Today we chat with mathematician Timothy Nguyen, PhD from MIT, currently working at DeepMind, and the man who showed that so-called Geometric Unity has no clothes

**David**: What drew you to explore gauge theory for your doctorate?

**Tim**: It was actually mostly due to my naivete. Mathematicians (usually) mean one thing by gauge theory (a branch of differential topology) which can be quite unrelated to what physicists mean by gauge theory (the mathematical language for understanding symmetries of elementary particles). I always wanted to stay close to physics and had assumed if I studied gauge theory in the math department I'd stay close to physics. Alas, my thesis, despite having the name "Seiberg-Witten" in it, had very little physics. Though at least I was exposed to the right structures (Dirac equation, Yang-Mills equations, etc) so that picking up physics through my own efforts was enabled.

**David**: As far as I can recall, I entered academia because I wanted to explore interesting ideas about the physical world with interesting people. I discovered that my colleagues are neither interested in interesting ideas nor are they themselves interesting. What was your experience in academia and why was it short-lived?

**Tim**: What a question! As for people not being interesting, I don't think I'm in the position to judge, since as an academic I was also overworked and so didn't have many hobbies to make me "interesting" in the usual sense. I think I can comment more on the "interested in interesting ideas", which I interpret to mean the childlike curiosity which one might regard as the prerequisite for being a scientist/researcher. I very much agree that most academics are not as curious as you might expect them to be, at least, once one leaves the very top institutions like MIT (where I did my PhD). I like to summarize it as follows: at MIT, everyone went to the colloquium whereas at other institutions I went to afterwards, it was much more optional (most likely the friends of the speaker who went). Though as a practical matter, researchers become siloed due to the technical barriers to entry and the high demands of specialization, I often got the sense that specialists *weren't even interested* in learning about different perspectives of their work. A not too far from the truth caricature would be like going to grad school to enter the church of your thesis advisor and advance the program therein without ever questioning why you're doing what you're doing. I'm genuinely curious what your experience has been in this regard.

**David**: On average I think the pressure in academia is not to produce smart, talented people, interested in the world, but to generate conformity and team players. As a theorist, I want to explore ideas but I find so many of my colleagues don’t know why the explanations for the observations of black holes are what they are. Bringing my ideas to some of these people can feel like talking to a wall or at best like catching a deer in the headlights. Do you think math is invented, discovered, or in-between?

**Tim**: I have not thoroughly thought about this question seriously enough to be committed to my answer, but my vague thoughts are that math is a blend of discovery and invention. It's a discovery in the sense that there is shared mathematical reality of ideas that mathematicians are jointly exploring - had mathematician X been killed or failed to prove theorem Y, surely it could have been done by another mathematician (in contrast to say a composer - it's hard to imagine anyone else would have written Beethoven's Ninth Symphony other than Beethoven). But math is also an invention in that the space of ideas that we arrive at is shaped by history, personality, human creativity, etc. Stylistic choices (the accepted levels of rigor, the style of presentation, etc) also indicate inventive/cultural aspects.

But if you press me on the nature of mathematical reality though, I'd be hard pressed to give you a solid characterization. There's a sense in which math provides a good map of the world (think of Wigner's "unreasonable effectiveness" of mathematics) but is the map the same as the territory? I will leave it at that.

**David**: How much and what kind of math do you use in your current work?

**Tim**: It varies (but for the most part, math plays a secondary role to being an empiricist in my line of work, which means writing code and running/evaluating experiments). Two of my papers on dataset distillation built upon the math involved in the so-called neural tangent kernel theory which is very beautiful mathematics. There I developed novel algorithms (math) and then implemented them to get state of the art results at the time on image-classification benchmarks (experiment). But my most recent paper on language models, for example, doesn't really use math beyond foundational linear algebra/calculus/probability required of all machine learning researchers.

**David**: In discussing so-called GU theory, I’ve heard you say that a partial unification project might be to get all the equations of physics, the quantum ones and the classical field equations of GR, to emerge from some unified superstructure that contains all the symmetries. What does that mean? Currently, the Schrodinger equation, the Dirac equation, the field equations of GR etc., can all be obtained within the context of the same formalism, i.e. they all have Lagrangians that carry the symmetries of the theory and from which the equations of the theory follow by the same minimization techniques. It seems like that unified structure already exists. Of course, despite a unified formalism, GR and QFT remain disunited. Can you explain what I am missing in this partial unification project that might be of value?

**Tim**: I'm not saying anything unique or insightful here. I mean unification in the sense of there, say, being a unified structure (e.g gauge group) that would unify all the 4 forces in physics. In the Standard Model, we have electroweak and strong (but they are not yet unified, the attempt to unify them goes under the name Grand Unification). While Schrodinger, Dirac, and GR can each have their own Lagrangian/Hamiltonian setup, the point would be to have say a single Lagrangian/Hamiltonian and a single theory that encapsulates all phenomena, rather than having a separate one for each case.

**David**: It seems reasonable to expect theories whose underlying symmetries are physical, to lead to greater intuition about the theory. Is that true? Are there aspects of QFT that you find more intuitive than others and do you have a sense of why that might be?

**Tim**: Symmetries are physical - as opposed to.... gauge symmetries? I'm not sure I understand the question. To be honest, I don't think QFT is intuitive at all! The formalism is very heavy and the computations are difficult. Though perhaps this is just a reflection of my very limited knowledge/expertise of the subject.

**David**: Thank you Dr. Nguyen!

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