The greatest unsolved problem in computer science...
Fireship explains P vs NP: the $1M unsolved CS problem where proving P≠NP may be mathematically impossible.
- Clay Mathematics Institute offers $1M for a proof of P vs NP, either direction.
- P vs NP was formally defined by Steven Cook in 1971; John Nash implied P≠NP in a 1955 NSA letter.
- NP-complete problems (SAT, traveling salesman, protein folding) are mutually reducible — solve one in polynomial time, solve all.
- Traveling salesman with 15 cities yields ~87 billion possible routes; verification is trivial, discovery is not.
- RSA encryption rests on the fact that multiplying two primes is easy but factoring the product is hard — yet this hardness remains unproven.
- If P=NP, all encryption (passwords, crypto wallets) becomes instantly crackable; also potentially cures cancer via protein folding.
- After 50+ years and thousands of papers, there is zero proof either way — every proof attempt hits structural barriers.
2026-03-09 · Watch on YouTube
