Many visualizations that I have always wanted but just didn't have the time to build, I now have.
To give an example, I wanted a simplified 8-bit computer to complement the 16-bit teaching computer I use and designed this in a few days with the help of claude:
When I did my microcontroller class with lecturer hand drawing an 8-bit computer, the registers, memory, instructions on the white board, it was v cool to understand how things worked under the hood.
Wondered if someone could make more simulations for what was being taught. Teaching is about deciphering a thing into it's components and seeing how they interact. Vibe coded simulations are a great tool for that.
Using LLMs to build out the nice-to-haves that I’ve always wanted but never had time for is one of their great use cases. Visualizations are a perfect use case for this because they don’t have to be perfectly architected, maintainable code. Getting to the correct visual output is good enough, and LLMs excel at iterating something until it looks right.
Terry Tao using coding agents to build apps means we're one step away from a Fields Medalist asking an LLM why his Docker container won't start, just like the rest of us.
There is infinite latent demand for software, most especially outside the traditionally software-focused spaces. If LLMs stopped improving today it would take us 10 years to catch up to the new software-writing abilities that have become available. This is a great illustration of that fact.
"as such [LLM-coded interactive] supplements are not mission-critical to the core of the paper, I again feel that the downside risk of using guided interaction with LLM agents to generate such visualizations is acceptable."
It's a tool. Good for some things but not others 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 mean just from the above quote it’s clear he doesn’t trust them for “mission-critical” tasks. And I doubt LLms have evolved significantly from their stochastic parrot nature over the last few years
> 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?
I don't understand what trust means in this context. Even if I were able to hire Donald Knuth to write all my code, I wouldn't "trust" it to be bug-free, let alone to be the right fit for my needs.
Running legacy educational Java applets, especially around math and physics, has been a longstanding popular use case of our CheerpJ Applet Runner extension, running Java bytecode in the browser via WebAssembly.
I am not sure how to feel about agents solving the problem via proper modernization. It's certainly positive that students will be able to interact with this content in a modern and more accessible way, but the educational use case for our product, although not commercially important, has always been a source of pride.
I always enjoy these "domain expert has fun using AI to do something in their domain" articles. But it's always a hobby project, never something serious.
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.
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
> always a hobby project, never something serious.
I don’t know what you’re reading, but always and never are strong words. I’ll predict by this time next year you’ll have seen some pretty serious AI uses, and can no longer say always/never. Widespread use of AI coding is brand new, and the models only just barely got good enough to do serious things. It’s way too early to be using words like always and never, but FWIW I’ve already seen some serious uses. There are good reasons personal blog posts rarely talk about ‘serious’ production code; it may be against organizational policy, it may involve code that isn’t’ public, it may reveal proprietary information, and more…
even though there's still a lot of work to push things over the finish line, i have enjoyed how much it has reduced the activation energy for starting and finishing "one of these days..." projects!
I am far from a mathematician but I am excited by the possibilities of using AI for generating more math. Math in my mind exists purely in the world of forms, and cannot be appropriated for profit, but is downstream to everything else. I am keen to see what this enables.
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.
The article's awkward opening statement proves it wasn't written by AI.
I have been interested in machine-assisted ways to do and teach mathematics from as far back as 1999, when I started coding several applets in Java 1.0, both for my complex analysis and linear algebra courses, to visualize various mathematical objects I was interested in (such as honeycombs or Besicovitch sets).
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.
His website using mathematical knowledge is refreshing. There's a small UI bug, but personally, I wish more educational materials were this rich in audiovisual content.
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.
Why are mathematicians a kind of programmers? Besides applied maths, aren't they more researchers that explore and discover, in contrast to the majority of programmers who are more like handymen?
Building visualizations with LLMs has been a major boost for my CS classes:
https://htmx.org/essays/universities-and-ai/#demos-visualiza...
Many visualizations that I have always wanted but just didn't have the time to build, I now have.
To give an example, I wanted a simplified 8-bit computer to complement the 16-bit teaching computer I use and designed this in a few days with the help of claude:
https://bdp.cs.montana.edu/
This is v cool.
When I did my microcontroller class with lecturer hand drawing an 8-bit computer, the registers, memory, instructions on the white board, it was v cool to understand how things worked under the hood.
Wondered if someone could make more simulations for what was being taught. Teaching is about deciphering a thing into it's components and seeing how they interact. Vibe coded simulations are a great tool for that.
Using LLMs to build out the nice-to-haves that I’ve always wanted but never had time for is one of their great use cases. Visualizations are a perfect use case for this because they don’t have to be perfectly architected, maintainable code. Getting to the correct visual output is good enough, and LLMs excel at iterating something until it looks right.
Terry Tao using coding agents to build apps means we're one step away from a Fields Medalist asking an LLM why his Docker container won't start, just like the rest of us.
This is a very humbling thought, thank you.
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/
I'm waiting for the reverse, coding agents asking Terry Tao if the proof they plan working on is worthy of a Fields Medal
There is infinite latent demand for software, most especially outside the traditionally software-focused spaces. If LLMs stopped improving today it would take us 10 years to catch up to the new software-writing abilities that have become available. This is a great illustration of that fact.
Terry Tao using coding agents feels like watching a Michelin-starred chef discover microwave dinners and get genuinely excited about them.
i'd imagine when microwaves first came out chefs were genuinely excited? it's pretty insanely magical to observe ... at first.
I wouldn't be surprised if that was actually more common than one might think
People are so confident that this just-a-tool will hit its limits any day now...
This makes me curious.
Are there any documented essays or reactions from the great chefs of back in the day reacting to the first microwave dinners?
Nice balanced perspective there at the end:
"as such [LLM-coded interactive] supplements are not mission-critical to the core of the paper, I again feel that the downside risk of using guided interaction with LLM agents to generate such visualizations is acceptable."
It's a tool. Good for some things but not others and generally not to be trusted.
> 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
Statistical gradient descent token vomiter. We can all say it together. Nothing about this is advanced or autonomous.
This is like saying humans are a self contained electron transport system, nothing special or advanced about that, just a scaled up nematode.
The same AIs are doing math research now, you know. At what point do you stop explaining it all away?
I mean just from the above quote it’s clear he doesn’t trust them for “mission-critical” tasks. And I doubt LLms have evolved significantly from their stochastic parrot nature over the last few years
> 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?
I don't understand what trust means in this context. Even if I were able to hire Donald Knuth to write all my code, I wouldn't "trust" it to be bug-free, let alone to be the right fit for my needs.
Running legacy educational Java applets, especially around math and physics, has been a longstanding popular use case of our CheerpJ Applet Runner extension, running Java bytecode in the browser via WebAssembly.
I am not sure how to feel about agents solving the problem via proper modernization. It's certainly positive that students will be able to interact with this content in a modern and more accessible way, but the educational use case for our product, although not commercially important, has always been a source of pride.
https://chromewebstore.google.com/detail/cheerpj-applet-runn...
This is amazing!
I always enjoy these "domain expert has fun using AI to do something in their domain" articles. But it's always a hobby project, never something serious.
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.
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...
Serious things tend to be long and tedious and potentially full of proprietary information.
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.
> always a hobby project, never something serious.
I don’t know what you’re reading, but always and never are strong words. I’ll predict by this time next year you’ll have seen some pretty serious AI uses, and can no longer say always/never. Widespread use of AI coding is brand new, and the models only just barely got good enough to do serious things. It’s way too early to be using words like always and never, but FWIW I’ve already seen some serious uses. There are good reasons personal blog posts rarely talk about ‘serious’ production code; it may be against organizational policy, it may involve code that isn’t’ public, it may reveal proprietary information, and more…
even though there's still a lot of work to push things over the finish line, i have enjoyed how much it has reduced the activation energy for starting and finishing "one of these days..." projects!
Using LLMs to generate dashboards is probably their most productive use case
I am far from a mathematician but I am excited by the possibilities of using AI for generating more math. Math in my mind exists purely in the world of forms, and cannot be appropriated for profit, but is downstream to everything else. I am keen to see what this enables.
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.
The article's awkward opening statement proves it wasn't written by AI.
I have been interested in machine-assisted ways to do and teach mathematics from as far back as 1999, when I started coding several applets in Java 1.0, both for my complex analysis and linear algebra courses, to visualize various mathematical objects I was interested in (such as honeycombs or Besicovitch sets).
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.
i would take this every single time over some Claude rewrite slop
His website using mathematical knowledge is refreshing. There's a small UI bug, but personally, I wish more educational materials were this rich in audiovisual content.
The more Terry talks about AI, the more I'm starting to feel like Terry may have some undisclosed conflicts of interest.
https://www.reddit.com/r/mathematics/comments/1tryyw7/terenc...
Or he just finds it an incredible time-saving tool to help him do more maths.
The well-known shadowy bias and conflict of interest of "I just enjoy experimenting with this new thing".
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.
A lot of mathematicians are worried: https://arstechnica.com/tech-policy/2026/06/mathematicians-w...
Mathematicians are a kind of programmers, the original ones.
Why are mathematicians a kind of programmers? Besides applied maths, aren't they more researchers that explore and discover, in contrast to the majority of programmers who are more like handymen?
Disagree. Programming is about sequences (behavior, state, data, etc), math is about relations.
"When it comes to a field I'm not an expert in, AI is a great tool."
Every time.
Yes, because AI gets the "shape" of something right. If you don't know the field you don't notice the pockmarked surface.
I think the opposite is true.
So does anyone familiar with the Gell-Mann amnesia effect.
Tao is not an expert in math research? That's a really high bar then.
LLM will do very good job in pure mathematics since it don't need the senses to logically understand/conclude a given topic.