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:
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.
I agree that visualization does not need to be perfect. One issue is that "correct visual output" depends on your expertise level. A visualization that is good to teach undergrads may be frustratingly bad to experts and researchers. Standards like "looking right" depend on the audience's ability to spot nuances and how focused they are on the fine details. If you want a visualization to work for the range of people from beginners to experts, you do need to focus a bit more on what it means for something to "look right" for multiple audiences, since the errors in the fine details may hinder a visualization's usefulness for more advanced audiences.
I've been using LLMs to create visualizations for math papers I come across. Prompting "Create a visualization for each segment of this article in the style of a 3 brown 1 blue video using manim." has yielded impressive results.
It helps me digest the content faster and allows me to read more articles than I otherwise would.
Sounds like 50/50 for the distribution? That means you are okay with a student getting a 40% across all your quizzes and then passing the class with a C-?
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.
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.
In my very small business, the supply of software has gone up (I'm building things), and they're custom to my business--so highly useful. Moreso than any off the shelf product could hope to be.
Only if you're working on a client consulting model perhaps, and not even then necessarily. There are lots of reports of vibe coded apps not holding up in production so they should be treated as prototypes. It's similar to the outsourcing trend where people reverted back to using in house talent once they realized how terrible most of the produced software was. The only difference is AI models get better but it remains to be seen if they can get to such an end to end stage that they can autonomously deploy to prod and diagnose any issues without human intervention. There have been some paths to that but I haven't seen it end to end yet.
Personal software is the future and a person building software for themselves tends to withstand enshittifcation. That's why I love when people open-source projects they love and are passionate about and I will always choose them over proprietary ones.
People always argue "well, Slack and Notion have distribution and the product isn't everything." Ok and? The person making it for themselves doesn't necessarily need distribution for it to be valuable. In fact, it's even more attractive that way.
Every time I wrote software that I was personally motivated to have and kept at it until it reached a comfortable equilibrium of utility, scope, and quality and then stopped? No one paid me.
Every time someone paid me to write software it was some combination of 1. not that interesting of a problem 2. no real utility i could see or touch, useful in some abstract way of making a number go up 3. involved a constant, painful maintenance burden 4. involved incident management of one kind or another 5. involved a long tail of details with no unifying principle other than a lot of implicit legacy constraints and stakeholders whose involvement waxed and waned with no seeming rhythm..
I'm a big fan of the new capability, it opens up new regimes of performance and correctness and capability for what I can achieve, that in turn grinds me up against math and theory that I had thus far been able to avoid, it's pushing me up the ambition ladder hard and that's a good thing.
But the change is a change in degree not in kind at least in the vibecode regime: it was always relatively fun and relatively easy to do one small program with modest requirements around defect rigor that had a big legible "oh cool!" surface that I didn't have to maintain. Fable doesn't seem any better than Opus at grinding detail work in the bowels of a compiler, but it sure can make an iPhone-scoped platform game with a bunch of bugs in it in a single shot?
If there's a job where you get paid for doing fun, high defect, "oh wow!" factor one-off software that you can immediately disavow any responsibility for? Fuck man, I should have had that job before Fable got that job.
Most of the stuff demoed on r/vibecoding are trivial programs, and they’re often buggy and full of holes. If that’s the type of software you produce then yes, you’ll probably be impacted. Thankfully that isn’t the majority of software.
It’s kind of like saying wedding photographers will be impacted because of the people posting on r/iPhoneography. Seems kind of silly doesn’t it.
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.
> 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.
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
Indeed. LLMs produce truly atrocious code, unmaintainable and unreliable. If you're vibecoding a toy to amuse yourself or something similar low-stakes, that's perfectly fine! For higher-stakes code, it's definitely not.
This is one of my favorite pieces of internet writing, up there with the SR-71 speed check and the Story of Mel. Every time I see it, I have to read it again and end up giggling through the whole thing.
> Marco Pierre White passionately defends chefs using microwaves. White dubbed microwaves “sensational things” and revealed he thinks they’re far better at preparing kippers than any other technique, like boiling or grilling
> José Andrés, a renowned Michelin-starred chef, New York Times bestselling author and internationally recognized humanitarian. He listed the microwave omelet as his number one foolproof dish and called it the “best fluffy omelet in the history of mankind!”
A more accurate analogy is Charles and Henry Greene using tech to construct an intricate rig to fasten the joints in a delicate jewelry box to fit inside the Gamble House. Yes, they could make the rig by hand, but time is a precious resource to people with so much to build.
What Tao and other artists of his caliber are demonstrating is that the tech is capable of building the rig. And the machine makers are incrementally demonstrating that the machine can make not only the jewelry box rig, but rigs to build rig-making machines.
Yep, I'm fairly certain that general learning algorithms acting upon an ANN (which is fairly general too, see the universal approximation theorem) can reach and surpass performance of the human brain. As we have approximately zero evidence that the human brain contains "magic," that is something that can't be modeled by an ANN of a practically feasible size. (I know about chaotic processes that can't be modeled precisely. The "magic" here would be the brain using such a process to make useful decisions. "Useful" not in a sense of a mixed strategiy. You can roll dice to do that.)
But, no, it's not "any day now." The required size and structure of the ANN is to be determined.
I thought the narrative a few months ago was that we had AGI[1]? What happened? It's not like these trillion dollar companies would have an interest in using AGI to hype up their technologies that they would need to replace a percentage of the global workforce over the next few years to justify their current valuations?
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.
It's probably a matter of short time until it's possible to disassemble any sophisticated software, rewrite it entirely with better features and usability, generate all needed artifacts, port to any platform. The only moat left is probably remote massive data storage. So if you want to replicate YouTube or TikTok, it's not impossible, but requires a lot more hardware assets than say anything that runs entirely locally (like operating systems or most video games).
How exactly do you envision this ? you will ask the ai to make youtube but better, people seperate the "what" from the "how" but they have a very complex relationship
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.
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…
Having started using Claude Code at work, I think coding as we now know it will probably no longer be a career path in 5 years at the outside.
I’m old. If I had to, I could retire tomorrow, albeit on a restricted budget. But I worry about the younger folks (like my 25-year-old nephew) who haven’t built up the resources to survive without working who are in the field right now. There’s going to be a mega disruption and writing code is going to go the way of calculating square roots by hand or hot metal typesetting. There will still people doing it, but it will very much be a niche endeavor.
It's a race to retool. If he can retool to an agentic coding environment quickly he will be OK. Might have to build up the skills outside of work if the current job doesn't allow for it, but I'm less worried about younger people realigning quickly. They're used to it, and younger people are so much more resilient/used to disappointment than we are (economic prospects have been so fucked for Zoomers for so long by so many "once in a lifetime" events and they still soldier on which is a huge testament to them).
Whether reviewing agentic code rather than writing it is a job he wants to do... Different question.
Its older people who can't or won't retool that are going to find that in the game of musical layoff chairs they won't have a chair left when the music stops (and some I've met haven't really internalized that they're even part of the game...)
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.
What do you mean not serious? He’s developing visual aids to teach students and to accompany his mathematical research papers. Also, not in this post, he’s been actively using LLMs to do real math research, that is, to prove theorems and solve problems.
Teaching, research and publication are the core activities of his job as a math professor. How does it get more serious than this?
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.
And then to write installers so your coworkers who aren’t liking instructions like “then make a gpg key and install pinentry-mac” can use the extremely useful vibe coded dashboards to make the prod site transparent and viewable, digestible to eyes.
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.
I have never seen a profitable enterprise that doesn’t have a core of people good at math defending the maximum money behavior. A lot more people graduate with math degrees than can get jobs in research maths, but finance, operations research, insurance companies, logistics, all can hire a lot of them. As a software engineer with a math degree, I find that some of software is like math, but not very often like research math and relatively few of my colleagues have math degrees.
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.
I wonder if LLMs modify their output when they realize they are interacting with a famous person.
By famous I mean someone whose biography is in the training data. All models know a lot more about Terrance Tao than they know about me, when he's working on his projects do the models know they don't need to explain "Besicovitch sets".
Since the system prompt likely includes something about not insulting the user, does the LLM modify it's responses if it realizes it's talking to famous politician, like "dont mention the time $politician was cancelled".
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?
Metamathematics, by Kleene, is programming in maths. Theoretical computer science is maths. A lot of foundations work is programming. Coding itself is like an extended problem set from a maths class. LaTeX itself is programming.
The difference to me is one of directionality - maths research is seeing a far off island and getting there by hook or by crook; bridge, draining the swamp, inventing an airplane or boat, whatever it takes. Software engineering is like covering a plain with tiles - every feature is ultimately filled in and the underlying beauty is obscured by a fractal of complexity required by the ever growing requirements.
I do not think he's shilling; I think you misread the tone of my comment. Added an extra word now to maybe make the intent clearer.
That said, I do think "honeymoon phases" are a real source of bias. But then I don't think he's going through one of those either. He's been trying to leverage these models for a while now after all.
He might still be under a more general "tech adoption trend" bias, but at that point I'd say the lines become a bit blurry.
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/
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.
I agree that visualization does not need to be perfect. One issue is that "correct visual output" depends on your expertise level. A visualization that is good to teach undergrads may be frustratingly bad to experts and researchers. Standards like "looking right" depend on the audience's ability to spot nuances and how focused they are on the fine details. If you want a visualization to work for the range of people from beginners to experts, you do need to focus a bit more on what it means for something to "look right" for multiple audiences, since the errors in the fine details may hinder a visualization's usefulness for more advanced audiences.
What format do you have it build? PNG? Svg? Open document drawing? I am interested.
I've been using LLMs to create visualizations for math papers I come across. Prompting "Create a visualization for each segment of this article in the style of a 3 brown 1 blue video using manim." has yielded impressive results.
It helps me digest the content faster and allows me to read more articles than I otherwise would.
LLMs to create and revise PIL (python image library) commands/params have saved me HOURs.
Regarding the changes to your grading weights: https://acbart.github.io/2026/04/19/proctored-grades/
Sounds like 50/50 for the distribution? That means you are okay with a student getting a 40% across all your quizzes and then passing the class with a C-?
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.
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.
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.
The humbling thought should be all the blue collar workers on r/vibecoding demoing their apps and games.
And then realizing they put together something that would have taken you a few days to do.
The supply of software is about to go way up, and that's going to massively impact demand unless every firm on earth is clamoring for more.
We're going to see if Jevons paradox holds true, or if wages get impacted drastically.
The supply of software has already gone up, and most of the new stuff is close to useless
In my very small business, the supply of software has gone up (I'm building things), and they're custom to my business--so highly useful. Moreso than any off the shelf product could hope to be.
Only if you're working on a client consulting model perhaps, and not even then necessarily. There are lots of reports of vibe coded apps not holding up in production so they should be treated as prototypes. It's similar to the outsourcing trend where people reverted back to using in house talent once they realized how terrible most of the produced software was. The only difference is AI models get better but it remains to be seen if they can get to such an end to end stage that they can autonomously deploy to prod and diagnose any issues without human intervention. There have been some paths to that but I haven't seen it end to end yet.
Personal software is the future and a person building software for themselves tends to withstand enshittifcation. That's why I love when people open-source projects they love and are passionate about and I will always choose them over proprietary ones.
People always argue "well, Slack and Notion have distribution and the product isn't everything." Ok and? The person making it for themselves doesn't necessarily need distribution for it to be valuable. In fact, it's even more attractive that way.
Every time I wrote software that I was personally motivated to have and kept at it until it reached a comfortable equilibrium of utility, scope, and quality and then stopped? No one paid me.
Every time someone paid me to write software it was some combination of 1. not that interesting of a problem 2. no real utility i could see or touch, useful in some abstract way of making a number go up 3. involved a constant, painful maintenance burden 4. involved incident management of one kind or another 5. involved a long tail of details with no unifying principle other than a lot of implicit legacy constraints and stakeholders whose involvement waxed and waned with no seeming rhythm..
I'm a big fan of the new capability, it opens up new regimes of performance and correctness and capability for what I can achieve, that in turn grinds me up against math and theory that I had thus far been able to avoid, it's pushing me up the ambition ladder hard and that's a good thing.
But the change is a change in degree not in kind at least in the vibecode regime: it was always relatively fun and relatively easy to do one small program with modest requirements around defect rigor that had a big legible "oh cool!" surface that I didn't have to maintain. Fable doesn't seem any better than Opus at grinding detail work in the bowels of a compiler, but it sure can make an iPhone-scoped platform game with a bunch of bugs in it in a single shot?
If there's a job where you get paid for doing fun, high defect, "oh wow!" factor one-off software that you can immediately disavow any responsibility for? Fuck man, I should have had that job before Fable got that job.
Most of the stuff demoed on r/vibecoding are trivial programs, and they’re often buggy and full of holes. If that’s the type of software you produce then yes, you’ll probably be impacted. Thankfully that isn’t the majority of software.
It’s kind of like saying wedding photographers will be impacted because of the people posting on r/iPhoneography. Seems kind of silly doesn’t it.
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.
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.
> 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 trust my hammer with nails but not screws… does that mean the hammer should generally not be trusted?"
I trust a hammer to be able to hit a nail, without breaking. But if the hammer is old and the wood brittle, I don't trust it anymore.
Using it for anything else (screws) has nothing to do with trust, but using the wrong tool.
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.
You could trust it to be probably correct but he wouldn’t have tried compiling it.
> 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
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?
They never will, because it seems to be a psychological effect among humans via the AI effect (see my sibling comment).
Indeed. LLMs produce truly atrocious code, unmaintainable and unreliable. If you're vibecoding a toy to amuse yourself or something similar low-stakes, that's perfectly fine! For higher-stakes code, it's definitely not.
This post inspired me to have Claude port my 30 year old high school German Java applet game to Javascript, complete with a faked git history:
https://github.com/bradfitz/koffer#der-verloren-koffe
Play online at https://bradfitz.github.io/koffer/js/
So neat seeing ~30 year old code come back alive.
Terry Tao using coding agents feels like watching a Michelin-starred chef discover microwave dinners and get genuinely excited about them.
I liked this article about an old recipe book and what cooking could have looked like if we took microwave cooking seriously: https://malmesbury.substack.com/p/my-journey-to-the-microwav...
This is one of my favorite pieces of internet writing, up there with the SR-71 speed check and the Story of Mel. Every time I see it, I have to read it again and end up giggling through the whole thing.
here you go, Michelin-starred chef:
> Marco Pierre White passionately defends chefs using microwaves. White dubbed microwaves “sensational things” and revealed he thinks they’re far better at preparing kippers than any other technique, like boiling or grilling
https://www.independent.co.uk/life-style/marco-pierre-white-...
And another one:
> José Andrés, a renowned Michelin-starred chef, New York Times bestselling author and internationally recognized humanitarian. He listed the microwave omelet as his number one foolproof dish and called it the “best fluffy omelet in the history of mankind!”
https://www.tasteofhome.com/article/jose-andres-microwave-om...
The comment specifically said "microwave dinners." That's frozen meals you just heat up in the microwave.
A microwave omelet is almost the same way, especially to a chef, many of which are very pretentious about their eggs.
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?
A more accurate analogy is Charles and Henry Greene using tech to construct an intricate rig to fasten the joints in a delicate jewelry box to fit inside the Gamble House. Yes, they could make the rig by hand, but time is a precious resource to people with so much to build.
What Tao and other artists of his caliber are demonstrating is that the tech is capable of building the rig. And the machine makers are incrementally demonstrating that the machine can make not only the jewelry box rig, but rigs to build rig-making machines.
People are so confident that this just-a-tool will hit its limits any day now...
People are so confident that this not-just-a-tool will show signs of ASI/AGI any day now...
Yep, I'm fairly certain that general learning algorithms acting upon an ANN (which is fairly general too, see the universal approximation theorem) can reach and surpass performance of the human brain. As we have approximately zero evidence that the human brain contains "magic," that is something that can't be modeled by an ANN of a practically feasible size. (I know about chaotic processes that can't be modeled precisely. The "magic" here would be the brain using such a process to make useful decisions. "Useful" not in a sense of a mixed strategiy. You can roll dice to do that.)
But, no, it's not "any day now." The required size and structure of the ANN is to be determined.
I thought the narrative a few months ago was that we had AGI[1]? What happened? It's not like these trillion dollar companies would have an interest in using AGI to hype up their technologies that they would need to replace a percentage of the global workforce over the next few years to justify their current valuations?
/s
[1]https://sequoiacap.com/article/2026-this-is-agi/
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
Ferran Adrià published a recipe for an omelette using potato chips.
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...
It's probably a matter of short time until it's possible to disassemble any sophisticated software, rewrite it entirely with better features and usability, generate all needed artifacts, port to any platform. The only moat left is probably remote massive data storage. So if you want to replicate YouTube or TikTok, it's not impossible, but requires a lot more hardware assets than say anything that runs entirely locally (like operating systems or most video games).
How exactly do you envision this ? you will ask the ai to make youtube but better, people seperate the "what" from the "how" but they have a very complex relationship
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.
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...
What makes this a hobby project? He’s a university professor so developing teaching material is part of his job.
> 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…
Having started using Claude Code at work, I think coding as we now know it will probably no longer be a career path in 5 years at the outside.
I’m old. If I had to, I could retire tomorrow, albeit on a restricted budget. But I worry about the younger folks (like my 25-year-old nephew) who haven’t built up the resources to survive without working who are in the field right now. There’s going to be a mega disruption and writing code is going to go the way of calculating square roots by hand or hot metal typesetting. There will still people doing it, but it will very much be a niche endeavor.
It's a race to retool. If he can retool to an agentic coding environment quickly he will be OK. Might have to build up the skills outside of work if the current job doesn't allow for it, but I'm less worried about younger people realigning quickly. They're used to it, and younger people are so much more resilient/used to disappointment than we are (economic prospects have been so fucked for Zoomers for so long by so many "once in a lifetime" events and they still soldier on which is a huge testament to them).
Whether reviewing agentic code rather than writing it is a job he wants to do... Different question.
Its older people who can't or won't retool that are going to find that in the game of musical layoff chairs they won't have a chair left when the music stops (and some I've met haven't really internalized that they're even part of the game...)
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.
That is how it starts, trust is built on hobby projects.
What do you mean not serious? He’s developing visual aids to teach students and to accompany his mathematical research papers. Also, not in this post, he’s been actively using LLMs to do real math research, that is, to prove theorems and solve problems.
Teaching, research and publication are the core activities of his job as a math professor. How does it get more serious than this?
Serious things tend to be long and tedious and potentially full of proprietary information.
Open science has plenty of long and tedious articles.
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
Using LLMs to generate dashboards is probably their most productive use case
And then to write installers so your coworkers who aren’t liking instructions like “then make a gpg key and install pinentry-mac” can use the extremely useful vibe coded dashboards to make the prod site transparent and viewable, digestible to eyes.
Using Fable with Anthropic Design skill works every time.
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.
I have never seen a profitable enterprise that doesn’t have a core of people good at math defending the maximum money behavior. A lot more people graduate with math degrees than can get jobs in research maths, but finance, operations research, insurance companies, logistics, all can hire a lot of them. As a software engineer with a math degree, I find that some of software is like math, but not very often like research math and relatively few of my colleagues have math degrees.
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.
Interesting point, I think you are right about it being upstream!
This is amazing!
I wonder if LLMs modify their output when they realize they are interacting with a famous person.
By famous I mean someone whose biography is in the training data. All models know a lot more about Terrance Tao than they know about me, when he's working on his projects do the models know they don't need to explain "Besicovitch sets".
Since the system prompt likely includes something about not insulting the user, does the LLM modify it's responses if it realizes it's talking to famous politician, like "dont mention the time $politician was cancelled".
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...
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?
Metamathematics, by Kleene, is programming in maths. Theoretical computer science is maths. A lot of foundations work is programming. Coding itself is like an extended problem set from a maths class. LaTeX itself is programming.
The difference to me is one of directionality - maths research is seeing a far off island and getting there by hook or by crook; bridge, draining the swamp, inventing an airplane or boat, whatever it takes. Software engineering is like covering a plain with tiles - every feature is ultimately filled in and the underlying beauty is obscured by a fractal of complexity required by the ever growing requirements.
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.
Tao is not an expert in math research? That's a really high bar then.
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.
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".
I do not think he's shilling; I think you misread the tone of my comment. Added an extra word now to maybe make the intent clearer.
That said, I do think "honeymoon phases" are a real source of bias. But then I don't think he's going through one of those either. He's been trying to leverage these models for a while now after all.
He might still be under a more general "tech adoption trend" bias, but at that point I'd say the lines become a bit blurry.
LLM will do very good job in pure mathematics since it don't need the senses to logically understand/conclude a given topic.