I work on math problems whose answers can be checked independently, with AI agents doing the computing under my direction.

Main results, strongest first

OEIS:

the On-Line Encyclopedia of Integer Sequences, the reference database mathematicians use for number sequences. Volunteer editors review every entry.

Erdős problems:

open problems posed by Paul Erdős, tracked on erdosproblems.com.

• Erdős problem 993Aug 4, 2026

  I extended the exhaustive check of an Erdős conjecture, open at the time, from every tree with up to 29 vertices to every tree with up to 32, about 165 billion more trees, and found no counterexample.

  A tree here is a set of dots, called vertices, joined by lines, all in one piece and with no loops. The conjecture says that if you count the ways to pick 1, 2, 3 and more vertices with no two joined by a line, the counts always rise and then fall, with a single peak. Checking cases cannot prove it, but one tree that broke the pattern would disprove it. I posted the check on the problem’s forum on August 2, 2026 and August 9, 2026. Two AI-assisted proofs followed in September, one for large forests only (September 21, 2026) and one for every forest (September 27, 2026, by university authors using OpenAI’s GPT 6.0 Astra). In October a Lean version of the all-forests proof was accepted by both proof checkers of Palomar, a public registry of computer-checked proofs. Neither paper has been refereed, and the community database of Erdős problems on GitHub still records the problem as open. If that proof holds, my check is an independent computation that agrees with it on every tree up to 32 vertices.

  Posted on the problem’s forum

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• Conjecture provedOct 7, 2026

  A conjecture I published with my OEIS counts of dependency charts was later proved by Roberto Blanco Gómez.

  I counted the dependency charts (labeled DAGs) in which each task waits on at most two others. These were the first OEIS entries for these counts, and they run to 100 tasks, far past the only earlier table, which stopped at 7. I noticed that when each count is divided by the number of tasks, the remainder follows a simple rule, and published that as a conjecture in OEIS A397711. His proof is posted as a preprint (not yet refereed), and an OEIS editor approved his note of the proof on my entry.

  Proof posted as a preprint by Roberto Blanco Gómez, on Zenodo

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• Take-away gamesJul 22, 2026

  I extended the published tables of 12 unsolved take-away games, and the expert who keeps those tables reran 4 of them with his own programs and got the same results.

  In a take-away game, two players take turns removing counters from heaps under a fixed rule, and for many such games nobody knows whether the table of values that decides the best moves ever starts repeating. In July 2026 I took the tables two to four times further than before. Achim Flammenkamp, who maintains the reference tables, reran the game 0.007 (known as Treblecross) over his old range and three other games over their full new ranges, on his own machines, and his page credits the work. He has since taken every one of the games further himself.

  Rerun by Achim Flammenkamp, his octal-game tables

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• ChemistryAug 17, 2026

  I reproduced a peer-reviewed census of benzenoid molecules, found 6 errors and sent the corrections to its authors.

  Benzenoids are molecules made of fused hexagonal rings of carbon. Reproducing the 2018 census in full turned up 6 errors (in its tables, a figure caption and the text), while everything else matched exactly. The authors have not yet confirmed them. I then extended the census’s breakdown tables two sizes further; the OEIS already had the totals at those sizes, and mine agree with them.

  Totals match OEIS A018190

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Where to go next

• Results →Each computed result in full, with how it was checked
• Fields →The work by subject: shapes, sequences, games, graphs, chemistry and methods
• Writing →What the results mean, in plain words
• Highlights →The strongest results first, each with its outside check
• Ledger →Every claim in one table, with a link to check it yourself
• About →Who I am and how the work is done

• Oct 24, 2026What a long-standing error in a math database means for anyone who copies reference valuesWriting
• Oct 24, 2026Why checking a math conjecture on every case up to a size is not a proofWriting
• Oct 20, 2026Verify Before You AcceptPaper
• Oct 4, 2026Before my AI pipeline could hunt for new shapes, it had to rebuild a known oneWriting
• Sep 26, 2026A new best-known dominating set for the twelfth Fibonacci cube, and a month-long run with no answerWriting