Aaronson did not graduate high school at 15 but got a GED from New York state, having skipped grades to escape an environment he found socially and academically unhappy, and his parents had to convince the state to make an exception to the age-17 GED rule.

Set theories that determine more and more busy beaver numbers must become more and more complicated (e.g. via large cardinal axioms asserting larger infinities), and there is no surefire systematic way to discover such axioms while being confident they remain consistent — sometimes proposed large cardinal axioms turn out inconsistent.

It does not take long to become the world expert on one particular tiny narrow problem, and once you've done that it leads to articles, projects, collaborations, and then expertise on progressively wider topics.

The theory that academia since the 1970s has become less open to new ideas may hold in social sciences and parts of medicine, but in physics, foundations of computing, and cosmology the opposite has happened — the arXiv preprint server removed journal gatekeeping, so the real problem now is too many bold ideas to sift through rather than barriers to publishing them.

The reason quantum teleportation (1990s) and quantum computing (1980s) came decades after quantum mechanics (1926) is that viewing entanglement as a usable resource only began with John Bell in the 1960s, computational complexity theory only developed in the 1960s-70s, and meanwhile both physics and the nascent field of classical computing had enormous other priorities, plus WWII diverted fundamental scientists.

There is probably no 'algorithm for creativity' because the phrase is almost oxymoronic — whatever such an algorithm output would no longer be creative since it would merely be that algorithm's output.

Breakthroughs do come from people outside academia, but most often these are people on academia's margins (who got or partially got a PhD then left), as with Yitang Zhang who proved infinitely many prime pairs at most 70 million apart while working odd jobs including making sandwiches; by contrast, untrained autodidacts who claim to have solved P vs NP usually simply don't understand the question.

Lack of knowledge about the economy and lack of ability to compute on the knowledge you already have are distinct kinds of deviation from omniscience; Nash equilibrium hardness concerns the latter (computation), whereas Hayek's knowledge problem and the economics of information concern the former, and economists have integrated information problems more successfully than computational ones.

Humans crossed a threshold from other animals via a succession of universality milestones — recursive language able to express thoughts of unbounded complexity, writing to transmit thoughts across generations, a number system referring to arbitrarily large numbers, and universal computing machines — all tied to explaining the world in explicit theories as no other animal can.

Just as the busy beaver function has fixed values (like BB(800)) that existing set theory provably cannot determine, there may be fixed questions — perhaps the hard problem of consciousness or why there is a universe at all — that what we currently consider an explanation will never suffice to answer; unlike Deutsch, Aaronson refuses to assert from first principles that all such things are explainable.

Shor's and Grover's algorithms should be viewed not as isolated specific algorithms but as basic design motifs of the quantum-algorithmic universe, analogous to how classical algorithms (dynamic programming, divide and conquer, greedy, linear programming, Gaussian elimination) are mostly built from a few motifs discovered early in classical CS — so their early discovery is unsurprising, not a failure of imagination.

Never has more learning resources been available; one can learn deeply by taking courses, talking to professors, and reading freely-available literature (e.g. all quantum computing papers on arXiv), and the barriers to becoming the world expert on one tiny problem are surprisingly low.

The modern concept of an extended 'teenagerhood' in which people aged roughly 12-18 are still children is largely a recent social construction; historically teenagers were apprentices learning a trade while working.

There is a developmental window in which children absorb languages effortlessly, after which learning a language becomes a difficult intellectual puzzle and one will never speak it as well as a native five-year-old.

David Deutsch was able to think seriously about quantum computing because he took the many-worlds interpretation seriously, motivated by wanting to demonstrate quantum mechanics is universally valid at all scales — a quantum computer doing interference between computations is conceptually like a superposition over a brain thinking different thoughts.

Although Bohr was right and Einstein wrong on the issue of local hidden variables, there is a deeper sense in which Einstein was the more right one, because he correctly insisted there was something about quantum mechanics not yet understood that needed to be understood — a question only resolved by Bell's inequality in the 1960s.

Early 20th-century physics was 'ripe' for the relativity and quantum revolutions, so if Einstein hadn't made his 1905 discoveries someone else would have soon after — except general relativity, which took Einstein a decade longer and might otherwise have been delayed by decades.

Whether older scientists' brains actually slow down or whether they simply have less motivation and free time is an open empirical question; Aaronson notes that when away from family obligations he can work as he did in his 20s, suggesting time and motivation may dominate over cognitive decline.

There is evidence a quantum algorithm might exist for computing edit distance between two strings (a fundamental problem in DNA sequence alignment) in roughly n^(3/2) time versus the best known quadratic-time classical dynamic-programming algorithm, though such a quantum algorithm has not yet been discovered.

Only a finite number of busy beaver values can be proven from the axioms of set theory because of Gödel's incompleteness theorem; currently only four values are known (BB(1)=1, BB(2)=6, BB(3)=21, BB(4)=107), with BB(5) known only to be at least about 47 million.