Some recurring tricks in the OpenAI math release

[u/mbintz]

Following OpenAI's big math paper release, the past couple days I've been getting some other LLM tools to comb through the whole dataset and look for recurring patterns. Partly because I was curious what we can infer about the internal OpenAI model through comprehensive analysis of the whole set of papers.

One thing that's turned up so far is the re-use of a few tricks (possibly new / non-standard ones) between papers, without direct internal citation. That is, when reading one manuscript, you wouldn't immediately know another uses the same idea.

Probably this comes from the proof-machines sharing a common workspace, and "inter-agent communication".

Below I'll use "=" loosely to indicate which parts should be compared. (I'll spare you the LLM summary of the math...)

Pair 1:
(a) Bloch’s conjecture for surfaces with p_{g}=0 [9/24]
(b) A high-arity counterexample to Pixton completeness in Chow [9/24]
(a, Lemma 3.3) = (b, Lemma 5.3)
(a, Lemma 5.1) = (b, Lemma 5.5)
Broadly (a, section 5.1-5.4) = (b, section 5.5-5.7)

Pair 2:
(a) Fujita’s freeness conjecture [9/23]
(b) The ordinary-double-point gap in every dimension [9/24]
(a, proof of Prop 3.2) = (b, Lemma 5.2)
(a, Lemma 3.1 and Eq. 5.5) = (b, Prop 4.1(i))
Broadly (a, section 4-5) = (b, section 4.2-4.4)

Pair 3:
(a) Minimal models and Mori fibre spaces for generalized log canonical Q-pairs [9/24]
(b) Bounded klt complements for Fano contractions [9/25]
(a, Lemma 8.3) = (b, Prop 14.3)
Broadly (a, Lemma 6.3 - section 8.3) = (b, Lemma 11.6 - Prop 14.5)

Pair 4:
(a) Sharp mass bounds for the two-dimensional O(4) model [9/23]
(b) The periodic spin-one Haldane gap [9/24]
(a, Lemma 2.1) = (b, Lemma 4.1)
(a, Prop 2.2) = (b, Prop 4.3)

Found these in Claude Code (Fable 5.1 calling Opus 5.5 and GPT Sol 6.1 subagents).

[u/changing_who_i_am]

What about broad/unique/unusual reasoning/process/methods? Like, what did it do that other models (or other humans) didn't, not just on one but across multiple problems? That's the more interesting piece IMO

[u/spyzoom]

Interesting. A ranked table with percentages of the heuristics used would probably be helpful for researchers / working mathematicians.

[u/BertMacklenF8I]

I doubt they're using Lexus Nexus lol