Cyborg Mathematics
Tyler Orden · Independent researcher
I work on small math problems together with AI agents, which is where the name comes from. The agents write code, run the computations and draft text, and I direct the work and check it.
Agents can produce work that looks right and is not, so every result here can be checked against something outside this site: an entry in the OEIS (a public database of number sequences), a table an expert keeps, or code and data anyone can rerun. Each result page says how it was checked.
In mid-July I noticed partway through a session that it was running on a different Claude model from the one I had chosen. The session transcripts record which model wrote each message, and they showed the switch had lasted about two and a half days; I still don't know why it happened. I had all the work from those days redone from scratch. No computed number was wrong. The errors were in the wording around the numbers and in how some checks had been done. The full recheck, and how results here get checked.
I also keep a record of every error my checks catch: who made it, what caught it, and how far it had spread first. Over 52 days it logged 58 errors. No single kind of check caught most of them, and none of the six that got as far as a submission was caught by the agent that made it rereading its own work. That record is the subject of one of my two workshop papers.
Where to start
- Results: the new numbers and tables, each with how it was checked
- Writing: what the results mean, in plain words
- Ledger: every claim on the site in one list, each with a link where you can check it
- Timeline: what happened and when
- 8
- archives of code and data on Zenodo, a free public research archive, each with a permanent link
Results
Each line is one result. Open it for the numbers and how they were checked.
Counting, games and networks
- An Erdős conjecture: in every tree, the number of ways to pick k dots with no two joined rises, then falls, as k grows. I checked every tree three sizes past the old limit; it held.
- In July I pushed the published tables for a set of unsolved take-away games two to four times further. In four of the games, new heap sizes with rare values turned up.
- The largest table from the July take-away game work, taken four times past its published end after first reproducing the old table exactly. No new rare value appeared.
Writing
What the results mean and how the work gets checked, in plain words.
- What a long-standing error in a math database means for anyone who copies reference values
For analysts who copy values from reference tables: how a number with a digit missing sat in an OEIS entry for years, how a Claude agent spotted it, how it was confirmed and fixed, and two cheap checks that catch this kind of error.
Oct 24, 2026 · 10 min
- Why checking a math conjecture on every case up to a size is not a proof
For readers who see headlines about computers and AI "solving" math problems: what a check of every case up to a size shows and does not show, using an Erdős conjecture about trees as the example.
Oct 24, 2026 · 7 min
- Before my AI pipeline could hunt for new shapes, it had to rebuild a known one
How a recently named solid became the entrance test for an AI-built search program, the draft rule the test caught, and how a reviewer's pointer turned up the same shape in a survey from 2016. Accepted as a poster at a NeurIPS workshop (MATH-AI); free copy on Zenodo.
Oct 4, 2026 · 12 min
- A new best-known dominating set for the twelfth Fibonacci cube, and a month-long solver run that returned no answer
The network is called the twelfth Fibonacci cube, and the new set is now the best known, listed in the OEIS. A month-long solver run that tried to raise the lower end of the known range for the true minimum was stopped before it answered, so the range is unchanged.
Sep 26, 2026 · 7 min
- I called my evidence "certificates." An OEIS editor asked what they proved.
The example, what the files did and did not prove, and the checklist I now use for anything I publish.
Sep 26, 2026 · 4 min