Scott Aaronson, a theoretical computer scientist at UT Austin, discusses the seismic shift in mathematics and theoretical computer science following OpenAI’s release of approximately 400 AI-discovered solutions to major open problems, including a proof of the Unique Games Conjecture that his wife Dana Moshkovitz had spent her career pursuing.
The event and its immediate impact
OpenAI released a massive dump of AI-generated solutions to open problems in math and theoretical computer science, solving roughly 10% of 4,000 problems fed to their models with three hours of compute each.
The release included crown-jewel results: a proof of the Unique Games Conjecture (Subhash Khot’s central open problem in hardness of approximation), solutions to the unitary synthesis problem (posed by Aaronson and Greg Kuperberg 20 years ago), and advances in mathematical physics.
Aaronson’s wife Dana, a complexity theorist, has spent the past two weeks trying to understand the AI proof of the Unique Games Conjecture, which she had worked on since they started dating in 2009.
The AI-generated manuscripts are poorly written — verbose on trivial points, silent on crucial steps — resembling brilliant but inexperienced graduate students who lack a mental model of their reader.
Researchers are now scrambling to digest these proofs, isolate key ideas, and write human-readable expositions; Aaronson notes this interpretation work is “great for us because it means we still have plenty to do.”
The changing role of mathematicians: from creators to interpreters
Aaronson compares the emerging role to literary scholars interpreting great works, or astronomers observing through a telescope — the “bear” (AI) is not a co-author, but the observed phenomenon.
The core of mathematical work has shifted: previously, value lay in the human journey of discovering solutions and the new understanding forged along the way; now AI “teleports” us to answers without forcing that insight-building process.
Aaronson acknowledges grief among mathematicians (especially younger ones) who entered the field for the experience of year-long, decade-long problem-solving and the associated “aha moments.”
Jacob Tsimerman (Olympiad winner, problem-solver) and Dan Freed expressed mourning not for mathematics but for mathematicians — the particular working style and identity tied to slow, deep struggle.
Aaronson worries most about PhD students who traditionally cut their teeth by solving well-defined open problems to make their names; that pathway has been “taken away.”
He rejects a Luddite response: the models will be widely available soon, and anyone will be able to solve hard problems; the field must adapt rather than demand AI companies stop.
Credit, authorship, and community norms
Two models emerged: OpenAI dumped raw solutions on GitHub with “OpenAI” as author (no human had understood most results); Anthropic contracted human experts (Virginia Vassilevska Williams and Josh Alman) to fully understand and write expositions with their names as authors.
Anthropic’s approach creates buy-in, point people who can answer questions, and human ownership — but gives the company power to choose which humans become emissaries.
Emerging norm: papers include “AI usage statements” (often at the end) detailing which parts used AI and which models; if a human fully understands, writes in their own words, and takes responsibility, their name goes on the paper — just as a biologist’s paper on bear behavior is not joint work with the bear.
Low-value behavior: feeding problems to a model, posting raw output with one’s name, expecting credit while others do the understanding work — “pulling a lever on a slot machine.”
Boaz Barak’s joke: in such cases the author should be “GPT-6” with acknowledgment “I’m so grateful to Scott Aaronson for suggesting this problem to me.”
The Association for Human Mathematics and the “rudeness” debate
The Association for Human Mathematics (AHM) released a statement decrying OpenAI’s drop, including the line “Mathematicians did not ask for this work to be done.”
Aaronson pushes back: open problems are by definition open to anyone — an unknown clerk (Ramanujan), a 17-year-old student, or a corporation one dislikes; we are not arbiters of who gets to work on them.
He agrees we must hold AI companies accountable on safety and alignment (he has worked on this for four years), but adaptation is our job, not others’ job to preserve our old world.
The backlash to OpenAI’s earlier Navier-Stokes solution (where they raced ahead of human researchers Tristan Buckmaster and Levent Alpöge using massive compute) shaped their cautious approach this time, including convening an advisory board (Timothy Gowers, Edward Witten, etc.) that ultimately said “release it.”
Why math fell first: crisp verification and reinforcement learning
Physics has not yet been inundated because its problems are less crisply defined — verification requires judgment calls (reasonable approximations, physical models) rather than mechanical checking.
Mathematical physics (where problems can be mathematically specified) has seen dramatic AI progress, including in the OpenAI drop.
Crisp conjectures (P ≠ NP, Unique Games) provide mechanical verification targets, enabling reinforcement learning on thousands of solution examples — a “fearsome blob of intelligence” aimed at a clear target.
Technical highlights from the OpenAI drop: unitary synthesis and black holes
Unitary synthesis problem (Aaronson & Kuperberg, 20 years ago): Can every n-qubit unitary U be applied efficiently given a classical Boolean function as an oracle? They conjectured no; AI proved yes — for every unitary there exists such a Boolean function.
This result has already been improved by researchers using AI: if P = PSPACE (a massive complexity collapse, bigger than P = NP), then any unitary describable in polynomial space can be applied efficiently.
Implication for quantum gravity: The unitary that decodes Hawking radiation from a black hole could be applied efficiently, meaning one could engineer a firewall at the event horizon (breakdown of spacetime) — though observing it requires jumping into the black hole and dying before communicating.
Daniel Harlow’s response: “Why should I care? P ≠ PSPACE.” Aaronson’s counter: to prove firewalls are hard, you must prove P ≠ PSPACE — a central open problem still unsolved despite AI progress.
P = NP, cryptography, and responsible disclosure
If Anthropic (or any lab) found a practical P = NP algorithm, it would break essentially all internet cryptography (HTTPS, Bitcoin, digital signatures, credit card transactions).
Responsible disclosure norms (90-day notification to affected parties) become impossible when the “affected party” is the entire world.
OpenAI conspicuously omitted cryptography from their 400-problem drop — a deliberate caution.
Aaronson expects AI models to discover breaks of widely deployed cryptosystems within 1–2 years; the field must seriously consider what responsible disclosure means (zero-knowledge proofs of capability? government notification? company decides?).
A practical P = NP would also accelerate AI itself by making model training vastly more efficient (finding optimal parameters without massive compute).
Chess analogy and the future of the field
Chess survived and thrived after Deep Blue (1997): never more popular, packed kids’ tournaments, streamers, celebrities — people decided they like it as a human activity, now using engines for analysis and training.
Aaronson hopes math follows a similar path: people will still enjoy understanding math, posing questions, and either solving them or having AI solve and explain them.
His deeper worry is civilizational survival through the AI transition; if civilization survives, a niche for math-lovers will be found.
Key challenge: developing students’ problem-solving abilities so they can judge AI output and do higher-level work, even for tasks AI now does better.
Second law of thermodynamics and computational complexity (unpublished work)
Aaronson and collaborators have an argument linking the second law to computational intractability: in certain classical reversible cellular automata, apparent entropy increase can be “unmasked” as pseudo-entropy if P = NP (or no one-way functions exist).
A Maxwell’s demon knowing the initial macrostate but not microstate could, if P = NP, efficiently reverse-engineer the initial microstate from observations, compress its memory, and circumvent the second law — revealing the entropy was never “true” entropy but pseudo-entropy (like pseudorandom generator output).
Caveats: chaos (infinite precision needed) and quantum uncertainty may block this in real physical systems; the argument works for non-chaotic classical dynamical systems.
Consciousness and Integrated Information Theory (IIT)
Aaronson considers IIT (Giulio Tononi’s theory with measure Φ) “just wrong” — it makes absurd predictions, e.g., a giant grid of XOR gates doing nothing interesting has vastly higher Φ than a human brain.
Tononi bit the bullet: the theory says the XOR grid is 1,000× more conscious, therefore it is; one should trust the theory over intuition.
Aaronson’s view: if a theory predicts a blank wall of logic gates is hyper-conscious, the word “consciousness” has become disconnected from what we meant; the burden is on IIT to explain why we should care about its Φ.
On AI understanding: Aaronson treats operational criteria as sufficient — if AI satisfies every test for understanding math (solving major open problems), it understands, regardless of consciousness or sentience; poor explanation ability doesn’t negate understanding (many brilliant humans are poor explainers too).
