Comment on math at Sydney. October 2026
When I applied for jobs in Fall 2024, I received an offer from the Sydney Mathematics Research Institute (SMRI). I asked what people knew of it, and the answer was mostly “nothing”, seasoned with concern that I’d disappear forever if I flew so far away. Having returned, my brief review is that it’s the place I know most aligned with contribution to the “long conversation¹” of mathematics. I was enriched by my time there, and would be happy to answer questions from anyone considering going.

Comment on AI disclosures. October 2026
Most AI disclosures I have seen are vague about the AI contribution (did it one-shot the problem? struggle but give directionally correct advice? totally unhelpful?), make no attempt to document how the AI was used (prompts, context, custom harness, tools...), or basic facts about resource consumption (money, time, model—GPT in May 2026 is very different from GPT in May 2025). Data sufficient for replication is impractical, but even a one-page explanation, stuffed in a dusty appendix, would improve on now-customary nothings like “Claude assisted in the writing of this paper”.

The case from honesty for such disclosures is left an exercise². There is also a case from existing convention, and from the field’s scientific goals. When ascribing claims to software in a paper, it is long-established convention to cite the software and provide source code, which is both a certificate for your claims and a way of informing the reader of your methods. If one (reasonably) feels LLMs are more like minds than software, then one should again acknowledge their contribution appropriately. “Alice supplied initial ideas that we developed into a counterexample” would typically entail Alice being an author of the work in question, and she would likely write something of the intuitions that led to her ideas. If Alice is an LLM, we might not understand or trust her post-hoc narration of her inuitions³, but a record of her process is the next best thing⁴. We should commit to really providing it.

Error in [CSW25]. October 2026
The statement of Theorem 3.20 should include “each join-irreducible is less than or equal to a unique maximal join-irreducible” in its bulleted list of conditions. Correction is on arXiv.

Comment on cleveref. May 2026
The “capitalize” option for cleveref is broken. To fix it, add \usepackage{thmtools} after \usepackage[capitalize]{cleveref} (thank you, Colin).

Comment on combinatorial journals. September 2025
Someone expressed to me confusion regarding two important combinatorics journals. Matters stand as follows: the editors of former flagships Journal of Algebraic Combinatorics and Journal of Combinatorial Theory, Series A resigned en masse in 2017 and 2020, respectively. They founded replacement journals Algebraic Combinatorics and Combinatorial Theory, which are where you should now submit papers (the originals are zombies). Editors at many other journals are moving likewise, e.g. Experimental Mathematics is now dead, replaced by the Journal of Experimental Mathematics. See here for more examples.

Clarification to [BES24]. March 2025
Sridhar Venkatesh observed that the definition of M-convexity given on page 25 is subtlely different from the one used in the proof of Proposition 5.3.3. Happily, the two definitions are equivalent by [Mur03, Section 4.2].

Error in [BES24]. March 2025
Matt Larson pointed out that the statement of Proposition 5.2.3 is false. A correction is on arXiv; main results are unaffected.

Clarification to [BES24]. January 2024
In an arXiv update, we have expanded the proof of Lemma 3.3.10, following comments by Matt Larson.

¹Mazur’s metaphor, which I learned from Geordie.

²Remark: if you’d like to see honesty, then don’t penalize it.

³AI introspection is an active area of research.

⁴Or maybe even the best thing. It is famously difficult to trace or summarize the arc of thought that leads to an idea. Despite unwieldy size, an archive of scratch work has the advantage of faithfully representing some part of the process, while post-hoc stories only approximate truth with fiction. In his much-discussed essay, Thurston describes familiar difficulty communicating his “real thoughts” via notes; one wonders what we might have gained by studying his scribblings, or better yet, by replaying the motion of his brain in variable circumstances, as one can do with LLMs.