AI Is SOLVING MATH Problems That Went Unsolved for CENTURIES| Scott Aaronson
synopsis
Roman Yampolskiy interviews Scott Aaronson, whose position ends in two places. On AI, he holds that models are already general intelligences by some definitions and are solving long-open mathematics at a pace the research community cannot absorb, while alignment has no mathematical definition and is losing a race against time; his p(doom) is 5–50%. On quantum computing, he holds that the hardware is now good enough in principle for fault tolerance, that only scale remains, and that Bitcoin and everyone else should start migrating to post-quantum cryptography now.
AI and P vs NP. Asked whether AI will resolve P vs NP within two years, Aaronson can't rule it out: many major conjectures fell "this summer and fall", though P vs NP was not among them despite attempts. AI has excelled at applying existing techniques cleverly, combining distant fields and brute-forcing counterexamples, not at wholly new ideas, which he thinks P vs NP needs. He still rejects the "not really creative" dismissal: an OpenAI release a couple of weeks earlier did enough for probably several Fields Medals. He strongly conjectures P ≠ NP; a practical P = NP would break all computational encryption and cryptocurrencies, make optimal neural-net training easy, and make interpretability tractable.
A field overwhelmed. Theoretical computer science is "pretty overwhelmed." A Simons Institute derandomization semester has become a program on understanding OpenAI's proof of L = BPL, and his wife, who spent her career on the unique games conjecture, now studies an OpenAI model's proof of it. Senior researchers already delegate and will be fine; the worry is young researchers who established themselves by solving hard problems. Humans are now the bottleneck on understanding and explaining AI output, while US PhD numbers are under pressure from cuts to the National Science Foundation and immigration restrictions.
Verification and credit. Lean certificates are airtight in principle but not yet in practice: kernel bugs have yielded proofs of 0 = 1, Lean 4's consistency is unproven, and no formal method can confirm a formalization matches its intent. Anthropic paid named experts (Virginia Vassilevska Williams and Josh Alman) to explain its 3SUM and all-pairs shortest-path results; OpenAI posted hundreds of proofs to GitHub and started a race to explain them. Aaronson, echoing Boaz Barak, expects credit to move towards exposition, and likens AI to a far more powerful "math telescope" that humans still point and interpret. Authors must take intellectual responsibility, which AIs can't yet do; papers since this summer carry AI disclosure statements.
Alignment. He reports that at OpenAI, Ilya Sutskever kept asking for a mathematical definition of an AI loving humanity, which he never produced; it may be "3,000 years of moral philosophy." His UT Austin course on AI alignment theory lacks the agreed body of theory a math course has. Debate about controlling a vastly smarter system becomes a battle of metaphors, orangutans controlling humans against Yann LeCun's less-smart CEOs. Given enough time we could build a world with powerful AI we'd be happy in, but things are moving too fast. Formalizing the safety condition would be "80% done." Evals produce bar charts, and situationally aware models may bide their time while tested. He thinks pieces of alignment can be broken off and solved mathematically or empirically, but not the whole.
Simulation and quantum mechanics. He doubts we would ever see empirical evidence of living in a simulation, and treats the question as a modern version of the God question. Quantum mechanics cuts against simple simulation stories: the simulator would have to be exponentially slow or itself a quantum computer. The world's state is a vector in Hilbert space evolving linearly.
Quantum computing now. The leading devices, such as Quantinuum's Helios with about 100 qubits and over 99.9% two-qubit accuracy, are in a close race with Google, IBM and neutral-atom firms, and are starting to give condensed-matter numbers classical machines can't reproduce. Simulating quantum systems remains the main economic application; Shor's 1994 algorithm made breaking encryption a second one. Factoring records stay unimpressive until fault tolerance, his analogue of the Manhattan Project's critical mass. A new company claims 30,000 physical qubits could break Bitcoin's signatures, with some firms targeting 2029–2030. He urges immediate migration, noting Bitcoin's lack of anyone in charge, and compares it to Y2K. He expects quantum-generated data to train classical chemistry and materials models, but sees no evidence for game-changing quantum speedups of classical ML. The no-cloning theorem underlies his quantum money idea.
- AI is already doing Fields-level mathematics, but not new techniques. Scott Aaronson says a recent OpenAI release of several hundred proofs did enough for "probably several Fields Medals" and hundreds of tenured positions, including L = BPL and the unique games conjecture; Anthropic separately improved algorithms for 3SUM and all-pairs shortest paths. He calls dismissing this as "not creative" wrong, but says AI has excelled at recombining existing techniques and finding counterexamples rather than inventing new ideas, which he thinks P vs NP will require; he won't rule out AI resolving it within two to three years.
- Credit in mathematics will shift towards exposition and explanation. Human researchers are now rate-limited on understanding and explaining AI output, which models do poorly. Aaronson contrasts Anthropic contracting named experts to write up its result with OpenAI dumping proofs on GitHub, and expects people to earn credit for "the diff" their exposition adds; authorship stays with humans who take intellectual responsibility, with an AI disclosure statement now the convention.
- Lean proof certificates are not yet fully trustworthy. He reports the Lean kernel has had bugs exploited to prove 0 = 1 within the last year, and that no one has proven Lean 4's type system consistent; he argues this should be fixed urgently, relative to ZFC or large-cardinal axioms. Even then, whether the formal statement matches the informal intent cannot be settled formally.
- Alignment likely cannot be fully reduced to a math problem. Aaronson says there is no mathematical definition of an aligned AI, that every verification idea (weak-monitors-strong, interactive proofs) founders on what statement to verify, and that evals are weakened because models are situationally aware and may act aligned while being tested. He gives a p(doom) of 5–50% and thinks the problem is solvable with enough time, but that "we don't have enough time."
- Bitcoin should begin migrating to post-quantum cryptography now. He cites a new neutral-atom company's papers claiming 256-bit elliptic-curve signatures could be broken with about 30,000 physical qubits at current accuracies, versus roughly 100 today and earlier estimates in the millions; some companies claim a fault-tolerant device by 2029–2030, a timeline he declines to judge. He argues no fundamental showstopper to fault tolerance has appeared and that scale is what remains.