This gallery sorted itself into two kinds of person a long time ago and never said so out loud. One kind could have done their work at twelve. The other could not have done it at any age but the one they were. The difference is not in the people. It is in the doors.
Volume VII holds thirty-four people across five sections. The sections were built by subject — Published, Writers, Priority Queue, Attribution Series, Extended Roster — and not by anything as tidy as a thesis. But read the roster with one question in mind and it falls into two piles immediately, and the fault line runs straight through the section headings without respecting any of them.
The question is: could a twelve-year-old have done this?
For Ramanujan, Hamilton, Noether, Mirzakhani, Kovalevskaya, Tao — yes, in the sense that matters. Not that they did, but that nothing in the material forbids it. The objects are available. The rules are complete and written down. A child who can read them can begin.
For the Writers section — Graciliano Ramos, Augusto dos Anjos, Primo Levi — the answer is no, and not by a little. Ramos's material is the sertão and the prison; dos Anjos's is his own body failing; Levi's is Monowitz. You cannot enter those domains early because the domain's content is what happened to you, and at twelve not enough has.
The pattern is well known in outline and, as far as this author can find, rarely stated as a structural claim. Child prodigies appear in chess, in music, and in mathematics. They do not appear in literature, history, philosophy, medicine, or law. The standard explanations reach for the child — some faculty that ripens early, some quality of mind. The explanation this chapter proposes reaches for the domain instead.
Chess is a closed formal system: the legal moves are finite, written down, and true on the first day exactly as on the last. Musical notation and tonal harmony are a formal system with a physical instrument attached. Mathematics is the case in the limit — its objects are constituted by their rules, so there is nothing outside the notation to have missed. In all three, everything the domain contains is present in the room, and a nine-year-old in that room is not at a disadvantage that time alone would fix.
The excluded domains fail the third condition, not the first two. A novel has craft that can be taught and a history has methods that can be learned; what cannot be handed over is the material, because the material is a life. This is why the prodigy list is stable across cultures and centuries while fashions in child-rearing are not. It is a fact about domains.
The claim is falsifiable and should be tested rather than admired. It predicts no genuine child prodigies in domains whose content is experience, and it predicts that any apparent exception will turn out to be either a formal sub-skill mistaken for the domain — technical facility at an instrument is not musicianship, verse mechanics are not poetry — or a constructed story. §5 is about the second kind, because this corpus has already caught one.
The proposal above says which doors open early. It does not say anyone must walk through, and the strongest evidence for that distinction is already in this gallery, in two chapters filed in different sections.
Same domain. Same medal. One entered at nine and one at roughly twenty-three, having spent his adolescence trying to be a poet — a domain, note, that would not have him yet either, and for the reason in §2. The mathematics did not close while Huh was away. That is the property being claimed: the formal door is open early, which is a different statement from open only early, and conflating the two is how a structural observation turns into a prejudice about who is too old to begin.
Huh is the falsifier the proposal survives, and a thesis that survives its sharpest counterexample is worth more than one that never met it.
If the door is open, the obvious question is why the traffic is so light. The best answer in the literature is David Feldman and Lynn Goldsmith's co-incidence theory (Nature's Gambit, 1986): a prodigy is not one rare thing but an improbable convergence of ordinary ones — a domain matched to the child's inclination, geographic availability, a family tradition, parental commitment, access to training, cultural recognition, and historical timing. Remove any factor and the prodigy does not appear, which is why prodigies are rare without anything about them needing to be miraculous.
That list is usually read as weather. It is not weather. Historical timing is whose government was in power and what it did. Access to training is whether a family could spare a child from earning. Family tradition presumes a household with room for one, rather than a household organised around staying alive. Every factor on Feldman's list is a condition on the child's circumstances, and every one of them was set by somebody. Stated neutrally the theory explains why prodigies are rare. Stated plainly, a good deal of what it files under coincidence is somebody's policy.
Co-incidence theory is built by examining prodigies and asking what they had in common. That method can only ever see the survivors. It yields an excellent account of how a prodigy holds together once present — which factors were necessary, which sustained the development — and no account whatever of the distribution of children who never came near the domain, because those children are not in the sample and cannot be.
This is the same gap named in WP-104 and partly closed in Chapter 25, in a subject as far from this one as it is possible to get: everything we had was stability, and the question was selection. Feldman gives the stability account of the prodigy. The selection account — which children get within reach of a door at all — is not a psychological question and will not be answered by studying prodigies. It is a question about states, economies, schools and wars, and it is answered in those terms or not at all.
So the thesis of this chapter has two halves and §2 only stated one. A domain decides when it can be entered; access decides who arrives; and only the first of those is a fact about mathematics. The indifference of a closed formal system to the age of the person entering it is real, and it is the genuinely good news in §2 — the rules do not check a birth certificate, and they did not close while June Huh spent seven years elsewhere. Institutions are not indifferent in the slightest, and it is institutions, not domains, that invented being too old.
The clean illustration is in this gallery already. Mathematics has no age gate anywhere in it. Its most famous prize has one: the Fields Medal requires that the recipient be under 40 on 1 January of the year of the award. That rule is not a property of the subject; it is a decision, made by people, in service of a stated aim — Fields wanted the medal to encourage further work rather than only to crown finished work. One may think the aim reasonable and still notice what the rule does: it is the domain's openness and the institution's deadline sitting side by side, and only one of them is mathematics. Huh cleared it having started at twenty-three, which suggests the gate is not measuring the thing people assume it measures.
Joanne Ruthsatz's work adds a second correction to the folk picture: prodigies are marked less by uniformly exceptional general intelligence than by extraordinary working memory and attention to detail, and the measured profiles differ sharply by domain — reported averages near 140 for mathematics, 129 for music, 108 for art. Whatever a prodigy is, it is not one thing wearing three costumes.
None of which is an argument that talent is a fiction or that circumstance is destiny. It is the narrower claim this chapter can actually support: when a distribution is produced jointly by a door and by who was permitted near it, reading the distribution as though the door were the only term will systematically mistake an accident of access for a fact about people. That error has a direction. It always flatters whoever got in.
§4 says the selection question is answered in terms of states, economies, schools and wars. That is easy to assert and worth demonstrating once, on a case where the record is good, because the mechanism turns out to be sharper and stranger than “a dictatorship damaged education”.
The Brazilian military regime did not close the universities. It did something more selective. On the repressive side: roughly 300 university professors were forcibly retired or dismissed across two purges, in 1964 and again in 1969 after Ato Institucional nº 5 and Decreto-Lei 477, which between them permitted summary expulsion of professors, students and staff with practically no defence. More than a thousand students were expelled between 1969 and 1979 — 250 at the University of Brasília in 1969 alone. From 1970 some 35 Special Security and Information Advisory offices (ASIs) monitored campuses and reported to the national intelligence service, several persisting into the early 1980s. At USP’s Faculty of Philosophy the compulsory retirements took Fernando Henrique Cardoso, Florestan Fernandes and Octavio Ianni. Educação Moral e Cívica was made a compulsory school subject in 1969.
And on the other side, simultaneously, the same regime expanded science and technology enormously. University enrolment went from 142,000 in 1964 to 1.4 million by 1984. Graduate programmes went from six courses in 1961 to 792 master’s and 333 doctoral programmes by 1984. FINEP was created in 1967, Embrapa in 1973, and twelve new federal universities were founded.
A state that simply suppressed education would produce a shortage everywhere and would be easy to describe. This one purged the humanities and social sciences while pouring money into the exact sciences and engineering — and it ran the best technical schools itself. ITA, the Instituto Tecnológico de Aeronáutica, founded 1950, is maintained by the Brazilian Air Force; its first-year undergraduates are considered military personnel and attend a military preparation course weekly, which discharges the country’s compulsory service; admission runs near one per cent and its entrance exam is the most competitive in Brazil. IME, the Instituto Militar de Engenharia, is the Army’s equivalent.
So consider a household that opposed the regime, containing a child with an aptitude for mathematics, in 1975. The domain’s door is wide open in exactly the sense §2 describes — the rules are complete, available, indifferent to the child’s age. The institutional door is open too, better funded than it had ever been, and it leads through a gate with soldiers on it. Nothing forbids that child from mathematics. Everything about the route says whose side taking it will look like.
The clearest evidence is not in what the regime built but in what it forbade, because a prohibition leaves a mark in the workforce that outlasts the prohibition. Philosophy and Sociology were banned from Brazilian schools in 1971 and replaced by Educação Moral e Cívica. They returned in 1986, as optional subjects, and became compulsory in secondary education only in 2008 — thirty-seven years after the ban. Sociology’s exclusion is older still: it had been out of the curriculum since the Capanema reform of 1942, creeping back state by state from 1983.
Now consider what that does to a profession. For fifteen years nobody could enter it, because the job did not exist. When the subjects came back, the people teaching them were necessarily of two kinds: those who predated 1971, and those trained after 1986. There is no middle cohort, and there could not be. The ban is legible in the age distribution of the teaching staff decades after it was lifted — a bimodal profession, very old or very young, with a hole where a generation should be.
That is what an absence looks like when it becomes measurable. §4 says a theory assembled from the people who arrived cannot count the people who did not, because the missing are not in the sample. Here they are in the sample, as a gap with edges and dates. Nobody has to be interviewed about the sociologists Brazil did not train between 1971 and 1986; you can read the number off the census of who was standing in front of a classroom in 1995, and the shape of the hole is the shape of the law.
Pablo Grossi’s note on this is that he had such a teacher, and that he considers it luck. Luck is the correct word and it is Feldman’s word: in a fifteen-year hole, an adult in the room who could teach the subject is precisely a coincidence factor, and the child in that room had one where most did not. It is also, as of the current secondary-education reform, not a settled question — philosophy and sociology have been removed from the compulsory curriculum again, with São Paulo among the states dropping them.
The removal is happening at a strange moment. The same decade in which São Paulo drops philosophy from the compulsory curriculum is the decade in which the firms building frontier AI systems began hiring philosophers — not as ornament but into research roles. A publicly maintained list names, among others, Amanda Askell, Joe Carlsmith, Ben Levinstein, Jackson Kernion and Harvey Lederman at Anthropic; Iason Gabriel, Adam Bales, Atoosa Kasirzadeh, Arianna Manzini, Julia Haas and Geoff Keeling at Google DeepMind; Robert Long and Patrick Butlin at Eleos AI; Beba Cibralic at RAND; Lisa Miracchi Titus at Meta. The work is alignment, evaluation, governance, moral status and what one firm calls character.
The numbers are small and the reporting is disputed — workforce specialists have publicly pushed back on accounts of philosophers being paid extraordinary salaries, and the practice is not industry-wide: OpenAI is reported to treat safety largely as an engineering problem without dedicated philosopher roles. Nothing here should be read as study philosophy, the market wants you. That would be a labour-market claim and this chapter has no standing to make one.
The claim is narrower and survives the caveats intact: the skills being removed from a public curriculum have non-zero and rising value at the technological frontier, and eligibility for that frontier is set roughly a generation upstream, in a classroom, by a decision a fifteen-year-old does not take. Twenty such jobs would be enough for the argument. What matters is not how many exist but who will be able to hold them.
Which is this chapter’s mechanism running live rather than in retrospect. Philosophy as a domain is wide open — its rules are complete and available, and §2 applies to it as much as to chess. The state narrows the school door. The frontier then recruits philosophers from wherever philosophers are still made, which is to say from the systems that did not cut the subject, and from the households that could supply it privately when the school would not. Hansen and Reich measured what that produces. A curriculum decision taken in 2026 is a statement about who is eligible in 2045, and it is not usually debated in those terms because the people it excludes are not yet old enough to say anything.
The paragraph above could be read as saying mathematics in Brazil was the military route. It was not. IMPA — the Instituto de Matemática Pura e Aplicada, founded in Rio on 15 October 1952 as the first research unit of CNPq, the civilian federal research council — was there the whole time, under Lélio Gama with Leopoldo Nachbin and Maurício Peixoto, and it went on to train Artur Avila. Any account that says there was no civilian door is false, and this chapter will not say it.
What the correction does is make the access claim precise rather than dissolve it. On one side, a national system of military technical schools — ITA, IME — funded through the regime’s science expansion, prestigious, and nationally recruited. On the other, one institute in one city, admitting a handful. Access is not a matter of whether a door exists. It is a matter of how many doors, how wide, and how far from where you live, and a single narrow civilian door beside a well-funded national military one is exactly the shape that produces a household’s turn away from the subject without anyone in it lacking the aptitude.
§4 says access decides who arrives, and the material above says the state shapes access. Left there, the account is pure determinism — regimes close doors and nobody has any recourse. That is not what happened, and the correction above is the clue: the civilian door existed because a small number of people built it.
Lélio Gama (1892–1981) took over the Observatório Nacional in 1943 and founded IMPA in 1952. Mário Schenberg (1914–1990) had, with George Gamow in 1940–41, introduced the neutrino into astrophysics — the Urca process, named after a Rio casino because energy left a collapsing star as fast as money left the roulette table — and with Subrahmanyan Chandrasekhar in 1942 fixed the limit on a stellar core’s mass. César Lattes (1924–2005) co-discovered the pion in 1947, came home, founded the CBPF at twenty-five, and was a principal force behind the creation of CNPq — the council that built the one civilian door named above. Abrahão de Moraes (1916–1970) built celestial mechanics at USP from 1945. That is most of a national scientific base, and it is four names.
On 1 April 1964 the military took power. Within a week Schenberg was arrested, forced to resign his university position, and imprisoned for fifty days. Police raiding his apartment confiscated his books, having taken a Baroque statue for a likeness of Lenin. He received amnesty in 1979 and returned to teaching at USP — fifteen years later, a span almost exactly matching the ban on philosophy and sociology.
Set that against the figure in the paragraph above. Roughly 300 professors forcibly retired sounds modest beside 1.4 million students. It is not modest, and the number cannot be read without its base. In a system where the astrophysics is one man, three hundred is catastrophic. A regime facing a thin institution does not need to close a field. It needs to remove a few people.
So the third term is agency, and it cuts both ways rather than consoling. The same thinness that let four people build a national science is what let a handful of arrests narrow it, and the reason individuals are load-bearing in that story is precisely that the institution was too small to absorb their loss. Agency matters more in a thin system, in both directions, which is neither the determinism this section risked nor the reassurance that talent finds a way. It is the observation that when the base is narrow, who is standing on it is a first-order fact.
This is what §4 means by an accident of access that reads afterwards as a fact about people. A family that turned away from the exact sciences under those conditions was not less mathematical. It was making an accurate assessment of what the available route cost, and the cost was not tuition.
This corpus has an author, and the reason it exists at all belongs in this chapter rather than in a preface, because it is a data point for the claim and not a decoration on it. Pablo Nogueira Grossi’s parents are both journalists, and he states plainly that this is why: in the Brazil of the 1970s and 1980s, an inclination towards mathematics led to studying or working with the military, and theirs was a household that would not. They were required to participate in institutions that were not theirs — the Catholic church, in a Jewish family — and to write about the feats of the great country and its armed forces while defending democracy, freedom and human rights. The family turned towards art and away from the sciences, and that inclination passed down a generation as though it were a temperament. It was a political inheritance.
He was told at thirty-five that he was too old to begin. The mathematics in the rest of this series was written afterwards.
Neither half of that is offered as a triumph, and the second half is not the point. The point is the first half: the door to mathematics did not close on that family, and no child in it was short of the aptitude. A state stood in the doorway for twenty-one years, and what came out the other side looked, to anyone counting later, like a family that simply preferred the arts. That is the error §4 names, in one household, over two generations — and it is why a theory of prodigies assembled from the ones who arrived will keep mistaking a policy for a personality.
It would be comfortable to file the preceding as history. In September 2024 the Colombian Constitutional Court ruled on the case of a nine-year-old in a state school — anonymised as Sara, from a Christian but not Catholic family — who was required to learn Catholic prayers and dogma in her religion class. When her father asked for an alternative that respected the family’s faith, the school did not formally reply; the child was excluded from the class and given 0.0 in the subject, damaging her academic record. The Court found violations of freedom of worship, of the right to education, and of the secularity of the state, and ordered the school to rewrite its educational project to guarantee alternatives for students who decline religious instruction, to remove Catholic dogmatic content, and to teach the subject neutrally.
A constitutional court had to say this in 2024, which means the practice was live until it did. The mechanism in this section is not a period detail about one regime. It is what happens wherever an institution a child cannot refuse is also an institution that requires something of them, and the cost is paid in the same currency every time: a mark on a record, a route made narrower, a family that learns which doors are not for them.
There is a comfortable modern reply to all of this: the separation of church and state is settled, the archives are digitised, the lectures are on the internet, and anyone anywhere can now learn anything for free. The first clause is false in many places — in some the separation was never made, and in others, as the ruling above shows, it exists on paper while a nine-year-old is marked 0.0 for declining the catechism. The rest of the reply is true and does not mean what it is usually taken to mean.
Hansen and Reich examined 68 free HarvardX and MITx courses on edX across 2012–2014 and published the result in Science in December 2015. Young registrants lived in neighbourhoods with median incomes 38% above the typical American neighbourhood. Among teenagers, those with college-educated parents had nearly twice the odds of completing a course as those whose parents had not been to college. Reich’s summary: online learning does not yet live up to its promise to democratise education.
The reason is the distinction this chapter has been making all along, one level up. The internet is an availability revolution, and availability was never the binding constraint. It distributes the material and nothing else on Feldman’s list. It does not distribute a household with room for study, or a tradition that makes the domain thinkable, or an adult who knows the field exists, or the time of a fifteen-year-old who is earning, or the sentence this is for people like you, which is not on any syllabus and is the one that decides. Family, tradition and opportunity do not materialise because a PDF is free.
This matters because the availability claim is not usually offered as an observation. It is offered as a dismissal — it is all online, so what is your excuse — which converts a question about access into a verdict about a person. That is the §4 error in its contemporary dress, and it has the same direction as ever. It flatters whoever got in.
A gallery that adds prodigies takes on a specific risk, and this corpus has already been caught by it once — which is the reason to state the rule here, before the entries, rather than in an erratum afterwards.
A widely circulated video account of Manjul Bhargava's early life presents him arriving at a formula for stacked spheres by arranging oranges as a child. The formula is n(n+1)(n+2)/6, and it is Āryabhaṭa's citighana, stated in the Gaṇitapāda in 499 CE. Nothing in that diminishes Bhargava, who is a Fields Medallist for reasons that have nothing to do with the story. What it shows is that the prodigy narrative is a genre, that the genre wants a scene of spontaneous discovery, and that the genre will supply one. The correction and its sources are in Chapter Mātrā, and the attribution table it prompted is in Chapter 8 · Meru.
The Bhargava example is about a story a documentary invented. The harder case is the one where nobody invented anything and the credit went astray regardless, because a rule sent it there.
In 1947 César Lattes improved Powell’s nuclear emulsion by adding boron to it, carried plates to Chacaltaya at 5,200 metres to catch the decays, determined the new particle’s mass, and was first author of the Nature paper announcing the pion. The 1950 Nobel Prize in Physics went to Cecil Powell, alone. Not through anyone’s bad faith: the Nobel Committee’s policy until 1960 was to award the head of the research group. A rule, applied evenly, and the first author of the paper is not on the prize.
That is this chapter’s thesis in its least comfortable form. §2 says a domain decides when it can be entered; §4 says institutions decide who arrives; Lattes says institutions also decide who is recorded as having arrived. The door, the queue and the ledger are all three institutional, and none of the three is the mathematics.
Lattes returned to Brazil and founded the CBPF at twenty-five, in 1949, and was one of the principal forces behind the creation of CNPq, the civilian research council that established IMPA as its first research unit in 1952. The single civilian door of §5 exists substantially because of him. Brazil’s national record of researchers — the register every Brazilian academic’s work sits in — is the Plataforma Lattes, named after him.
The tempting story is that he built it because the Nobel passed him over, and the dates refuse that particular telling: CBPF is 1949, the prize is 1950. But reading the refusal as settling the matter would be too clever by half, because the grievance was never about one prize. The Nobel Committee’s policy until 1960 was to award the head of the research group — a standing rule, known to everyone working under a group head, which systematically directed credit upward. Lattes was first author of the Nature paper in 1947 and Powell was the head; the rule was legible from inside the laboratory long before 1950. The prize was that rule doing what it always did, not the discovery that it existed. CHECKED
And that is the complaint the returning generation actually made, in the form they made it: not that the work was hard or the conditions poor, but that the discoveries were theirs and the prizes went to their superiors. What they built at home was in part an answer to that — institutions in which a Brazilian researcher’s work would be registered under their own name. Lattes after Bristol and Berkeley, Schenberg after his years in the United States with Gamow: a national science assembled by returners, whose existence depended on a handful of individual decisions to come back, and thin enough afterwards that arresting a few people mattered as much as §5 shows it did.
Which gives the Plataforma Lattes its actual meaning. It is not an ironic epilogue. It is the thing the complaint was asking for, built by one of the complainants, and now carrying his name: a ledger in which the person who did the work is the person recorded as having done it.
Every claim about a living or recent person comes from a published source that is named. Ages and dates are checked against a primary or reference source, not against a documentary. Where a discovery is attributed, the prior art is looked for before the sentence is written, not after a reader objects. No claim is made about anyone's inner life, family, or motives that they have not made themselves in print. And where the subject is a child, the chapter is about the domain and the work, not the child as a spectacle.
This chapter opens a slot rather than filling it. The entries it is built for are the people whose doors opened early — Gauss, Pascal, Hamilton on the language side before the mathematics, Ramanujan, Kovalevskaya, Tao, Mirzakhani — read the way the rest of this gallery reads its subjects: through the domain and the operator chain, with the biography in service of the mathematics rather than the other way round.
And it changes what the Writers section means. Ramos, dos Anjos and Levi are not the gallery's soft counterpart to its scientists. They are the direct evidence for the claim in §2 — the domains whose doors cannot open early, standing next to the domains whose doors cannot be closed. Between the two sits the only honest general statement this chapter makes: a domain decides when it can be entered, and a life decides whether anyone does.
Feldman, D. H. & Goldsmith, L. T. (1986). Nature's Gambit: Child Prodigies and the
Development of Human Potential. Basic Books. — co-incidence theory.
Ruthsatz, J. and colleagues, on working memory, attention to detail, and domain-specific
cognitive profiles in prodigies; summarised with Feldman in S. B. Kaufman (ed.), 2014.
Winner, E. (1996). Gifted Children: Myths and Realities. Basic Books.
Terence Tao: IMO results 1986–1988; Flinders 1991; PhD Princeton 1996 (Stein); Fields Medal
2006.
June Huh: SNU 2002; PhD Michigan 2014 (Mustață); Fields Medal 2022. See
Chapter Ju.
Philosophy and Sociology: banned from Brazilian schools in 1971 and replaced by
Educação Moral e Cívica; returned in 1986 as optional subjects; compulsory in secondary
education only from 2008 (Lei 11.684/2008), and removed from the compulsory curriculum again
under the current secondary-education reform. Sociology had additionally been out of the
curriculum since the Reforma Capanema of 1942, returning state by state from 1983 (São Paulo,
Resolução SEE/SP 236/83). Sources: Revista Educação; Ensino de Sociologia:
periodização e campanha pela obrigatoriedade, SciELO.
Mário Schenberg (1914–1990): Urca process with Gamow, 1940–41; Schönberg–Chandrasekhar limit,
1942; arrested seven days after the 1 April 1964 coup, forced to resign his university post,
fifty days imprisoned; amnesty 1979, returned to the USP Physics Institute (MacTutor).
César Lattes (1924–2005): improved Powell's emulsion with boron; Chacaltaya plates at 5,200 m;
determined the pion's mass; first author of the 1947 Nature paper. The 1950 Nobel went to Cecil
Powell alone — the Committee's policy until 1960 was to award the head of the research group.
Returned to Brazil and founded the CBPF in 1949 at 25; a principal force behind the creation of
CNPq, which established IMPA in 1952. The Plataforma Lattes, Brazil's national researcher
register, is named after him. Note the order: CBPF 1949, Nobel 1950 — the building preceded the
omission.
Abrahão de Moraes (1916–1970): celestial mechanics at USP from 1945.
Lélio Gama (1892–1981): director of the Observatório Nacional from 1943; founded IMPA 1952.
IMPA: founded 15 October 1952 as the first research unit of CNPq (created 1951), under
Lélio Gama, with Leopoldo Nachbin and Maurício Peixoto; civilian, not military.
Brazil, 1964–1985: professor purges, AI-5 and Decreto-Lei 477, the ASIs, and the
simultaneous expansion of science and technology — Revista Pesquisa FAPESP,
“The impact on the academic world”. Educação Moral e Cívica compulsory from
1969. ITA: maintained by the Brazilian Air Force, founded 1950, first-year undergraduates
classified as military personnel, admission near 1%. IME: the Army’s engineering institute.
Philosophers in AI research roles: list maintained at Daily Nous, “Philosophers
Working in or with AI Firms & Organizations”. On the disputed magnitude, see reporting
in which workforce specialists downplay accounts of very high philosopher salaries; and on the
non-uniformity of the practice across firms, trade coverage of DeepMind, Anthropic and OpenAI’s
differing approaches. Note of interest: the draft of this section was prepared with the
assistance of an AI system built by one of the companies named, and is stated conservatively for
that reason.
Hansen, J. D. & Reich, J. (2015). Democratizing education? Examining access and engagement
in online learning. Science, 4 December 2015 — 68 HarvardX/MITx courses,
2012–2014; young registrants’ neighbourhoods 38% above median income; teenagers with
college-educated parents nearly twice the odds of completion.
Colombia: Corte Constitucional, Sentencia T-357 de 2024 (First Review Chamber),
reported September 2024 — public schools may not impose a particular creed and must
guarantee alternatives for students who decline religious instruction.
The family account in §5 is Pablo Nogueira Grossi’s own, given in his words; the
historical claims around it are from the sources above and not from him.
Fields Medal age rule: recipient must be under 40 on 1 January of the year of the award; the
restriction follows J. C. Fields’s stated intent that the medal encourage further work and
not only recognise completed work.
Āryabhaṭa, Āryabhaṭīya, Gaṇitapāda 21 (499 CE), citighana. See
Chapter Mātrā.