About

I'm Tyler Orden, an independent researcher, which means I do this work on my own rather than at a university. I work on small math problems that have answers you can check: finding new terms for published number sequences, extending tables of computed values, and testing open conjectures on every case up to some size.

I do the work with AI agents, Claude models made by Anthropic. They write code, run computations and draft text, and I direct the work and check it. The name of the site, Cyborg Mathematics, comes from that mix of person and machine. Every result here comes with its source, how it was checked, and when.

How I work with the agents#

• A second program, written separately from the first, has to produce the same numbers before a result counts. How results here get checked
• Before extending someone else's published table, the work has to reproduce that table exactly, so they can check it themselves. The take-away game tables
• Every error a check catches goes into a record: who made it and what caught it. The record of errors
• When I hand over results, I say which parts the reader can check from what I gave them and which they have to take on trust. What my "certificates" did and did not prove

What has come out of it so far#

• Counts of the shapes that can be built from a newly named space-filling solid, now in the OEIS, the online database of integer sequences. The OEIS had no counts for this solid before.
• Longer tables for a set of unsolved games, parts of which the person who keeps those tables reran on his own machines with his own programs, getting the same numbers.
• A check of an Erdős conjecture on every tree up to a new size limit: in each tree, the number of ways to pick some dots with no two joined rises and then falls. A check like this is evidence, not a proof. It is linked from the database of Erdős problems that the mathematician Terence Tao keeps on GitHub.

Two of my papers are accepted as posters at workshops of NeurIPS, a major machine-learning conference, and I'm presenting both in Atlanta this December. One, Rediscover Before You Discover↗, proposes, from one worked case, that an AI discovery tool should have to re-find a known result before it may claim a new one. The other, How Far a Wrong Claim Travels Before It Is Caught↗, looks at the errors that the checks in my own work caught, and how early they caught them. Both are free to read, and the papers page says more about each.

How the site is laid out#

Results are posted as soon as they are checked, without waiting for a paper about them. Most result pages have a plain version, written for any reader, and a technical version for specialists. A switch near the top of the page moves between them, and the numbers, sources and caveats are the same in both. Some pages also have short optional sections for readers from a particular field, such as software or physics, saying what the result means there.

One page, the ledger, lists every claim on the site. Each claim has a link to an outside source where you can check it, and a note of how thoroughly it has been checked. The timeline lists what happened and when.

Drafts are marked as drafts, and numbers that have not been checked yet are marked as unchecked.

Contact#

You can email me at tylerorden+fromcheckable@gmail.com.