Essay · Section B24 September 2026

Knowledge belongs to all; the means of knowing, to a few.

In January 1913 a clerk at the Madras Port Trust, with no degree and no laboratory, posted a letter crowded with formulas to G.H. Hardy at Cambridge. Hardy, after studying it with J.E. Littlewood, concluded that it could only have come from a mathematician of the highest class. Srinivasa Ramanujan needed nothing from the world except paper, a stamp and a reader able to check his work. That is why mathematics has been the most democratic of the sciences. A proof is as valid in Kumbakonam as in Cambridge, anyone patient enough can verify it, and what it proves belongs to everyone.

This year the most famous problems in mathematics have begun to fall to machines. According to reports this week, a model built by the AI company Anthropic produced in July a counterexample to the Jacobian conjecture, which had stood for eighty-seven years. On 8 September OpenAI announced that an unreleased internal model had solved the Navier-Stokes existence and smoothness problem, one of the Clay Institute’s million-dollar Millennium Prize Problems, by running 10,000 autonomous AI agents for 88 hours. These claims are still being examined, and one is already disputed. The truths may still belong to everyone; the means of finding them now belong to a handful of companies in two countries. When OpenAI announced on 29 July that 1,00,000 scientists, mathematicians and engineers could use its frontier models free, Indian, Russian and Chinese institutions were left out, most likely because of geopolitical tensions, the report says. And as President Trump receives President Xi in Washington, the rules for this technology are being discussed by two capitals, while the rest of the world, in one commentator’s phrase, risks becoming a rule-taker.

The prompt names a tension as old as learning. Knowledge, once found, tends towards the commons: it can be copied without being used up. The means of producing it, whether instruments, money, institutions or now computing power, tend towards concentration. When the two drift apart, knowledge becomes power over those who lack the means. This essay argues that the gap is now wider than at any time since the nuclear age, that it threatens not only India’s share of discovery but the character of knowledge itself, and that the answer lies not in resentment but in building capacity, insisting on verifiability and claiming a seat where the rules are written.

The pattern is old. The printing press made books cheap; about a century later the Church issued its Index of Prohibited Books. The nuclear age made the pattern explicit. The Treaty on the Non-Proliferation of Nuclear Weapons of 1968 defined a nuclear-weapon state as one that had exploded a device before 1 January 1967, and so froze the hierarchy of that moment into law. India refused to sign, and after its 1974 test it faced the newly formed Nuclear Suppliers Group and decades of technology denial. In 1998 Jaswant Singh, writing in Foreign Affairs, called the arrangement nuclear apartheid. Thucydides had set out its logic twenty-four centuries earlier in the Melian dialogue: “the strong do what they can and the weak suffer what they must.”

What is new is that concentration now reaches inside knowledge itself. In 1942 the sociologist Robert K. Merton described the ethos of science as four norms: findings are common property; claims are judged by impersonal standards, not by who makes them; scientists are disinterested; and every claim faces organised scepticism. Machine mathematics strains at least two of these. The companies do not release the prompts that produced their proofs; a Harvard mathematician complained of “a certain amount of intentional mysticism around how they arrive at certain results”. And the proofs are hard to read. The Bristol number theorist Andrew Booker says the AI “writes like an alien sometimes”, and Columbia’s Michael Harris describes a nightmare in which a machine produces an incomprehensible proof of the Riemann hypothesis and humans simply have to accept it. A truth that its receivers cannot understand must be taken on trust, and trust flows towards whoever owns the machine.

The counter-argument is strong. Science has always depended on costly instruments held by a few, and knowledge still spread. Firms that spend billions on computing have a fair claim to control what they built. Frontier AI can serve war as well as peace, and withholding it from rivals may be prudence rather than prejudice, as nuclear export controls were. Rules written by two great powers are better than none: a Sino-American understanding not to collide by accident protects everyone. And unreadable proofs are not new. When Kenneth Appel and Wolfgang Haken proved the four-colour theorem in 1976, with a computer checking cases no human could, many mathematicians were uneasy; in 2005 the proof was formally verified in a proof assistant, and the unease faded. Today’s models can already translate proofs into Lean, a language in which a machine checks every step.

These objections show that expensive means need not destroy a commons. They do not show that a commons survives on its own. It survives when the means are governed as shared institutions. The CERN Convention, in force since 1954, says that the organisation “shall have no concern with work for military requirements” and that its results “shall be published or otherwise made generally available”; India became an associate member in 2017. When the partners in the Human Genome Project met in Bermuda in 1996, they agreed to release sequence data within twenty-four hours, which helped keep the human genome in the public domain. The Green Revolution reached India because the wheat varieties Norman Borlaug bred in Mexico were shared through publicly funded international research. What matters is not the cost of the instrument but the charter under which it works.

For India this points to three duties. The first is capacity. Denial has always been answered best by building: C-DAC was set up in 1988 when advanced supercomputers were hard to obtain, and its PARAM 8000 followed in 1991; the cryogenic technology that American pressure kept Russia from transferring in the early 1990s was mastered at home and flew on a GSLV in 2014. The IndiaAI Mission, approved in 2024 with an outlay of ₹10,371.92 crore, must become compute that a researcher in a state university can actually use. The second is verifiability. Indian academies should give full credit only to machine proofs that can be formally checked and whose methods are disclosed, in the spirit of the Leiden Declaration on Artificial Intelligence and Mathematics of June 2026. The third is voice. The Global South, S. Jaishankar said in New York this week, sits in the front row of crises and the back row of decision-making. India, which chairs BRICS this year, can help bring together the middle powers, including the countries behind this week’s Norwegian and Finnish call for control of frontier AI models, so that the rules are not written in two capitals alone.

Isaac Newton wrote to Robert Hooke that if he had seen further, it was “by standing on the shoulders of Giants”. Those shoulders were open to anyone who could read. Ramanujan climbed them from a clerk’s desk because a stranger in Cambridge was willing to read his work. The Ramanujan of 2026 may need more than paper and a stamp. He may need computing power, access and a seat in the room where the rules are made. A theorem does not care who proves it. A nation must care who can.