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 whose answers anyone 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 agents (Anthropic) working under my direction write code, run computations and draft text; I choose the problems, direct the work, check it, and decide what is published. 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.

What has come out of it so far#

• 3^▲ papers accepted by each workshop's program chairs as workshop posters. Two are at workshops of NeurIPS 2026, a major machine-learning conference, in Atlanta in December 2026. Rediscover Before You Discover↗, at the MATH-AI workshop, 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. How Far a Wrong Claim Travels Before It Is Caught↗, at the AI-Native Academia workshop, looks at the errors that the checks in my own work caught, and how early they caught them. The third, Verify Before You Accept: 33 Days of Incident-to-Rule Practice in an Operator-Supervised Agent Hierarchy, was accepted at the 3rd Workshop on Lifelong Agents, part of AIAS+ 2026, and I presented it as a poster at the workshop in San Francisco on November 7, 2026. It studies the records of my own team of AI agents: what the lead agent's rule of re-running or checking work before accepting it caught, and what got past it. All three are free to read, and the papers page says more about each.
• 50^▲ entries in the OEIS, the online database of integer sequences, credit this work, 26^▲ of them new sequences I authored; most of the rest are older entries I extended, with new terms or with notes recording longer computations. Among them are the counts of the shapes that can be built from the Josehedron, a newly named solid that fills space; the OEIS had no counts for this solid before.
• Longer tables for a family of unsolved take-away games. Achim Flammenkamp, who keeps the reference tables for these games, reviewed my solver code for one of the games, reran parts of the work on his own machines with his own programs, got the same numbers, and credits the work on his page.
• A check of an Erdős conjecture that I extended from every tree with up to 29^▲ vertices to every tree with up to 32, about 165 billion^▲ more trees. A tree here is a set of dots, called vertices, joined by lines, all in one piece, with no loops; the conjecture says that in every tree, the number of ways to pick some vertices with no two joined rises and then falls. A check like this is evidence, not a proof.
• Two of my pull requests (proposed changes) were merged by the mathematician Terence Tao into teorth/erdosproblems, the GitHub repository of Erdős problem data he maintains (erdosproblems.com itself is Thomas Bloom's site). One adds the OEIS tree-count sequence to the problem above, and its description cites my check; the other links seven more problems to their OEIS sequences. That makes eight problems in all whose database entries now show an OEIS link I added. A merge records the links; it is not an endorsement of the check.

How I work with the agents#

• A second program, written separately from the one that produced a result, has to produce the same numbers before the result counts. Both programs are usually written by Claude agents, so results are also compared with sources outside the work wherever one exists. More in 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, as with the take-away game tables.
• Every error a check catches goes into a record: who made it and what caught it. More in 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. One case is told in what an OEIS editor asked about my "certificates".

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 the main claims on the site, each with a link 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.