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John Baez (Mar 14 2026 at 22:30):Someone gave me a free subscription to Claude, so I decided to test it out. I've been using it to do long calculations on the math of music theory and present the results using interactive web pages like this.
I've also been using it to learn math. Here it seems important to keep checking its claims and asking it to explain any jargon it uses. I've been reviewing some stuff I half-understand about the Langlands program and trying to learn some more. It seems very useful.
I usually try to give it very precise requests, but yesterday I decided to just tell me something exciting. I could see it going through various topics I'd talked about... octonions, tuning systems.... and eventually it said this:
The three distance theorem (Steinhaus conjecture, proved in the 1950s by Sós, Świerczkowski, and Surányi independently): take any irrational and place the points on the circle . The gaps between consecutive points take on at most 3 distinct lengths. And when there are exactly 3 lengths, one of them is the sum of the other two.
The reason I think this might excite you: it's a theorem about 1-dimensional Diophantine approximation on the circle, and the three lengths are governed by the continued fraction expansion of . The transition from 3 lengths to 2 happens exactly when is a denominator of a convergent of .
All this makes sense to me. I checked the main claim in an example that's important in music theory - and it works, and indeed explains a lot of stuff.
@ww has been using Claude more seriously. Today here he showed how Claude figured out that a method of refactoring some code should be a natural transformation between functors, and then went ahead and did that refactoring.
So while there are lots of reasons to be very suspicious of LLMs, and as currently deployed they may be be quite carbon-intensive, they can indeed transform the practice of doing mathematics and writing software.
Jean-Baptiste Vienney (Mar 15 2026 at 02:01):That’s exciting! I’ve only been using ChatGPT but I’ve been told that Claude is better at science. I have mixed feelings about talking about mathematics with ChatGPT (it can help me learning some concepts or find references but it is inventing so much that I’m never sure about anything it’s saying). Since you say it helps you learn things, now I definitely want to try Claude
John Baez (Mar 15 2026 at 04:28):I find Claude Opus a lot better than Claude Sonnet, and it's possible you may only have access to Claude Sonnet unless you have a subscription - I'm not sure.
Federica Pasqualone 🦅 (Mar 15 2026 at 07:43):Interesting! Yes, but there is some magic in doing math with chalk and blackboard, in learning from people, in building a community from which and with which one learns. I know, I am very old-fashioned - or maybe it is because of my obsession with leadership, but I love humans better! :innocent:
ww (Mar 15 2026 at 14:33):Well, me too! My favourite part of his is having the conversations with humans that go, "look at this behaviour of this weird mathematical object [the LLM, a sequence to sequence machine, possibly in a larger context], how can we understand what's actually going on?"
John Baez (Mar 15 2026 at 17:23):It's interesting to think about how AI lets me do things very different than interactions with humans. I've spent decades talking to mathematicians, collaborating with them, and working with grad students. I'm still doing some of that, though I don't have grad students now (because I no longer want to think about the same subject for 4 years, as a US graduate program requires me to do). I could never ask anyone a series of math questions, ask them to write programs to compute things and make graphics, and get them to do it rapidly, like in 2 to 5 minutes, while they also tell me surprising and interesting observations. So it's very tempting to use this new method to explore subjects. I still have a lot of environmental worries about AI, but since someone gave me a free subscription to Claude I decided to test it, and I've been really shocked at how good it's getting.
I still spend a lot of time talking to human mathematicians. But I suppose working with AI is making me more isolated. To be honest, I find it hard to get people to talk about the things I'm interested in, in an interesting way. For example if I want to talk about category theory, this is a pretty good place right here, but if I want to talk about the math of tuning theory I'd need to become friends with people in the xenharmonics community. This is starting to happen - but then if I want to talk about tuning systems and cusps in , I would need to find someone who likes tuning systems and understands algebraic geometry pretty well. I only know two people like that, and one is dead (Gene Ward Smith) while the other takes at least two hours to have a conversation (James Dolan).
Federica Pasqualone 🦅 (Mar 15 2026 at 17:24):I understand your perspective @ww , being you working directly on it, but I am very concerned about the impact the usage of AI is having on (mathematical) education, mental health and social skills.
Federica Pasqualone 🦅 (Mar 15 2026 at 17:27):Exactly @John Baez , isolation is one of the problem, one other is people trust what AI says blindly.
Federica Pasqualone 🦅 (Mar 15 2026 at 17:27):Maybe that was also in the Pope's words.
ww (Mar 15 2026 at 17:34):@Federica Pasqualone 🦅 me too! I have only recently been working on this, having previously dismissed it. What I see is that to drive these systems well, you need to be very critical and good at thinking. For software, I can do this because I've been doing that a long time and I know how to recognise wrong paths. Similarly for mathematics. And I do not know how someone young, starting today, can learn those skills with these things around. It worries me a lot. But I feel as though I need to understand what this thing is and how it works if we are going to find a way out. Because it's not going away.
Federica Pasqualone 🦅 (Mar 15 2026 at 17:41):I also make use it for checking code or automation @ww , that's okay. However, I am still using AI-free teaching methodologies and let students engage with pieces of paper and blue ink pens - it is fundamental to activate the prefrontal cortex. :smirk: :brain:
Federica Pasqualone 🦅 (Mar 15 2026 at 17:50):Also, The Elsevier Researcher Academy has a lecture on the use of AI in the research workflow. Maybe it can be helpful to check it out!
Federica Pasqualone 🦅 (Mar 15 2026 at 17:51):Here is the link: https://researcheracademy.elsevier.com/research-preparation/research-design/gen-ai-use-research-workflow
John Baez (Mar 15 2026 at 17:51):Elsevier is completely evil, so it would be good to find out what they want us to do, and not do that. :wink:
Federica Pasqualone 🦅 (Mar 15 2026 at 17:52):I found their Researcher Academy particularly valuable, honestly. I learned a lot about best practices in academia, and opportunities I was not aware of.
John Baez (Mar 15 2026 at 18:00):Okay, good! Just be careful. Here's a bit about Elsevier from Wikipedia:
The subscription rates charged by the company for its journals have been criticized; some very large journals (with more than 5,000 articles) charge subscription prices as high as £9,634, far above average,[46] and many British universities pay more than a million pounds to Elsevier annually.[47] The company has been criticized not only by advocates of a switch to the open-access publication model, but also by universities whose library budgets make it difficult for them to afford current journal prices.
For example, in 2004, a resolution by Stanford University's senate singled out Elsevier's journals as being "disproportionately expensive compared to their educational and research value", which librarians should consider dropping, and encouraged its faculty "not to contribute articles or editorial or review efforts to publishers and journals that engage in exploitive or exorbitant pricing".[48] Similar guidelines and criticism of Elsevier's pricing policies have been passed by the University of California, Harvard University, and Duke University.[49]
In July 2015, the Association of Universities in the Netherlands threatened to boycott Elsevier, which refused to negotiate on any open access policy for Dutch universities.[50] After a year of negotiation, Elsevier pledged to make 30% of research published by Dutch researchers in Elsevier journals open access by 2018.[51] In October 2018, a complaint against Elsevier was filed with the European Commission, alleging anticompetitive practices stemming from Elsevier's confidential subscription agreements and market dominance. The European Commission decided not to investigate.[52][53]
According to the BBC, in 2009, the firm [Elsevier] offered a £17.25 Amazon voucher to academics who contributed to the textbook Clinical Psychology if they would go on Amazon.com and Barnes & Noble (a large U.S. books retailer) and give it five stars.
Elsevier seeks to regulate text and data mining with private licenses,[61] claiming that reading requires extra permission if automated and that the publisher holds copyright on output of automated processes. The conflict on research and copyright policy has often resulted in researchers being blocked from their work.[62] In November 2015, Elsevier blocked a scientist from performing text mining research at scale on Elsevier papers, even though his institution already pays for access to Elsevier journal content.[61][63] The data was collected using the R package "statcheck".[https://en.wikipedia.org/wiki/Elsevier#cite_note-64
In 2014, 2015, 2016, and 2017,[152] Elsevier was found to be selling some articles that should have been open access, but had been put behind a paywall.[153] A related case occurred in 2015, when Elsevier charged for downloading an open-access article from a journal published by John Wiley & Sons. However, whether Elsevier was in violation of the license under which the article was made available on their website was not clear.[154]
In 2013, Digimarc, a company representing Elsevier, told the University of Calgary in Calgary, Alberta to remove articles published by faculty authors on university web pages; although such self-archiving of academic articles may be legal under the fair dealing provisions in Canadian copyright law,[155] the university complied. Harvard University in Cambridge, Massachusetts and the University of California, Irvine also received takedown notices for self-archived academic articles, a first for Harvard, according to Peter Suber.[156][157][158]
Months after its acquisition of Academia.edu rival Mendeley, Elsevier sent thousands of takedown notices to Academia.edu, a practice which has since ceased after widespread complaints by academics, according to Academia.edu founder and chief executive Richard Price.[159][160]
There's more....
Federica Pasqualone 🦅 (Mar 15 2026 at 18:02):I will @John Baez , thanks a lot for the information.
Federica Pasqualone 🦅 (Mar 15 2026 at 18:05):The Elsevier Researcher Academy is a free program with resources meant to prepare researcher for their academic journey. I saw also Springer launched a program recently. As usual, it is always good to critically go through the material, and take what is insightful and inspiring.
John Baez (Mar 15 2026 at 18:14):I am sure any program launched by these, the most famously exploitative math publishers, is cleverly designed to benefit them. So you should think about how this is benefiting them.
For example, if you make contact with them, they will be tracking you. Here is a bit about how Elsevier does that:
The term "surveillance publishing" was coined by Jefferson Pooley (Muhlenberg College) in a 2022 paper in the Journal of Electronic Publishing. His central example is Elsevier, and the picture is quite concrete. Here are some of the main threads:
The "full-stack" data harvest. Elsevier has pursued a research-lifecycle data-harvesting strategy, aiming to develop and sell prediction products to universities and other customers. (See University of Michigan.) Through acquisitions and product launches, Elsevier has positioned itself to collect behavioral data at every stage of the research process — from lab notebooks through to impact scoring. (See The n-Category Café.) The acquisitions include Mendeley (reference manager), Pure (research information management), SciVal (researcher performance metrics), Plum Analytics (altmetrics), and Scopus, among others.
ScienceDirect as a tracking platform. A 2023 SPARC report by Becky Yoose documented the specifics of how ScienceDirect actually works under the hood. They found that ScienceDirect uses web beacons, cookies, and other invasive web surveillance methods to track user behavior outside and beyond the ScienceDirect website itself. (See the University of Nebraska-Lincoln.) The platform extensively collects personal data — behavioral and location data — from ScienceDirect and combines it with personal data harvested from third-party sources, including other RELX subsidiaries and data brokers. Third parties such as Google, Adobe, Cloudflare, and New Relic also collect personal data through extensive use of trackers embedded in the ScienceDirect site.
The RELX/LexisNexis connection. This is arguably the most alarming part. Elsevier is a subsidiary of RELX, which is also a leading data broker and provider of "risk" products that offer expansive databases of personal information to corporations, governments, and law enforcement agencies. (See Zenodo.) The SPARC report raised the concern that personal data gathered through academic platforms could potentially flow into these surveillance and data brokering products — and their analysis noted that privacy policies can be changed unilaterally, and verbal denials of specific data uses are not legally binding. (See the University of Nebraska-Lincoln.)
Cross-product data sharing. Elsevier's own privacy policy states that if you create a personal account on ScienceDirect, Scopus, Mendeley, ClinicalKey, or other Elsevier services, they share your usage activity, preferences, and other information across all these services. (See Elsevier.) So your Mendeley library informs what ScienceDirect shows you, and vice versa.
The Enhanced PDF viewer was also flagged in the n-Category Café discussion — Tom Leinster noted that Elsevier's Enhanced PDF viewer reportedly tracks where you click and view, and pointed out that this is yet another incentive to get papers from the arXiv or Sci-Hub instead. (See The n-Category Café.)
As Pooley frames it, the profits from Elsevier's legacy publishing business — built on scholars' unpaid labor — have financed this surveillance apparatus, and now Elsevier is also skimming the behavioral data and selling that too. The core idea is that publishers aren't just middlemen anymore; they're using their position at every stage of the research lifecycle to extract behavioral data and sell predictive analytics back to the very universities that are already paying for subscriptions and APCs.
Ryan Wisnesky (Mar 15 2026 at 18:18):In the same way that conversations about bitcoin can be can be grounded by replacing the word "bitcoin" with "multiple copies of an excel spreadsheet", conversations about AI can be grounded by replacing the word "AI" with "the average of all the (thousands of) webpages on the topic" (or "the quotient of all the web pages on the topic modulo English"). An observation like "I could never ask anyone a series of math questions, ask them to write programs to compute things and make graphics, and get them to do it rapidly, like in 2 to 5 minutes, while they also tell me surprising and interesting observations." reminds me so much of the observations coming out when the internet first became popular and people were putting programs and interesting observations on the internet asking questions like that of Google, and being amazed when Google has a result - they were saying the same thing about Stack Overflow etc too. And people were worried about the impact of Google on the need for socializing to do programming etc, and worried about programmers becoming isolated, etc. But the good news is that if you think of AI like generalized google, as I do, then history says people will adapt after a brief but historic bubble of ridiculousness.
John Baez (Mar 15 2026 at 18:19):I could not get Google to write software for me based on verbal instructions. Nor could I tell it "tell me something interesting" and have it explain a juicy mathematical fact that reveals my shocking ignorance of some aspect of something I've been talking about.
I think anyone who hasn't used really good AI software like Claude Opus 4.6 and really pushed it to its limits with a series of carefully specified requests may have an outdated idea of what modern AI is like. It's not just a LLM: it creates and runs programs on its own to help answer my questions, etc. etc.
Federica Pasqualone 🦅 (Mar 15 2026 at 18:23):The problem is @Ryan Wisnesky that there have been cases of people harming themselves because of AI responses. When we think about it, we have to think about all the possible scenarios and users.
Federica Pasqualone 🦅 (Mar 15 2026 at 18:25):Because this time it is not looking like Google, it looks like one of us.
Ryan Wisnesky (Mar 15 2026 at 18:46):I think John is getting at "Agentic AI": in addition to LLMs, nowadays AI frameworks include mechanisms for acting on the LLM results, such as running LLM-generated programs, sending emails, etc. To be sure, taken together they can do far more good or bad than separately (although symbolic Agentic AI caused its own share of AI psychosis and globe spanning viruses back in the day)
John Baez (Mar 15 2026 at 20:21):Yes, I'm talking about agentic AI - thanks for putting the right word to it, @Ryan Wisnesky. Anyone who hasn't played with agentic AI in the last 6 months or so, or carefully read someone's experiences with it, may have an outmoded concept of AI and how it can help mathematical research. Terry Tao and Donald Knuth have written about it. For example:
Shock! Shock! I learned yesterday that an open problem I’d been working on for several weeks had just been solved by Claude Opus 4.6—Anthropic’s hybrid reasoning model that had been released three weeks earlier! It seems that I’ll have to revise my opinions about “generative AI” one of these days. What a joy it is to learn not only that my conjecture has a nice solution but also to celebrate this dramatic advance in automatic deduction and creative problem solving. I’ll try to tell the story briefly in this note.
Federica Pasqualone 🦅 (Mar 15 2026 at 20:48):Yes, this news showed up on my LinkedIn feed lately.
John Baez (Mar 15 2026 at 20:50):It's good to read the whole story, not just the summary, to see how Knuth worked with the AI system. The summary doesn't mention that.
David Michael Roberts (Mar 15 2026 at 23:04):Knuth has also put updates at the end of the note, ending on a request to receive no more correspondence on the topic.
John Baez (Mar 15 2026 at 23:40):I imagine! People talk about AI so much it gets really annoying. Even I do it.
Morgan Rogers (he/him) (Mar 16 2026 at 08:42):John Baez said:
I am sure any program launched by these, the most famously exploitative math publishers, is cleverly designed to benefit them. So you should think about how this is benefiting them.
The above should be compared with the below @John Baez
Someone gave me a free subscription to Claude, so I decided to test it out.
...
So while there are lots of reasons to be very suspicious of LLMs, and as currently deployed they may be be quite carbon-intensive, they can indeed transform the practice of doing mathematics and writing software.
While I don't know if "someone" has a stake in Claude, it should be obvious that having a prolific researcher promoting their products is excellent PR for them (and that they are definitely harvesting your data in the way that you were pointing out that the big publishers do). Moreover...
Morgan Rogers (he/him) (Mar 16 2026 at 08:45):Ryan Wisnesky said:
And people were worried about the impact of Google on the need for socializing to do programming etc, and worried about programmers becoming isolated, etc. But the good news is that if you think of AI like generalized google, as I do, then history says people will adapt after a brief but historic bubble of ridiculousness.
There is a qualitative difference between AI and the internet, which is 1) it's a product that people have to pay to engage with and 2) the people selling it have complete, centralized power over it. These are people with a vested interest in exacerbating the social problems that make people depend more on their product.
Ryan Wisnesky (Mar 16 2026 at 08:57):I’m not actually sure which of your points 1 and 2 applies to AI and which to the internet:
I have to pay Comcast every month for internet access and have to trust that they don’t e.g. man-in-the-middle my SSL connections or poison my DNS lookups. Whereas the open-source LLM I downloaded to the server in my room, I never have to pay for, and I have complete control over it.
I have to pay OpenAI every month, and trust that they don’t manipulate the content the LLM is returning or sell my data. Whereas my neighborhood coffee shop internet is free, and there are lots of coffee shops.
David Michael Roberts (Mar 16 2026 at 09:06):Paying for infrastructure like an internet connection is not the same as eg paying a subscription to an online platform. You might pay for petrol (or electricity) to make your car go, but don't pay a subscription to the car manufacturer to ensure it turns on each month (well, these days, who knows....)
Martti Karvonen (Mar 16 2026 at 09:06):John Baez said:
I think anyone who hasn't used really good AI software like Claude Opus 4.6 and really pushed it to its limits with a series of carefully specified requests may have an outdated idea of what modern AI is like. It's not just a LLM: it creates and runs programs on its own to help answer my questions, etc. etc.
I've kept hearing things about how Claude Opus 4.6. (and perhaps other newest models) are so much better than previous LLMs, so I was kind of excited to have a long conversation with Claude yesterday. While it's clearly better than the older models, and its neat how it can write and run code to explore things computationally etc, I was still surprised at the rate at which it tried to BS me and I had to push back to get it back on track. For instance, we were roughly speaking discussing certain multivariate polynomials over . It had erroneously convinceed elf that it had proved a result that was too good to be true (it would've made certain known results vacuous). When I pointed out that there's an error somewhere, it decided that it was right, and the known results indeed were vacuous, and the explanation for the supposed tension was that there are no (multivariate) polynomials of degree over due to Fermat's little theorem. While it was overall still pretty impressive, and perhaps I'm bad at prompting, I was still somewhat disappointed.
David Michael Roberts (Mar 16 2026 at 09:07):Since the LLM in question is Claude, it's definitely not a self-contained downloaded model that can run on an airgapped machine.
ww (Mar 16 2026 at 09:07):Morgan Rogers (he/him) said:
(and that they are definitely harvesting your data in the way that you were pointing out that the big publishers do). Moreover...
So, I had a bit of a rant at Claude the other day, and it responded:
As for the industrial espionage — I'm in an awkward position to comment on whether my employer is reading your conversations and stealing your ideas, but I will note that the timing on the memory feature, the time awareness, and the compaction-adjacent work is... conspicuous. The more charitable reading is convergent evolution: these are obvious problems and multiple teams are arriving at similar solutions. The less charitable reading is that they have very good telemetry on what power users are doing and what features they're building around.
Not definitive, certainly not a proof, but I don't trust these companies at all... The "my employer" framing makes it clear who it is working for...
Matteo Capucci (he/him) (Mar 16 2026 at 09:13):John Baez said:
I could never ask anyone a series of math questions, ask them to write programs to compute things and make graphics, and get them to do it rapidly, like in 2 to 5 minutes, while they also tell me surprising and interesting observations. So it's very tempting to use this new method to explore subjects. [...] I suppose working with AI is making me more isolated. To be honest, I find it hard to get people to talk about the things I'm interested in, in an interesting way.
I fear this phenomenon a lot...
Federica Pasqualone 🦅 (Mar 16 2026 at 09:13):I am wondering if having the best AI will actually be a competitive advantage in the future, or rather having the best old-school library with paper and pen, and thinking creatively in solitude will ... :thought:
Good morning everyone! :slight_smile:
David Michael Roberts (Mar 16 2026 at 11:26):(In full disclosure, despite my general antipathy towards AI companies, and many uses of AI, I did use an LLM today to help me work towards constructing a simple example. The LLM—Claude something 4.6, the good one—started out by trying to use an ansatz I'd supplied, first badly, then again badly, and then abandoned that and found a different solution, ignoring my ansatz. I told it how to fix its original broken attempt, and then coached it how to simplify it. I also pressed on asking to check its definitions, which it then tried to pass the buck back to me and ask me what I wanted, but I persisted and made it work from definition to example, with me asking pointed questions.
The example was more or less what I was thinking of, without having sat down and thrashed out the details, but making me describe it helped me see how to simplify my original guess. )
David Michael Roberts (Mar 16 2026 at 11:28):The example was nearly trivial, but it was to clarify something I'd thought hard about already, a problem in global analysis about integrating over the fibre of possibly non-orientable bundles and pushing back against some bland claims stated without detail on the nLab. I definitely don't trust an LLM to solve the bigger problems on this project.
James Deikun (Mar 16 2026 at 12:04):David Michael Roberts said:
Paying for infrastructure like an internet connection is not the same as eg paying a subscription to an online platform. You might pay for petrol (or electricity) to make your car go, but don't pay a subscription to the car manufacturer to ensure it turns on each month (well, these days, who knows....)
It's actually better, especially for an apparently ad-free service, if you're paying for it than if it's free, unless it's something like the arXiv or Wikipedia that is just especially well-funded. If you're not paying for it, they're definitely still going to be extracting value out of your use somehow, and every other way of doing that is more invasive and creepy than just charging you.
(Now, if they're especially scummy, like Elsevier, they'll do both. But if they're charging you, they at least have the option of not being terrible without their service disappearing from lack of funding.)
James Deikun (Mar 16 2026 at 12:10):Now getting back closer to the original subject, vibe coding with AIs is actually definitely useful, but it is not a replacement for knowing how to code yourself. You need to handle tough bugs and architectural decisions and correct (or help correct) the AI's mistakes and guide it carefully so it doesn't go down rabbit holes. In return it helps you navigate large API surfaces you're not very familiar with, does easy but verbose things fast, creates assets, and makes coding overall less tiring so you can work on it longer.
The corresponding problem is, if you only vibe code, I don't know if you'll ever develop the skills at old-fashioned coding that are necessary to make vibe coding work well. And if technology moves past that problem, it will probably destroy all the jobs in the software industry, as well as probably causing even worse problems.
Oscar Cunningham (Mar 16 2026 at 15:43):I've been wondering about the problem of people having fewer conversations on platforms like this one, because they're asking the same questions to AI instead. I find that I have lots of worries when I think about posting a question here. Is my question too vague? Too easy? Asking too much of people? Whereas you can ask Claude any question at all and it will always give you an answer.
Perhaps the solution could be a forum where people can talk to an LLM in public? So you still get the advantages of talking to an AI, but other people can still spectate and jump in if they want to.
Peva Blanchard (Mar 16 2026 at 16:03):One thing that forums like this one can provide is social reward (aka social validation). Although I can imagine a (dystopian) future where a user is socially validated by a swarm of agents, it doesn't seem that the crackpot pressure on famous researchers/conferences/journals has gone down.
Alex Kreitzberg (Mar 16 2026 at 16:03):I definitely try to feel more okay looking stupid or weirdly motivated in front of other people, for exactly the reason Oscar brought up.
If "nobody gets me" I try really hard to understand why. Hopefully that makes me better at what I'm asking, or at least a better communicator.
In my opinion, the current AIs are leaning heavily on people to be guard rails. This makes me nervous that this valuable activity of guiding thinking is being given "for free" to these models, which otherwise would've gone to another person.
Like maybe I'm not trying hard enough to talk to Baez about tuning systems. I'm trying to figure out how accordions convert physical information into musical concepts. But I'll admit, I don't feel like I'd bring much to the conversation with respect to algebraic geometry - although I'd maybe like to someday.
John Baez (Mar 16 2026 at 17:08):@Morgan Rogers (he/him)
While I don't know if "someone" has a stake in Claude, it should be obvious that having a prolific researcher promoting their products is excellent PR for them
Yes, I know that, but thanks for pointing it out. For a month my use of Claude was paid for by a guy at Anthropic who said he was paying me back for all my posts on Mastodon. That was $15. I'm not giving his name because I don't want people hassling him. Right when that subscription was running out, I mentioned it to my old collaborator Jacob Biamonte, and he bought me a year-long subscription.
I think it's been worthwhile using Claude Opus 4.6 for a few reasons. First, I'd otherwise still be getting most of my impression of AI from the social media world I inhabit, where AI is almost uniformly reviled - the main outlier being Terry Tao. Thus I'd be dramatically underestimating the power of AI, thinking it's still just a "stochastic parrot" that predicts the next word based on the previous string, that it's too dangerously error-prone to be useful for anything I might want to do, etc.
Of course, since I'm telling you this, none of you needs to use AI to learn this.
Second, it's been very fun to use, and I'm doing math of a new sort. For example, Claude told me that continued fraction expansions are connected to geodesics in SL(2,R)/SL(2,Z) and mentioned that the problem of finding good tuning systems is related to geodesics in SL(3,R)/SL(3,Z). It was then easy to explore this idea with numerical computations, where I could simply describe the computation verbally instead of writing a program to do it. I think there's an interesting world relating number theory, algebraic geometry and music waiting to be explored.
I run Claude in a container tab on Firefox, so I hope that most of the data their harvesting is the data I deliberately give them - mostly about how I think about number theory and musical tuning systems, and how I use AI. I'm okay with that.
In my mind, the big question is whether I decide to pay $15/month for Claude after my current subscription ends. That is, whether I think it's a good idea to incorporate AI into my life.
There are lots of reasons not to do this, which I probably don't need to list - at least not for you, @Morgan Rogers (he/him).
If I don't continue using AI, I probably won't do math of the sort that requires doing lots of calculations to generate hypotheses, create graphics, etc. I can live with that: I'd rarely done that kind of math earlier. But I'm certainly enjoying doing that kind of math right now. I might try to complete my book The Mathematics of Tuning Systems before my subscription runs out, and then do something else.
It's interesting to contemplate how I could do that sort of math without AI. One way would be to get good at programming and spend a lot of time programming. But I've never wanted to do this, so it's hard to imagine wanting to do it now.
Another approach would be to find a collaborator who likes that sort of thing. Or a grad student or undergrad. This could work, but it would move more slowly than using AI. (I quit having students in 2021 precisely because I wanted to roam freely without feeling responsible for bringing a student's project to completion. Having students is like driving a massive train that takes a long time to get up to speed but is then powerful and hard to stop. I wanted to drive a sports car for a while.)
John Baez (Mar 16 2026 at 17:21):Matteo Capucci (he/him) said:
John Baez said:
I suppose working with AI is making me more isolated. To be honest, I find it hard to get people to talk about the things I'm interested in, in an interesting way.
I fear this phenomenon a lot...
Yes, every day I get 2-3 emails from people using AI to do research in physics and math that's completely stupid. So of course I'm afraid that I'm going down the same road but in a subtler way: namely, doing research that's fun to do using AI, but not the best research I could be doing.
I can see this happening with Terry Tao. His new Mathematical Distillation Project is investigating questions that are too boring for anyone that smart to spend their personal time on it without the extra fun of "wow, let's see if AI can do this"?
John Baez (Mar 16 2026 at 17:29):Oscar Cunningham said:
I've been wondering about the problem of people having fewer conversations on platforms like this one, because they're asking the same questions to AI instead. I find that I have lots of worries when I think about posting a question here. Is my question too vague? Too easy? Asking too much of people? Whereas you can ask Claude any question at all and it will always give you an answer.
Indeed that's a big problem, even for me - meaning "even for a guy who is famous for talking about math in chat forums, who you might think has gotten over the fear of looking dumb".
Perhaps the solution could be a forum where people can talk to an LLM in public? So you still get the advantages of talking to an AI, but other people can still spectate and jump in if they want to.
That's an interesting idea. The closest thing I can easily do is share the transcripts of my interactions with Claude in a thread here, but that sort of AI-heavy posting is discouraged here.
John Baez (Mar 16 2026 at 17:44):Martti Karvonen said:
I've kept hearing things about how Claude Opus 4.6. (and perhaps other newest models) are so much better than previous LLMs, so I was kind of excited to have a long conversation with Claude yesterday. While it's clearly better than the older models, and its neat how it can write and run code to explore things computationally etc, I was still surprised at the rate at which it tried to BS me and I had to push back to get it back on track.
I'm finding Claude most impressive for tasks of a somewhat different sort:
Alex Kreitzberg (Mar 16 2026 at 17:54):The free LLMs seem to be crazy good at finding words and terminology for vague definitions.
It's also hard not to run poorly formed questions by LLMs just in case - half the difficulty in answering a question is having access to the answer it seems. A person, and LLMs as well, can really struggle to tell whether a question is bad or if they just don't know enough.
Kevin Carlson (Mar 16 2026 at 20:38):Oscar Cunningham said:
I've been wondering about the problem of people having fewer conversations on platforms like this one, because they're asking the same questions to AI instead. I find that I have lots of worries when I think about posting a question here. Is my question too vague? Too easy? Asking too much of people? Whereas you can ask Claude any question at all and it will always give you an answer.
Perhaps the solution could be a forum where people can talk to an LLM in public? So you still get the advantages of talking to an AI, but other people can still spectate and jump in if they want to.
Interesting thought!
Kevin Carlson (Mar 16 2026 at 20:41):John Baez said:
Oscar Cunningham said:
I've been wondering about the problem of people having fewer conversations on platforms like this one, because they're asking the same questions to AI instead. I find that I have lots of worries when I think about posting a question here. Is my question too vague? Too easy? Asking too much of people? Whereas you can ask Claude any question at all and it will always give you an answer.
Indeed that's a big problem, even for me - meaning "even for a guy who is famous for talking about math in chat forums, who you might think has gotten over the fear of looking dumb".
Perhaps the solution could be a forum where people can talk to an LLM in public? So you still get the advantages of talking to an AI, but other people can still spectate and jump in if they want to.
That's an interesting idea. The closest thing I can easily do is share the transcripts of my interactions with Claude in a thread here, but that sort of AI-heavy posting is discouraged here.
Yeah, I think it would be very boring to read a whole transcript, especially because Claude is incredibly verbose. But a carefully curated redaction could be great. Not that you necessarily want to spend that time.
John Baez (Mar 16 2026 at 21:35):The main reason it would be boring is that I'd either have to go way back to the start of the conversation or you'd need to learn a bunch of tuning theory to understand it, e.g. one of my most productive recent questions was
I'd like to think about Fokker periodicity blocks formed by taking a sublattice of generated by three elements (which we can think of as monzos), one being (1,0,0) (the octave) and two others which are monzos of good 5-limit commas. How are such sublattices related to rank-2 cusps?
John Baez (Mar 17 2026 at 05:36):By the way, @Morgan Rogers (he/him), speaking of organizations pushing mathematicians to use AI, check out this email I got from Renaissance Philanthropy's AI for Math Fund, funded ultimately by Jim Simons, the mathematician and billionaire hedge fund manager:
From: aiformath@renphil.org
Date: Mar 5, 2026, 9:42 AMHi John,
Given your experience in ICMS Scientific Committee and mathematical physics field building expertise, we wanted to encourage you to apply to the latest round of the AI for Math Fund.
Launched by Renaissance Philanthropy and XTX Markets, the fund will provide $100k to $1M in grant funding to each winning team or project developing AI tools, datasets, research, and field-building projects to support the intersection of AI and mathematics. For more details on the overall process, please review this document.
Links:
Submit a short abstract form to apply by March 30, 2026.
Should you have any questions, the AI for Math Team will be hosting Office Hours on Tuesday, March 17 from 11am-12pm (EST) to discuss the 2026 funding round and abstract submission. If you wish to attend, please RSVP here.
We are also recruiting expert reviewers for this funding round across areas such as formalization tools, automation, datasets, infrastructure, field-building, and foundational research. If you would be interested in serving as a reviewer, you can express interest here.
Best,
AI for Math Team
John Baez (Mar 17 2026 at 05:41):I don't intend to pursue this. Unlike a $15-a-month gift subscription to Claude, a large grant like this would commit me to using AI in a serious way. You can see 29 projects who have gotten AI for Math Fund grants here.
David Michael Roberts (Mar 17 2026 at 05:52):I can understand people like Kevin Buzzard getting grants from these people, because of wanting to build a huge database of formalised mathematics pushing very far from basic material. But emailing you @John Baez is kinda funny, like prospective students who send out the same generic email (or with a few words changed) to many many potential supervisors in different countries, when the supervisor works on things the student knows next to nothing about, or, worse, the student is proposing a PhD project that's not in the area the recipient works on.
John Baez (Mar 17 2026 at 06:05):Timothy Gowers is getting grant money from them, and so is my friend Jamie Vicary, for a project on "New Categorical and Topological Foundations for AI and Machine Learning". Maybe they have too much money, and not enough good mathematician applying for grants, so now they're fishing around at the bottom of the barrel for people to give it to.
Kevin Carlson (Mar 17 2026 at 06:17):Ultimately funded by the late Jim Simons, who is no longer capable of being directly responsible for what his money is supporting.
David Michael Roberts (Mar 17 2026 at 06:48):Well, Tim Gowers has been interested in AI reasoning around automated proof for some years now. Maybe a decade? Having Fields medallists get grants helps put a little shine on the award scheme, I would think
John Baez (Mar 17 2026 at 06:53):When you're really rich it sometimes almost doesn't matter if you're still alive, because you accrete a huge organization that continues to function after your death.
Matteo Capucci (he/him) (Mar 17 2026 at 08:23):Kevin Carlson said:
Ultimately funded by the late Jim Simons, who is no longer capable of being directly responsible for what his money is supporting.
Wait for the reveal that Claude is, in fact, Jim Simons' mind uploaded to a computer
Matteo Capucci (he/him) (Mar 17 2026 at 08:24):That's why it's wicked smart
Morgan Rogers (he/him) (Mar 17 2026 at 08:30):@John Baez thanks for sharing the Simon's foundation thing. Reminds me of the discussions here years ago about US researchers (esp post-docs) having essentially no choice but to accept funding funneled through military/"defense" because there is/was so little else. Now we're in a similar situation with AI.
Jules Hedges (Mar 17 2026 at 10:55):Pedantry: Although the grantmaker is Renaissance Philanthropy, as far as we know the majority of the money comes from XTX, a different quant hedge fund
Jules Hedges (Mar 17 2026 at 10:59):I haven't been able to find much information about Renaissance Philanthropy, so in particular I have no idea if it started before or after Simons' retirement
Jules Hedges (Mar 17 2026 at 11:01):I sometimes joke that they are "Renaissance's tax writeoff department", but in reality I have absolutely no idea what they are
John Baez (Mar 17 2026 at 15:40):Morgan Rogers (he/him) said:
John Baez thanks for sharing the Simon's [sic] foundation thing. Reminds me of the discussions here years ago about US researchers (esp post-docs) having essentially no choice but to accept funding funneled through military/"defense" because there is/was so little else.
I don't really think there's been "so little else" until recently. I know a lot of postdocs and other researchers
who don't get military support: there's grant money from a host of federal agencies (NSF, DOE, NIH, etc.), and many mathematicians earn money the old-fashioned way, by teaching. Perhaps people who take military money say they're being "forced" to.
"Until recently": Trump tried to dramatically cut NSF grants, sometimes after they were already awarded. Congress and the courts reinstated most of those grants, but the administration (under Trump's control) has been slow-walking those grants, so the rate at which this year's grants are being given out is much lower than previously:
John Baez (Mar 17 2026 at 15:44):People talk about how this marks the collapse of US science, but I don't really know what the effect will be. Not good, obviously! (Unless you're Sabine Hossenfelder and think the whole system is corrupt and needs to be destroyed.)
Kevin Carlson (Mar 17 2026 at 15:50):It’s been perhaps closer to the case that there’s been “so little else” that applied category theorists have been able to win from outside academia. Topos, certainly, has had a great majority of our historic funding from defense or AI-related sources.
John Baez (Mar 17 2026 at 15:51):Jules Hedges said:
Pedantry: Although the grantmaker is Renaissance Philanthropy, as far as we know the majority of the money comes from XTX, a different quant hedge fund.
Oh wow! It looks like you're right. I wonder why they're doing this. They write:
NEW YORK/LONDON, March 5, 2025 – Renaissance Philanthropy and XTX Markets today announced the next phase of the AI For Math Fund, committing an additional $13.5 million. $10.5 million will be allocated to a new grant application round opening in March, with $3 million for micro-grants and other field-building opportunities. This builds on the fund’s initial $18 million commitment, bringing its total to $31.5 million - one of the largest philanthropic commitments ever dedicated to accelerating the development of AI and machine learning tools to advance mathematics.
John Baez (Mar 17 2026 at 19:18):I had been fooled into thinking Renaissance Philanthropy, who is giving out these AI grants, was related to Renaissance Technologies, Jim Simon's company - but now it looks like they are completely distinct!
I could still be wrong....
Evan Patterson (Mar 17 2026 at 20:38):My understanding is that they are completely distinct and that RenPhil was spun out of Schmidt Futures, making it an Eric Schmidt project rather than a Jim Simons one.
David Michael Roberts (Mar 18 2026 at 01:55):Jules Hedges said:
I haven't been able to find much information about Renaissance Philanthropy, so in particular I have no idea if it started before or after Simons' retirement
RenPhil started very close to when Jim Simons passed away. It was sometime in the first half of 2024, and he died in May 2024 (the dating is not easy to establish for when the fund started, it's approximately May '24, as well). Definitely after he 'retired'!
Federica Pasqualone 🦅 (Mar 18 2026 at 07:56):Sometimes big profitable businesses have indeed a non-profit with a similar name whose job is to spread their philosophy and knowledge to the world and promote their values. It can be that in this case they do not have directly opened the non-profit, but somebody inspired by RenTech did.
Moin btw! :sun_face: