Could AI Find Physics We Can’t Understand?

Episode Overview

• Theoretical physicist and mathematician Hirosi Ooguri speaks with Curt Jaimungal about whether artificial intelligence can discover the fundamental laws of nature, the mathematical foundations of quantum field theory and string theory, and whether humans will be able to understand an AI-generated theory of quantum gravity.
• The conversation begins with the philosophical distinction between timeless mathematical truth and approximate physical truth, exploring why the Planck scale represents the ultimate boundary of reductionist science and why space and time cease to make sense below it.
• Ooguri contrasts the rapid progress of AI in pure mathematics with its limitations in theoretical physics, detailing how formal proof assistants allow automated verification in math while theoretical physics lacks a rigorous mathematical foundation for its core frameworks like quantum field theory.
• Tracing the history of unification from quantum mechanics to the AdS/CFT correspondence and the Swampland program, Ooguri explains how gravity constrains low-energy physics, why string theory might take humans 2,250 years to verify, and how his own decades-old PhD calculations unexpectedly connected to sporadic simple groups.
• The episode concludes with an examination of the daily habits required for deep theoretical research, including how Ooguri structures his schedule to protect long periods of concentration from the immediate gratification of administrative tasks.

Key Concepts

• Natural vs. Artificial Languages Across Physical Scales: Natural languages like English or Japanese evolved to describe everyday human experiences at scales ranging from a centimeter to a kilometer. However, physics probes elementary particles at $10^{-18}$ meters, the Moon's orbit at $10^9$ meters, and galaxies at $10^{18}$ meters. Mathematics serves as an artificial language capable of describing all possible worlds across these extreme scales, whereas physics seeks to identify which single mathematical possibility corresponds to our actual universe. As a pragmatist, Ooguri notes he cannot make a practical distinction between whether the physical world is mathematics or is merely described by it, since reality is defined by what is observable and describable.
• Mathematical Truth vs. Physical Truth: Mathematical truth is genuine and timeless; given a set of axioms and rules of logic, a mathematical proof was true 3,000 years ago and remains true today. Physical truth is always approximate because it relies on empirical observation currently bounded between $10^{-18}$ meters (the Standard Model) and the cosmic horizon (with the caveat that our knowledge within these bounds could still be incomplete if dark matter turns out to be a very light particle).
• The Planck Scale and the End of Reductionism: Historically, physics has progressed by peeling the "cosmic onion" to probe smaller and smaller microscopic scales. However, confining a particle within the Planck length concentrates so much energy that it creates a black hole. Citing Nima Arkani-Hamed, Ooguri explains that colliding particles at higher energies to probe below the Planck length simply creates larger black holes. Just as Heisenberg's uncertainty principle means simultaneous position and momentum do not exist, space and time cease to make sense below the Planck scale. Consequently, unifying general relativity and quantum mechanics represents the "final boss" of reductionism, ending the quest toward smaller scales.
• The Verification Bottleneck for AI in Physics vs. Mathematics: In coding and pure mathematics, large language model (LLM) outputs can be automatically verified by running the code or checking proofs in formal verification systems like the Lean proof assistant. These mathematically equivalent processes enable reinforcement learning with verifiable rewards (RLVR). In March 2026, Ooguri noted that LLMs were at the level of a beginning graduate student in theoretical physics; while AI in mathematics has now surged well beyond that level, theoretical physics remains bottlenecked because its statements are approximate and lack rigorous mathematical foundations, preventing automated certification. (Ooguri hedges that he refuses to speculate on what LLMs will do in the next few years or even weeks, having been proven wrong many times).
• The Navier-Stokes Milestone and Resource Scaling in AI Math: At the International Congress of Mathematicians (ICM) in Philadelphia in July, attendees polled which of the 6 remaining Millennium Prize Problems (out of 7 total) would be solved first, voting Navier-Stokes most likely and the Yang-Mills existence and mass gap problem least likely. About a month later, OpenAI solved the Navier-Stokes problem, building on prior mathematical contributions, alongside claiming to have solved 100 fundamental questions in mathematics. Ooguri notes that after OpenAI heard a rumor (which he hedges may have been erroneous) that someone at Anthropic had solved it, OpenAI realized the problem was solvable with existing techniques, deployed tens of thousands of agents, and poured $15 million to $20 million into cracking it.
• The Mathematical Difficulty of Quantum Field Theory (QFT): Formulated in the late 1920s by Heisenberg, Pauli (in 1929), and Dirac to unify quantum mechanics (1925-1926) with special relativity, QFT required decades to move beyond classical approximations until Feynman, Schwinger, and Tomonaga developed renormalization. It took 50 years to crystallize the Standard Model in the mid-1970s and another 40 years to verify it experimentally (90 years total, culminating in the Higgs boson). QFT remains mathematically unrigorous because fields take values at every point in space, creating infinite degrees of freedom that require infinite-dimensional calculus. While mathematicians like Martin Hairer (building on ideas by Giorgio Parisi) have used statistical mechanics lattices and stochastic nonlinear partial differential equations to formulate QFT in 2 and 3 spacetime dimensions, dimension 4 (1 time, 3 space) remains an unsolved Millennium Prize Problem. Interesting QFTs exist in 5 and 6 dimensions, while beyond 6 dimensions the infinities are so severe that interacting QFTs probably do not exist.
• Why a False Yang-Mills Proof Would Be Revolutionary: While physicists assume the Yang-Mills existence and mass gap conjecture is true because the Standard Model's predictions are experimentally tested to extreme precision, Ooguri explains that proving the conjecture false would be far more exciting than proving it true. A disproof would reveal a fundamental flaw in our understanding of elementary particles and the Standard Model, potentially unlocking new physics to explain dark matter or dark energy.
• Transcending the Lagrangian Formulation: Echoing Nathan Seiberg's arguments that the Lagrangian formulation of QFT must be transcended, Ooguri explains that over the last three decades, taking limits of string theory has revealed valid quantum field theories and conformal field theories (CFTs) that satisfy unitarity and bootstrap properties but have no obvious Lagrangian description—or cannot have one at all.
• The Swampland Program and Gravity's Imprint on Low-Energy Physics: Under Ken Wilson's Nobel Prize-winning renormalization paradigm, quantum field theories without gravity allow model builders to write almost any low-energy effective Lagrangian and expect a consistent ultraviolet (UV) completion. In 2005, Cumrun Vafa proposed the "Swampland" program, showing that including gravity imposes strict consistency constraints on low-energy effective theories. In 2006, two foundational conjectures emerged: the Weak Gravity Conjecture (Vafa, Arkani-Hamed, et al.) and the Distance Conjecture (Ooguri and Vafa), the latter echoing Albert Einstein's Autobiographical Notes that a fundamental theory should have no arbitrary parameters (all parameters must be expectation values of fields).
• Overcoming the "Lamp-Post Effect" via AdS/CFT: Critics note that Swampland conjectures derived from string theory models may suffer from a "lamp-post effect" (only seeing what string theory allows). To prove these principles independently of string theory, Ooguri uses Juan Maldacena's 1997 AdS/CFT correspondence. In 2018, Daniel Harlow and Ooguri used AdS/CFT to prove that quantum gravity in Anti-de Sitter (AdS) space cannot have global symmetries (only gauge symmetries), confirming a 50-year-old speculation by John Wheeler. Following a proposal at Strings 2022 in Vienna, Ooguri and collaborators (Yifan Wang in 2024; Shota Komatsu, Yuya Kusuki, and Marco Meineri four years after 2022) proved parts of the Distance Conjecture in CFT language. These constraints directly impact cosmic inflation, where the inflaton field varies beyond the Planck scale, shaping predictions for primordial gravitational waves in Cosmic Microwave Background (CMB) polarization to be tested by experiments like LiteBIRD in the next decade.
• Vacuum Decay and the Fate of Our Universe: In 2016, Ooguri and Vafa conjectured that non-supersymmetric AdS vacua supported by fluxes must be unstable. Because 10-dimensional flat Minkowski space is an absolutely stable solution to string theory while our universe has positive dark energy, our universe is expected to eventually decay via quantum processes into a stable solution like 10D flat space—though Ooguri stresses this relies on the "big assumption" that string theory is correct and that all string theory vacua are connected.
• The 2,250-Year Timeline for String Theory and the Dog-Refrigerator Analogy: Unifying special relativity and quantum mechanics took ~2 years (1925 to 1927/1929), whereas finding a candidate unification of general relativity and quantum mechanics (string theory gravity discovered by Scherk, Schwarz, and Yoneya in 1973-1974) took ~50 years—making quantum gravity 25 times harder ($50 / 2 = 25$). Multiplying the Standard Model's 50-year formulation and 40-year verification by 25, Ooguri estimates that if left to humans, string theory will take 1,250 years to yield a realistic model of our universe and 1,000 more years to verify experimentally, totaling 2,250 years (comparable to the ~2,000 years required to verify the ancient Greek atomic hypothesis). If AI solves quantum gravity much sooner, humans might face a biological cognitive limit: just as Ooguri's late Westie dog, Rosie, knew food was in the refrigerator but lacked the intelligence to ever understand how a refrigerator works, humans may be incapable of understanding an AI's theory of quantum gravity.
• Mathieu Moonshine and Mock Modular Forms: In his 1989 PhD thesis, Ooguri calculated the elliptic genus of a K3 manifold (a simplified Calabi-Yau manifold), producing an infinite sequence of positive integers (90, 462, 1540, 4554, 11592...). Twenty years later in 2010, during a thunderstorm at the Aspen Center for Physics with Tohru Eguchi and Yuji Tachikawa, Ooguri checked a mathematical encyclopedia on his laptop and discovered his thesis numbers (divided by 2) matched the dimensions of irreducible representations in the character table of the Mathieu group $M_{24}$ (the largest Mathieu sporadic simple group). Named "Mathieu Moonshine" (echoing Richard Borcherds' Fields Medal-winning Monster Moonshine), this sequence organizes into mock modular forms—objects first studied by Srinivasa Ramanujan in 1920 in a letter to G.H. Hardy and rediscovered in the early 1980s by George Andrews in Trinity College Library as "Ramanujan's Lost Notebook."

Quotes

• At 0:00:00 - "I'm afraid there might be a situation where AI give us answer to fundamental question in theoretical physics, and we wouldn't be able to understand it, just like my dog would not have understood how a refrigerator works." - Framing the central epistemological risk of AI solving quantum gravity beyond human comprehension.
• At 0:00:25 - "If it is left for humans, it might take 2,250 years to verify the prediction of string theory. But AI may be able to solve it." - Introducing his scaling estimate for the human timeline of quantum gravity versus potential acceleration by AI.
• At 0:06:45 - "I realized there is a truth in the world, and I can know about it. And I wanted to know more about it." - Reflecting on his childhood realization in 5th or 6th grade after using geometry and a 12-story building's height to estimate the radius of the Earth and verifying it in an encyclopedia.
• At 0:07:34 - "Our universe is realization of just one of these possibility, and I wanted to know what this world is, rather than the world of all possibilities." - Explaining why he chose to focus on theoretical physics rather than pure mathematics.
• At 0:08:06 - "I don't think I can make practical distinction between them, because the world I observe is the world what I can describe." - Addressing the philosophical question of whether the universe is fundamentally mathematical or merely described by mathematics.
• At 0:12:20 - "I have a limited lifespan, so I would like to spend it to the things that I can know." - Explaining his pragmatic approach to choosing tractable scientific questions over unanswerable metaphysical ones.
• At 0:15:50 - "We expect that the notion of space and time itself cease to make sense in scale smaller than Planck scale. So it does not even make sense to ask question on what happens in scale smaller than Planck scale." - Explaining why black hole formation at the Planck length brings an end to spatial reductionism.
• At 0:21:05 - "Mathematical truth is in some sense genuine truth, that as far as you assume the axiom and the rule of logic, then there is a unique answer, and it's true 3,000 years ago and it is true now." - Defining the timeless, absolute nature of mathematical proof.
• At 0:21:38 - "That is in some sense always approximate truth, because it's based on our empirical observation, and then we deduce that and deduce the laws of nature." - Contrasting the empirical, approximate nature of physical laws with the absolute truth of mathematics.
• At 0:26:21 - "In physics, it's harder to do, because as I said, statements are supposed to be only approximately true, and so many statements in physics are not mathematically rigorous. And so there are no sort of automatic certification process that you can run to do the reinforcement learning in most of the physics, in particular in theoretical physics." - Explaining why AI has advanced much faster in formal mathematics and coding than in theoretical physics.
• At 0:34:36 - "Physicists know that the model must exist mathematically, partly because it works, and its prediction is one of the most precise in physics, and it has been tested many times in experiment." - Discussing why physicists confidently use four-dimensional Yang-Mills theory despite it lacking a rigorous mathematical foundation.
• At 0:46:57 - "We need to add something to our understanding of even the Standard Model of particle physics, because it's built on assumption that Yang-Mills theory makes sense mathematically. So if it is proven wrong, then there is something we have misunderstood about the world of elementary particles that we thought we understood." - Explaining why a disproof of the Yang-Mills Millennium Prize Problem would be far more scientifically exciting than a proof.
• At 0:52:00 - "We have come up with example of quantum field theory that satisfies these properties, that satisfies all the property we expect quantum field theory to satisfy, that seemingly do not have Lagrangian description, or in some cases seems to be impossible to have Lagrangian description." - Highlighting how string theory limits have forced physicists to rethink what quantum field theory is beyond classical Lagrangians.
• At 0:54:25 - "It was clear to them that this problem was solvable in existing technique, so they can deploy tens of thousands of agents and then pour 15 million or 20 million to solve it." - Describing how OpenAI mobilized massive compute and financial resources to solve the Navier-Stokes problem after hearing a rumor about Anthropic.
• At 1:05:20 - "Once you include gravity, then that's not true anymore. You cannot do arbitrary thing, that the consistency of gravity and quantum mechanics, there is an imprint of consistency in the low-energy world." - Summarizing the core insight of the Swampland program in contrast to Ken Wilson's renormalization paradigm.
• At 1:19:15 - "In some sense, unification of quantum mechanics and general relativity is a final boss that we need to defeat." - Framing quantum gravity as the ultimate culmination of microscopic reductionism in physics.
• At 1:48:37 - "And there they were, right in front of my eye, the numbers that I calculated in my PhD thesis, actually times two, divided by two. So I was like, wow, this must have something to do with the symmetry of a finite simple group." - Recounting the 2010 Aspen thunderstorm discovery of Mathieu Moonshine connecting K3 manifolds to the $M_{24}$ sporadic group.
• At 1:53:44 - "I still think that string theory is the most promising approach. Different people have different perspective, and that's fine. I think that science works as a market economy of ideas." - Reflecting on his year spent studying and publishing a highly cited paper in Loop Quantum Gravity in the early 1990s before returning to string theory.
• At 1:59:27 - "He used to say that if you wake up in the morning and if you say, 'Well, today I'm going to do mathematics,' you are too late, you can never be good mathematician by doing that. You have to go to sleep thinking about mathematics, and by the time you wake up, you should always be, already be in the world of mathematics." - Sharing a maxim from former RIMS director Mikio Sato on the subconscious immersion required for deep research.
• At 2:03:58 - "Even if you are working on a good problem, a very large fraction of the days, at the end of the day it seems like you've done nothing. You might have spent most of the day staring at a sheet of paper, and I really mean it more or less literally, or finding excuses for wasting time because you can't think of what else to do." - Archival clip of Edward Witten illustrating why theoretical physics requires immense tolerance for unproductive days.

Takeaways

• Quarantine shallow administrative work from deep research hours: Because fundamental research is like wandering a desert without a map (as Nobel Laureate Hideki Yukawa wrote in Tabibito), most days yield no visible progress, creating a strong psychological temptation to retreat into administrative tasks that offer immediate gratification. Emulate Ooguri's schedule by strictly reserving mornings (7:00 AM to noon at home) for uninterrupted deep work, and quarantine all administrative meetings and seminars to the afternoon.
• Prime your subconscious before going to sleep: Apply Mikio Sato's maxim by reviewing and immersing yourself in your hardest intellectual problem right before bed so that you wake up already inside the mental workspace of the problem, rather than wasting morning energy trying to initiate focus from scratch.
• Reframe physics problems as formal mathematical or combinatorial problems to leverage AI: Because theoretical physics lacks automatic verification, look for ways to translate physical questions into pure math where reinforcement learning can be applied—just as Ooguri's team turned the entanglement structure of holographic CFTs into a combinatorial inequality classification problem ("The Holographic Entropy Cone") and used reinforcement learning to classify 6-party inequalities.
• Collaborate across disciplines with optimization and AI specialists: When tackling problems that explode combinatorially, seek out collaborators with specialized algorithmic backgrounds; Ooguri's team achieved vastly stronger results on holographic entropy inequalities after partnering with a University of Tokyo graduate student who had studied at Stanford, founded a company, and returned to academia to study optimization.
• Test rival scientific frameworks from the inside before dismissing them: Treat science as a "market economy of ideas" by actively investigating competing theories. In the early 1990s at Kyoto University, Ooguri spent over a year studying Loop Quantum Gravity and wrote one of the field's most cited papers ("Topological Lattice Models in Four Dimensions" in 1992), which allowed him to evaluate its limitations firsthand and return to string theory with grounded conviction.
• Measure the value of a theory by its cross-disciplinary fertility: Following Henri Poincaré's Science and Method, evaluate abstract research not just by immediate experimental verification, but by how broadly it generates breakthroughs across other fields—such as how topological string theory and K3 surface calculations generate new conjectures and discoveries in pure mathematics.
• Use everyday observations and back-of-the-envelope scaling to check your intuition: Practice estimating macroscopic or complex quantities from simple known anchors, whether estimating the Earth's radius from a 12-story building using the height of movie monsters (40 to 50 meters) as a ruler, or estimating the timeline of string theory by scaling the historical ratio of special-relativistic QFT (2 years) to quantum gravity (50 years).
• Seek model-independent proofs to avoid the "lamp-post effect": If your research relies heavily on specific model assumptions, look for dualities or broader mathematical frameworks (like using general CFT bootstrap properties instead of specific string compactifications) to prove that your conclusions hold universally.
• Document and preserve unexplained numerical patterns in your work: When calculations yield precise sequences or structures you cannot immediately explain—like the integer sequence in Ooguri's 1989 PhD thesis—publish and retain them clearly; decades later, new tools or cross-disciplinary conversations may reveal them to be keys to major structures like Mathieu Moonshine.
• Keep administrative structures lean to protect researchers' time: If you lead an organization or academic division, minimize bureaucratic layers. Ooguri notes that Caltech (~300 professors, ~230 undergraduates per year) operates with no departments, colleges, or deans—only 6 division chairs, the president, and the provost—allowing leadership to remain active researchers.
• Pair light daily physical movement with passive learning and remote coaching: Maintain physical health without derailing research schedules by stacking habits: Ooguri uses an elliptical trainer for 20 minutes while listening to podcasts and maintains consistency through 30-minute virtual 1-on-1 pilates and yoga sessions with a trainer in Japan (repeating recorded sessions on off days).
• Focus your finite lifespan on tractable, well-defined questions: Recognize when a question lies beyond the boundary of empirical or logical decidability (such as asking what happens spatially below the Planck scale or debating unobservable metaphysical realism) and deliberately redirect your cognitive energy toward problems that can actually be known and described.