The era of Big O speedrunning?

Many long standing algorithmic boundaries just got broken:

Problem Old bound New bound Source
3SUM on \(n\) polynomial-bit integers \(O(n^2)\) \(O(n^{1.9992})\) Anthropic
APSP on a directed graph with \(n\) vertices and polynomially bounded integer edge weights \(O(n^3)\) \(O(n^{2.9995})\) Anthropic
Subset Sum on \(n\) integers \(O^*(2^{0.5n})\) \(O^*(2^{0.49n})\) OpenAI
Multiplication of two \(n\)-bit integers \(O(n \log n)\) \(O\big(n \log^{1-2^{-182}} n\big)\) OpenAI
Exact discrete Fourier transform of length \(n\) \(O(n \log n)\) \(O\big(n \log^{1-10^{-13}} n\big)\) OpenAI
Exact single-source shortest paths in a directed graph with nonnegative real edge weights, with \(n\) vertices and \(\Theta(n \log^{3/4} n)\) edges \(O(n \log n)\) \(O(n \log^{11/12} n)\) Vals.ai

They just proved these bounds could be broken, but didn't put effort into lowering the exponent. There's probably low hanging fruit in each of those.

Chart of the claimed integer multiplication exponent saving per submission to CrocSwap/integer-mult-bounds, October 7-8, 2026, rising from about 10^-18 to about 4.1 × 10^-5.
Image: Rohan Arun

This website will track status on the problems, make it easy for people and agents to get started, and show speedrun-style leaderboards.

Inspired by the very successful NanoGPT speedrun, and hoping to bring similar progress and interest to our classic problems.