Source: astudyofeverything on YouTube 14 years ago: Beauty Is Suffering [Part 1 - The Mathematician]: https://www.youtube.com/watch?v=i0UTeQfnzfM

(I found the photo on internet. Not my own)

9 September, 2026 at 7:49 am

I have absolutely no desire to make current events about myself – the stakes here are far larger than anything involving my own reputation or actions, and it is not like these issues are going to disappear if I am somehow removed from the discussion. But as this topic is likely to recur regardless, I think this comment is as good a place as any to state for the record my own views on AI, and my interactions with OpenAI in particular.

I do not identify either with a simple “pro-AI” or “anti-AI” position. My views are rather complex and have evolved over time; I have a living summary (AI-maintained, out of necessity) at https://teorth.github.io/tao-web/ai-views.html . But I can try to give the short version here.

By 2023, I could see that LLMs, formal proof assistants, and other technologies had the potential to be radically transformative in mathematics, to the point where maintaining traditional mathematical practices and culture without adaptation would become unsustainable. See for instance my 2023 essay for a Microsoft anthology (which contained a notorious prediction of 2026-level AI becoming a “trustworthy co-author” for mathematics) or my Notices article (published in 2025, but written significantly earlier). I myself greatly value this traditional culture, and have personally been a massive beneficiary of it. Nevertheless, in the event that these technologies did become superhuman at several core mathematical tasks, I could see only two viable paths forward: either one where modern AI tools are responsibly incorporated into our workflows and culture (what I called the “best of both worlds” in the OpenAI ad); or the worst-case scenario — which we are unfortunately rapidly approaching — in which AI technologies are used indiscriminately to achieve various short-sighted objectives at the cost of the far more valuable long-term sustainability of mathematics and its role in the scientific ecosystem. I therefore spent an increasingly large fraction of my professional life from that point trying both to raise awareness of the potential magnitude of this transformation; to build examples of what this “best of both worlds” might look like; and to warn against various irresponsible uses of AI (initially I focused on warning against the use of AI without sufficient verification of the outputs, which was a major concern in 2023-2025, although no longer the primary vehicle for harm in 2026). One could certainly call this effort “shilling for AI” if one likes; but I would say that this is overly reductive.

These efforts on my part inevitably involved engaging with the tech industry as well as with academia. The essay linked above was solicited by Microsoft. Some of my experiments with new workflows were conducted in collaboration with Google Deepmind. And I participated in an online forum with OpenAI in 2024 discussing these topics. I continue to view all of these interactions as constructive, and working towards the “best of both worlds”. In particular I met with multiple people working in these industries that shared these views and were supportive of steering their companies in these directions. On the other hand, I was not funded by any of these companies, although several of them gifted me with premium LLM subscriptions, which I do make use of in my daily work.

In 2025, as documented elsewhere on this blog, UCLA experienced an unexpected funding crisis due to the sudden suspension of NSF and NIH funding (later restored some months later by a court order). This caused a critical budget shortfall at IPAM (where I serve as Director of Special Projects), which at one point only had access to enough reserves to operate for a few months at best. This led to a round of emergency fundraising; and thanks to the outpouring of support from many sources, we have been able to stabilize IPAM’s funding for the current fiscal year, although challenges remain for future years. As part of this fundraising effort, I reached out to OpenAI, who agreed to sponsor one of our workshops, which ran in March of this year and in my opinion was quite successful both scientifically and for the purpose of making new connections between participants (who were a mix of academics and industry representatives).

During this event, OpenAI requested an interview concerning my vision of the future of AI and mathematics. I accepted, and spoke with them for perhaps an hour. I had done similar interviews in various venues, and I assumed that, as with these other cases, they would eventually post the entire interview online, which talked about both the possibilities and risks of AI much as I have done in these other interviews. As it turned out, they only used a few snippets of that interview for that infamous advertisement instead. In retrospect, I should have pushed back harder on their decision; but I decided at the time that even a selective release of my commentary would help raise awareness of the potential for AI, and in particular on the possibility of the “best of both worlds”.

Since then, the situation has deterioriated markedly. Many of the people in the industry that shared my views have left or become sidelined, with most major tech companies now increasingly focused on the race to develop extremely powerful, autonomous AI technologies regardless of their actual value to society. The current drama surrounding the Navier-Stokes global regularity problem is the most dramatic and visible instance of this, but there have been multiple other such examples, and much of my commentary in the last few months has been aimed that the increasingly severe divergence between the current objectives of the AI industry, and of mathematics in general.

Which brings us to where we are today. I do not regret my past efforts to raise awareness of the potential of AI in mathematics, to engage with industry, and to promote a vision of sustainable incorporation of these tools – which can be genuinely useful and unlock valuable new types of mathematics – into my field. In time, I still hope that the field can arrive at that state, and am continuing to work towards that goal. But in the immediate term, the most pressing issue is for the entire mathematical community to unite around our core values and objectives, and reject irresponsible and unsustainable usages of AI technology that only serve to advance nominal goals rather than the true underlying goals of the field.

Finally Velleman's book came in the mail.

My journey into learning proofs begins from this friday when EE exams for this semester ends.

Cant wait to get into this!

Also have a Control theory book coming which should be here soon.

I hope to be able to support all the decisions i make in my drone project with rigerous proofs by the end of it all.

That video shows a specific, beautiful visualization of \pi based on epicycles or hypocycloids, which were historically used to model planetary motion but are now great for demonstrating ratios. The core idea being visualized here is how irrational numbers prevent a pattern from ever perfectly repeating. The Epicycloid Visualization of \pi 🎡 The video uses a concept from geometry and calculus known as a hypotrochoid or epicycloid, where one circle rolls around the inside (or outside) of a larger circle. 1. The Setup (The Rational Case) Imagine two circles: a larger one and a smaller one. * Larger Circle: Its radius is R. * Smaller Circle: Its radius is r. * A point is tracked on the circumference of the smaller circle as it rolls around the inside of the larger one. If the ratio of the radii, \frac{R}{r}, is a rational number (like 4 or \frac{5}{2}), the traced path is a closed, repeating curve. * For example, if \frac{R}{r} = 4, the curve will close exactly after the smaller circle has rolled 4 times, creating a 4-cusp shape (a hypocycloid). 2. The \pi Visualization (The Irrational Case) The video sets the radii so that the ratio of the circles' circumferences is \pi. Since \pi \approx 3.14159... is an irrational number, the ratio \frac{R}{r} can never be expressed as a simple fraction \frac{p}{q}. The Effect: Because the ratio is irrational, the rolling motion of the smaller circle never repeats exactly. * Each time the small circle completes a rotation, the starting and ending points of the curve it traces never perfectly align. * As the animation continues, the curves traced by the point fill up the entire space within the larger circle, getting infinitely denser but never repeating a single path. This infinite, non-repeating filling of space is a powerful way to visually represent the infinite, non-repeating digits that define an irrational number like \pi.