On Saturday night, mathematician Elliot Glazer published a new version of an AI-assisted manuscript about how to tell integers apart from other fractions. His first release, on Nov. 5, described a polynomial with 292,890,231,905 variables. The Nov. 7 revision gives an equation in 394 variables whose terms are available for readers to inspect. The paper claims the smaller equation does the same job as the original.
GitHub dates the revision to 8:41 p.m. Eastern and records a test of the newly posted files at 8:43 p.m. About 42 minutes earlier, Glazer had prepared a version with a 498-variable equation. Both smaller versions have degree four, meaning that the exponents in any term add up to at most four. The two versions use the same enormous fixed integer to express some coefficients, the numbers that multiply terms in the equation. That makes 498 to 394 the closest comparison. Saturday’s revision also gives a 411-variable version with every coefficient written in decimal.
SnowRock counted 6,338 distinct terms and 394 distinct variables in the published table, in line with the manuscript. The highest degree we found was four. To establish what the equation does, a proof has to cover every rational input, including ones no computer has tried.
An equation that picks out the integers
Rational numbers are fractions such as 3/2 or −7/5. Integers are the subset that can be written with a denominator of one. To use the proposed equation, put a rational number in the first slot, then ask whether there are any rational values for the other 393 slots that make the equation equal zero. The paper claims there is such a choice for every integer and none for any other fraction. For input 3, some set of values would work. For 3/2, every possible set would fail.
The question is related to a problem David Hilbert posed in 1900. He asked for a procedure that could take any polynomial equation with integer coefficients and decide whether it has an integer solution. Yuri Matiyasevich’s work completed a proof in 1970 that no procedure can always do that. Researchers also ask what happens if the solutions can be fractions. An OpenAI preprint released in October claims a negative answer for that version, and Glazer’s manuscript builds on its methods. Glazer’s claim is that a single polynomial can mark off the integers inside the rationals. If it holds, it would provide a way to translate integer-solution problems into rational-solution problems directly, by using the new equation to enforce which inputs count as integers.
What the checks cover
Glazer’s project credits OpenAI’s Astra 6 and Sol 6.1 and Anthropic’s Claude Opus 5.5 in developing the November manuscript, with Claude Fable 5.1 used for review. It also credits Gabriel Conant, working with ChatGPT, for reductions used in an earlier revision. The project gives readers code to check the coefficient table and some of the algebra used to get there. Those checks address whether the smaller formulas follow from the specified construction. The first GitHub run failed to reproduce the new table on Linux. A second passed on Linux and failed a file portability test on Windows. After two fixes to how the checks find files, both systems passed by 8:57 p.m. The passing checks establish that those tools can reproduce the table.
The public revision history shows why that distinction matters. A GitHub reviewer reported using a Claude research system to examine the Nov. 5 paper and flagged places where the authors needed to check cited results or spell out steps. The project responded in Version 10. A follow-up then pointed out a missing link in how the paper applied work by the mathematician Kazuya Kato. Version 11 added an argument connecting the two objects the paper needed to match. The latest revision keeps that repair and records which parts its own reviewers checked.
A separate reader, Carlos Toledo, reported rechecking finite calculations and 48 supporting files written for Lean, a program that checks proofs step by step. Toledo also posted a Lean proof that reaches the project’s conclusion if eight additional assumptions are granted. Toledo says he used Claude agents for that work. The project’s own Lean file still leaves its main result unfinished. Mathematicians now have both a concrete equation and a record of the arguments used to shrink it. The part that would settle the claim is a check of the remaining arithmetic arguments for the equation’s behavior on all fractions.
