Genius can form entirely outside formal institutions

Ramanujan had almost no formal higher education. He failed out of college twice because he neglected every subject except mathematics, and his primary source of advanced material was a single, outdated compendium of theorems called Carr's Synopsis of Elementary Results. From this thin scaffold he built, in isolation, results that professional mathematicians in Europe hadn't reached. Kanigel uses this to challenge the assumption that world-class mathematical ability requires elite pedigree, mentorship, or institutional resources from an early age.

What Ramanujan lacked in formal training he made up for in obsessive, undirected exploration — he filled notebooks with formulas for years before anyone outside his immediate circle recognized their value. His case suggests genius is not always cultivated; sometimes it is simply discovered, often too late and often by luck, rather than produced on schedule by the systems built to find it.

Takeaway: talent can develop in total isolation from the institutions we assume are necessary to produce it.