Interactive toys for the greatest unsolved problems, curious sequences, and beautiful structures in mathematics. Pick one. Play.
From playful undecidables to working AI: a multi-agent system attacking frontier research problems.
Enter any number. Halve if even, triple-plus-one if odd. It always reaches 1 — but nobody can prove it.
Unsolved 🔗Every even number > 2 is the sum of two primes. See the prime pairs arc across a number line.
Unsolved 🌀Plot integers on a spiral, highlight the primes. Mysterious diagonal lines appear from nowhere.
Prime Mystery 🔬The most famous fractal. Click to zoom infinitely deep. Endless complexity from z² + c.
Fractal 🎵Jump forward or back — whichever hasn't been visited. The arcs paint themselves into art.
Curious 🐜Two rules, one ant. 10,000 steps of chaos — then a highway emerges. Emergent order from nothing.
Automaton 👫Primes differing by 2 — (11,13), (41,43). Are there infinitely many? Watch them thin out.
Unsolved 🎲How many primes below x? Plot π(x) against its approximations. The $1M question lives here.
Millennium Prize 🔺Color Pascal's triangle by remainder. Mod 2 = Sierpinski. Mod 3, 5, 7 = other fractals.
Fractal 🌊The butterfly that started chaos theory. Two nearly identical points → wildly different futures.
Chaos 🧮The hardest function in math. Watch Turing machine champions write as many 1s as possible before halting.
Uncomputable 🌀Collatz meets the Halting Problem. A rigorous, original formulation that is provably undecidable.
Undecidable 📜One explicit polynomial in 16 variables. Pure integers, no machines. A named instance of Hilbert's 10th — provably undecidable.
Hilbert's 10th ◇Can one collection of polygons be cut and reassembled into another? Scissors, glue — and undecidability.
Geometry ⚛️Predict a quantum measurement outcome above a threshold. Nature itself performs uncomputable processes.
Quantum 🌪Does this deterministic system enter a chaotic attractor? Even fully predictable equations can hide the uncomputable.
Dynamical Systems 🧭Is this triangulated space a sphere? In high dimensions, no algorithm can always tell you.
Topology 🤖Will this AI ever violate a safety rule? Rice's theorem says: no universal checker exists.
AI Safety 🏛The complete Rondanini–Mirrane collection. Seven problems across six domains. All provably unsolvable.
The Collection 🌿Nine paradoxes of being. Identity, meaning, regret, empathy, love — questions that live inside consciousness.
Human 🧭Six paradoxes of societies. Progress, values, collective will, culture — questions that emerge from coordination.
Civilization 👁Six paradoxes of seeing. Representation, reality, illusion, silence — the space between seeing and knowing.
Perception ⏳Six paradoxes of temporality. The present, the arrow, impermanence, continuity — questions from inside the flow.
Time 🎼Nine paradoxes of sound. Tuning, silence, resolution, authorship — the bridging exhibit that touches every wing.
Music