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Small-Scale Question Sunday for August 10, 2025

Do you have a dumb question that you're kind of embarrassed to ask in the main thread? Is there something you're just not sure about?

This is your opportunity to ask questions. No question too simple or too silly.

Culture war topics are accepted, and proposals for a better intro post are appreciated.

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Does anyone have a bead on the use of public (free?) LLMs for reasonably complex1 mathematics? Anything decent? Is there anyone writing on their personal use of it for that purpose somewhat regularly? Maybe some tips for structuring a prompt?

1 - Actually, I hope to keep this particular problem entirely real-valued.

Gemini 2.5 Pro is the best free LLM, because Google lets you use a nigh unlimited amount on AI Studio. All the other models of comparable quality are paywalled, but G2.5P is up there as one of the best nonetheless.

I've heard credible claims that a version that was allowed to think longer/in-parallel won IMO Gold this year, in conjunction with more bespoke models. I might be misremembering, but some people claimed to have gotten golds using just the public version and a lot of prompting.

Is there any indication that jumping to a paid, but publicly-available model is a significant improvement for math? I'm probably not going to spend the time right now to create my own bespoke setup.

Do any of the folks you've read talk about how they do their prompting? Like, can I just plop significant amounts of LaTeX straight from one of my papers into it for problem setup? Is there a better way of going about it?