have left an empty universe — nobody knows why matter survived
-
Some materials conduct electricity perfectly at temperatures no theory can explain
-
Something is pushing the universe apart faster and faster — and it may be changing
Chemistry 5 open
-
Life is built almost entirely from left-handed molecules, and nobody knows why
-
We still can't make fertilizer the gentle way that bacteria do
-
We still can't explain how ordinary chemistry turned itself into life
-
We still can't explain why glass is a solid
-
We're not sure whether water is secretly two different liquids
Engineering & AI 6 open
-
We made a star in a lab — we still can't plug one into the grid
-
Nobody knows how to guarantee an AI wants what we meant
-
The perfect wire exists — but only in a deep freeze or a diamond vise
-
Deep learning works far better than our math says it should
-
AI still confidently invents facts — and we can't fully make it stop
-
We deploy AI systems whose inner workings nobody can explain
What this is
A blackboard of the questions that are still open — the ones textbooks quietly skip past. Each entry states precisely what is unknown, how long it has resisted, what the best minds have managed so far, and what happens the day it falls. Every date, prize, and progress claim is cited to an authoritative source; nothing is invented or embellished.
- now — a curated board across four fields, sources verified at curation time.
- next — status watch: when a problem on this board falls, the board says so, fast.
- later — the frontier: who is attacking each problem, and with what.
When one of these falls, you’ll want to have known.
A short note when a problem falls, moves, or joins the board. Rare by nature.
Opens your mail app with a pre-filled note — a one-click form is coming.