Interactive toys for the greatest unsolved problems, curious sequences, and beautiful structures in mathematics. Pick one. Play.
Enter any number. Halve if even, triple-plus-one if odd. It always reaches 1 โ but nobody can prove it.
Unsolved ๐Every even number > 2 is the sum of two primes. See the prime pairs arc across a number line.
Unsolved ๐Plot integers on a spiral, highlight the primes. Mysterious diagonal lines appear from nowhere.
Prime Mystery ๐ฌThe most famous fractal. Click to zoom infinitely deep. Endless complexity from zยฒ + c.
Fractal ๐ตJump forward or back โ whichever hasn't been visited. The arcs paint themselves into art.
Curious ๐Two rules, one ant. 10,000 steps of chaos โ then a highway emerges. Emergent order from nothing.
Automaton ๐ซPrimes differing by 2 โ (11,13), (41,43). Are there infinitely many? Watch them thin out.
Unsolved ๐ฒHow many primes below x? Plot ฯ(x) against its approximations. The $1M question lives here.
Millennium Prize ๐บColor Pascal's triangle by remainder. Mod 2 = Sierpinski. Mod 3, 5, 7 = other fractals.
Fractal ๐The butterfly that started chaos theory. Two nearly identical points โ wildly different futures.
Chaos ๐งฎThe hardest function in math. Watch Turing machine champions write as many 1s as possible before halting.
Uncomputable ๐Collatz meets the Halting Problem. A rigorous, original formulation that is provably undecidable.
Undecidable ๐One explicit polynomial in 16 variables. Pure integers, no machines. A named instance of Hilbert's 10th โ provably undecidable.
Hilbert's 10th โCan one collection of polygons be cut and reassembled into another? Scissors, glue โ and undecidability.
Geometry โ๏ธPredict a quantum measurement outcome above a threshold. Nature itself performs uncomputable processes.
Quantum ๐ชDoes this deterministic system enter a chaotic attractor? Even fully predictable equations can hide the uncomputable.
Dynamical Systems ๐งญIs this triangulated space a sphere? In high dimensions, no algorithm can always tell you.
Topology ๐คWill this AI ever violate a safety rule? Rice's theorem says: no universal checker exists.
AI Safety ๐The complete RondaniniโMirrane collection. Seven problems across six domains. All provably unsolvable.
The Collection ๐ฟNine paradoxes of being. Identity, meaning, regret, empathy, love โ questions that live inside consciousness.
Human ๐งญSix paradoxes of societies. Progress, values, collective will, culture โ questions that emerge from coordination.
Civilization ๐Six paradoxes of seeing. Representation, reality, illusion, silence โ the space between seeing and knowing.
Perception โณSix paradoxes of temporality. The present, the arrow, impermanence, continuity โ questions from inside the flow.
Time ๐ผNine paradoxes of sound. Tuning, silence, resolution, authorship โ the bridging exhibit that touches every wing.
Music