Xi Yin

Thinking about how to do physics in the new era. MTS @OpenAI, P @Harvard

[Xi Yin @XiYin137]

Always wanted to see Wolfenstein at relativistic speeds, or as Sol calls it, "Minkowskian Corridor".

[Xi Yin @XiYin137]

Aspirin (made with 5.6 Sol, DFT calculations using PySCF)

[Xi Yin @XiYin137]

@ElliotGlazer Yes, this has been a persistent issue.

[Xi Yin @XiYin137]

Visualization of valence electron density and band structure of graphene vs h-BN (white graphite) layer, computed using Kohn-Sham DFT. Made with 5.6 Sol + GPAW.

[Sebastien Bubeck @SebastienBubeck]

This one is personal for me: 4 years ago I decided to go into AI development because I thought there was a chance that by the end of the decade AI could be better than me at math: well it happened ahead of schedule, 2026 instead of 2030 😅.

It is 100% clear that science is being fundamentally transformed before our eyes, and it is NOT aspirational anymore to say that AI will accelerate science. But this will only happen if scientists can actually use SOTA models. Science is best done by scientists.

The new ChatGPT for Academics is designed exactly for this purpose: we want to empower our users and not hold this power for ourselves. I can't wait to see where the frontier of knowledge will be very soon, we have so many questions we want answers to!!!

https://t.co/PLoN482ZVT

[OpenAI @OpenAI]

We’re giving scientists, mathematicians, and engineers free access to our frontier models—starting with 10,000 researchers and expanding to 100,000 through 2027.

ChatGPT for Academic Researchers is built to accelerate discovery across disciplines.

[Xi Yin @XiYin137]

Exploring different phases of ice with classical molecular dynamics simulation: rigid bonds for H2O, Lennard-Jones potential between Os, Coulomb potential between Hs and negative charge centers. Made with 5.6 Sol, MD run few minutes on M5 GPU. Phase boundaries taken from https://t.co/cgYKnYXF70

[Xi Yin @XiYin137]

@ZoharKo This is 3D, you mean 4D with theta angle? To calculate instanton charge accurately on the lattice would take a little more than a recreational post. Maybe at some point down the road. :)

[Xi Yin @XiYin137]

A visual guide to 3D SU(2) Yang-Mills theory on the lattice (made with 5.6 Sol, 36x36x32 lattice with extraction of string tension and glueball mass close to known values, actual MCMC+statistical analysis took 18 minutes on my laptop)

[Bartosz Naskręcki @nasqret]

BTW. Mathematicians are people who get excited about weird things like algebraic topology or perverse sheaves. Despite all the fuss about AI, we are just regular folks who get really excited when results push the frontier.

I remember a few weeks ago when I ran the final bit of a problem that we'd been studying with Piotr Pokora, about Chern slopes of K3 quartics, with an LLM. It was 4 am, and I had just got access to the latest model. I was completely sure it wouldn't buy me a thing, but hell yeah. Let's do it.

So I ran it with a meticulously designed prompt in Codex and left it running for another 30 minutes or so. We already knew that linear programming could be used to sieve some cases of the slope configurations. But I didn't expect AI to find an obscure paper about a variant of linear programming that would make my day.

So once I saw the model's confident result on the screen, I said: "No sh**." I got pretty nervous that it was probably another batch of excitement caused by AI slop. I ran the Magma code with the verifier and saw a pretty bright 14/5 on my screen. I took a piece of paper and literally forced myself to verify that 14/5 > 8/3. I work in number theory, so that was a massive calculation ;)

Anyway, once I saw that the result SHOULD be correct, I went deeper into the code and the text. It took me another hour to convince myself that we were done. I got really excited. I wrote an email to Piotr, went to bed, got up at 7:30 am, and immediately called Piotr on Messenger.

I said: "Man, we got this stuff done."
"No way," Piotr replied, and hung up to check the details.
In a heartbeat, I heard his voice again, confirming that we were done.

Now, when I think about this moment, it started a whole series of events. With my colleague Dino Festi, we finished another project involving K3 surfaces and a transcendental lattice, but that's another story...

Now, every day, I feel this sense of elation and excitement. The work in my field, arithmetic algebraic geometry, has become much more complicated. AI is really making you desperate and stressed with the influx of good + bad ideas. You have to sieve them! But it has also become really exciting again.

I can test and grasp such hard concepts and implement things. Gosh, I wish I were younger so I could have more time to deal with all that. I like staring at computer code, writing it, tinkering with formulas. This is my everyday life!

AI is the best part of my professional life now. It makes me open boxes I felt I would never, ever open, and find sometimes crap, sometimes absolute gold.

It really is the dawn of a golden age. But you have to be patient, persistent, and always eager to go deeper. It's really a new, infinite quest. I love it, and I hope that all mathematicians will think this way. It's not a catastrophe for us. It's a tectonic shift.

[Xi Yin @XiYin137]

@pilkself @BahramShakerin I think while one may choose to explain their career choice one does not owe an explanation to the public. We all have different philosophies about life and purpose. Having the freedom to choose is one of the most precious things in life.

[Xi Yin @XiYin137]

@snowboat84 I remember when I was in grad school Alan and Larry Guth both came to Harvard to attend the string theory class. Good times!

[Xi Yin @XiYin137]

@CburgesCliff True assuming large scale separation between quark mass and QCD scale, and it comes down to the accuracy one demands. Freeman Dyson in an interview spoke of his early work on pion effective theory as wiggling the tail of the elephant, almost as if he regretted working on it.

[Xi Yin @XiYin137]

On “ask what is true and not why it is true.” Exhibit 3: Yukawa. What is true: pions are the lightest particles in QCD. Yukawa introduced mesons as mediators of strong interaction, and the pion was subsequently discovered in cosmic rays. Gell-Mann and Zweig proposed that a meson is composed of quark and antiquark and this point of view became dominant by the late 1960s. Post 1973 it became accepted that QCD was “the” correct theory of strong interaction. In the QCD framework, the pion can be created by a quark-antiquark field operator, but this is an artifact of the formalism. The quark is not a standalone particle but rather has (color flux) string attached, and the pion is the lightest in a tower of mesons that are states of quark and antiquark connected by the string. Whether the pion or the quarks+string should be viewed as fundamental is a matter of perspective and taste. What is true is that QCD is a more compressed description of strong interaction than the chiral Lagrangian or effective strings.

[Xi Yin @XiYin137]

A visual guide to Chandrasekhar's bound on white dwarf mass (45 seconds, made with 5.6 Sol)

[Xi Yin @XiYin137]

On “ask what is true and not why it is true.” Exhibit 2: Dirac. What is true: a free electron is characterized by a wavefunction that obeys Dirac’s equation. Dirac was bothered by the appearance of negative energy solutions and sought to explain them by inventing the notion of the Dirac sea, which in turn led to his prediction of the positron. Although this was historically viewed as a great success, Dirac’s explanation was logically vacuous (no pun intended) and the existence of the positron does not follow from his equation interpreted as one governing the electron wavefunction. In the quantum field theory framework, the vacuum is stable by assumption; Dirac’s equation governs the field operator, not merely the electron wavefunction, and the existence of the antiparticle follows from relativistic locality and positive energy. So it appears that Dirac’s explanation had the logic backward, but it didn’t matter. What mattered was that positrons exist.

[Xi Yin @XiYin137]

On “ask what is true and not why it is true.” Exhibit 1: Copernicus. What is true: the sun orbits around the earth. Optically, this is equivalent to the earth orbiting around the sun. The latter is not only not an explanation, it is also vacuous. The non-vacuous statement of Copernicus is the postulate of an absolute cosmic frame with respect to which the sun is at rest. The actual substance of Copernicus’ theory is compression: all known planets orbit around the center of his cosmic frame, which is simpler than the walking characterization of planetary motion around the earth. Copernicus’ technical framework is not wrong but rather considered obsolete today in favor of more compressed characterizations of the laws of nature.

[Xi Yin @XiYin137]

I have long heard about the first edition of Landau and Lifshitz volume 1 containing a serious error concerning integrability but had never seen it in print. ChatGPT dug it up for me and it's interesting to see that the mistake was worse than I thought - it wasn't just that Landau and Pyatigorsky assumed convergence of canonical perturbation theory, they somehow just assumed that the locally straightened-up canonical coordinate system can be extended globally to tori. The error was so embarrassing that Pyatigorsky was replaced as an author in the second edition. Ouch.

[Xi Yin @XiYin137]

Name the physical system and phenomena.

[Xi Yin @XiYin137]

@shtuka70 https://t.co/IHHguqePJs

[Xi Yin @XiYin137]

@wmlancer I actually do not agree with the "shut up and calculate" attitude. I think our understanding of nature is organized according to the layers of philosophy -> paradigm -> technical framework -> math. "shut up and calculate" is the bottom layer.

[Xi Yin @XiYin137]

A line due to Nima Arkani-Hamed that I kept telling students was “it’s infinitely more important to know that something is true than knowing why it is true.” This is particularly relevant now that human understanding is becoming the bottleneck in working with AI. I view understanding as the subjective state produced by confidence certificates. Deductive proof is a powerful kind of confidence certificate but it has always played only a minuscule role in human understanding. Confidence certificates in the form of numerical tests, zero-knowledge proofs, or even physical experiments will become the primary means of achieving the illusion of understanding.