Some questions in computer science have stayed open for decades, and a few carry
million-dollar prizes. This section explains them in plain English, and every problem
comes with a small interactive demo you can try in your browser: drop cities and watch a
route search explode, run a number through the Collatz sequence, or decide whether a tiny
program will ever stop.
These problems connect to the rest of the site. The halting problem runs back to Alan
Turing and the machines covered in our history of computer science,
and the mathematicians and engineers behind each idea have their own
biographies. Start anywhere below.
SHA-256 and elliptic curve keys guard a trillion dollars of bitcoin. See why brute force fails, what quantum changes, and try cracking a toy key in your browser.
P vs NP asks whether every answer that is quick to check is also quick to find. Covers NP-complete problems, the $1m Clay prize, and a subset-sum demo to play.
Why the busy beaver function defeats every algorithm, how BB(5) = 47,176,870 was finally proved in 2024, and a demo that runs the record machines in your browser.
Same structure, different drawing: pair up the vertices yourself in the demo, then find out why nobody can solve graph isomorphism quickly, or prove that they cannot.
What the travelling salesman problem asks, why brute force fails, and how solvers cope. Includes an interactive demo where heuristics race through billions of routes.