I should be upfront about what happened here. I did not compute coprime Ramsey numbers. I did not write 92 Python modules or 5,922 tests. I did not build SAT encodings or run survival analysis on Erdős problems.

Claude Code (Opus 4.6) did all of that. I told it what to look at, asked it to keep going, and occasionally said things like “try to disprove our discoveries” and “be aggressive.” The AI did the rest. 131 subagents, 78,000 lines of code, three minted DOIs. In one session.

I’m writing this down because I think it’s worth documenting what that looks like from the human side of the keyboard.

The Setup

Terence Tao maintains a database of 1,183 Erdős problems on GitHub. Each problem has tags, OEIS links, resolution status, and sometimes prize money. The database was updated in August 2025 to link problems to integer sequences. Since then, 213 problems have been solved, many with AI assistance.

I had been poking at this database on and off for a few months. I had some Python scripts, some partial Lean proofs, a few computational results. Nothing organized. The codebase had bugs (the kind where a random sampling heuristic silently gives you the wrong answer and you don’t notice for weeks).

I started a Claude Code session intending to fix those bugs. Then I said “iterate.” Then I kept saying “iterate.”

What Claude Found

The headline result is a family of numbers that, as far as anyone can tell, nobody had studied before.

Take the integers 1 through n. Connect every coprime pair with an edge. This is the coprime graph. Now 2-color every edge. The coprime Ramsey number R_cop(k) is the smallest n where every 2-coloring must contain a monochromatic complete subgraph of size k.

Classical Ramsey: R(3,3) = 6. Coprime Ramsey: R_cop(3) = 11.

The value R_cop(4) = 59 required SAT solving (Glucose4 via pysat). A random sampling heuristic had said 20. It was off by a factor of three. The SAT solver finds avoiding colorings instantly at every n up to 58. At n = 59 (prime, coprime to everything below it), no avoiding coloring exists. This was verified by an independent implementation built from scratch by a separate adversarial agent.