Before LLM there has already been Fields medalist[0] who creates professional software[1].

[0]: https://en.wikipedia.org/wiki/Martin_Hairer

[1]: https://www.hairersoft.com/

This is a very humbling thought, thank you.

I'm waiting for the reverse, coding agents asking Terry Tao if the proof they plan working on is worthy of a Fields Medal

> It’s a tool. Good for some things but not for others and generally not to be trusted.

I agree completely you always need to check the work of LLM agents, but it does strike me as a tiny bit funny to anthropomorphize AI by using ‘trust’ while warning against anthropomorphizing the AI by using unchecked output. ;) Generally speaking, “trust” in AI has been going up very quickly as the models & harnesses improve, and as people figure out effective workflows.

I trust my hammer with nails but not screws… does that mean the hammer should generally not be trusted? The problem with AI is we don’t know the difference between nails and screws. (This may be where my analogy breaks down. :P) But I feel like saying don’t trust it isn’t as helpful as saying something like you should expect to spend more time planning and iterating than before, and you should expect tot spend more time reviewing and checking output than before, and learn how to use skills and context and subagents, and learn to use AI on some non-production low-consequence projects first. Saying ‘generally not to be trusted’ implicitly suggests not using AI, and doesn’t leave the reader with how to use AI. The goal is to build trust by building good workflows and by understanding what works well and what doesn’t, right?

> and generally not to be trusted

There are many AI bulls who adamantly disagree and cite Tao’s statements about LLMs for mathematical proofs as an example of how advanced and autonomous these systems already are

I wouldn't be surprised if that was actually more common than one might think

i'd imagine when microwaves first came out chefs were genuinely excited? it's pretty insanely magical to observe ... at first.

Terry Tao has actually been one of the more prominent voices in the math community exploring AI for cutting edge mathematical discovery. This particular post is a bit softer but he has also written a lot about using AI assistance for serious core research

Nov 2025: https://terrytao.wordpress.com/tag/artificial-intelligence/

https://academy.openai.com/public/blogs/terence-tao-ai-is-re...

> hobby project

It sounds more like a project that suits the tool.

The measured argument for these things all along is that this novel technology is uniquely capable, but not universally so. The phase we're in, collectively, is all about finding uses that fit it well and charting the boundaries of those that don't.

One of the most natural fits is for modest or supplementary efforts where the of imperfections and noise it introduces are irrelevant. But something being modest or supplementary doesn't relegate it to "hobby" status -- like a workshop jig, it can make all kinds of difference in how quickly and how well you reach your "serious" end.

What makes this a hobby project? He’s a university professor so developing teaching material is part of his job.

That is how it starts, trust is built on hobby projects.

But he's also using AI for formally verified math and for ideas in solving math problems. The part about it being ok because it is a supplement just means ok that these aren't formally verified and may have bugs, and may also mean ok to not credit the AI for the paper as it is just a visual supplement and not the main work.

Serious things tend to be long and tedious and potentially full of proprietary information.

It may be a question of perspective, but in my mind mathematics is upstream to everything else, including physics, biology, etc. And it doesn't just exist in the human mind or the "world of forms", as in Platon's realm of ideas. It's more fundamental than that, closer to the foundation from which all existence emerges. Our reality is like a shadow of a shadow, a fleeting illusion, compared to the eternal reality that gives birth to all lesser realities.

As for profit, there's a reason why governments and AI companies are hiring philosophers and mathematicians. It's not to make the world a better place for everyone, or to encourage the progress of human knowledge; but to gain cutting-edge advantages over their competitors. Same reason why theoretical physicists were prized before/during the Second World War.

It’s very much Terrence Tao style. His style is having long sentences that could have been broken down into shorter sentences but he chose not to. It doesn’t really affect reading comprehension.

When it comes to coding, non-programmers do not have to be in a defensive position worried that their job is under risk, instead they just see a great tool that saves them time, especially doing boring coding like dashboards, visualizations, interactive web-pages, or doing experiments that they otherwise would not have time for.

Or he just finds it an incredible time-saving tool to help him do more maths.

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