Before the catalogue of people who took shortcuts, the people who did not. None of these had the resources the situation seemed to require, and the interesting part in every case is the specific method rather than the determination.

Michael Faraday read the books he was binding.

Apprenticed to a bookbinder at fourteen with almost no formal schooling, he read the volumes passing through the shop, taught himself from an encyclopaedia article on electricity, and took obsessive notes at public lectures. He bound those notes into a book, sent it to Humphry Davy, and was hired. He went on to discover electromagnetic induction, which is why there is electricity in your wall. Michael Faraday

Ramanujan worked from one second-hand textbook.

A book of around five thousand theorems, stated without proof. Working alone in Madras with no university training, he rederived a large part of nineteenth-century mathematics and then went past it, producing results that took the field decades to catch up with. The absence of proofs in his source shaped how he worked for the rest of his life: he saw results first and justified them afterwards. Srinivasa Ramanujan

Katherine Johnson asked to be in the room.

A Black woman computing trajectories at NACA and then NASA under segregation, excluded from the editorial meetings where the work was discussed. She asked, repeatedly, whether there was a law against her attending. There was not, so she went. John Glenn would not fly until she had personally checked the electronic computer's numbers. Katherine Johnson

Temple Grandin used the thing she was told was a deficit.

Autistic, non-speaking until nearly four, and a visual thinker in a field that communicated in prose. She could model a cattle facility in her head and walk it from the animal's eye level, which is precisely why she saw the shadows and reflections that were causing panic. Roughly half the cattle in North America are handled in systems she designed. The perceptual difference was the qualification. Temple Grandin

Barbara Oakley failed maths, then taught it.

She flunked her way through school mathematics and science, joined the army, learned Russian, and only retrained as an engineer in her mid-twenties. Having learned the material the hard way and late, she could see the mechanics that people who found it easy had never had to notice, and turned that into one of the most-taken online courses in the world. Barbara Oakley

Jaime Escalante refused the expectation.

At a school in East Los Angeles written off by everyone including its own district, he taught calculus to students nobody had entered for the exam before. When eighteen of them passed in 1982 the board assumed cheating and made them sit it again. They passed again. Jaime Escalante

The Polgár sisters were a hypothesis someone tested.

László Polgár argued that expertise is trained rather than born, and raised his three daughters on deliberate, structured practice from early childhood. All three became elite chess players and Judit became the strongest female player in history. It is a sample of three with an obviously invested experimenter, which is the honest caveat — and it remains the most direct attempt anyone has made to test the claim on purpose. the Polgár sisters