Korva is a scroll of the internet’s best ideas.
Heroes existed because of a bottleneck
One mind per idea
Society knows far more than any single human, but it moves ideas around through individuals. A theorem has to be written so one grad student can learn it or one professor can teach it to another. Ideas more complex than one human can hold are possible, but only if they break down into pieces a single brain can follow. So every idea added to the shared pool could be understood by one mind, and one mind had to come up with it first.
The heroes of math
The people who conceived those almost impossible ideas became the heroes, and mathematicians were perhaps the most heroic of all. Isaac Newton invented calculus and classical mechanics all by himself. Grigori Perelman, working from a little room in Russia, solved a famous problem that had bedeviled the profession for decades, and Andrew Wiles did something similar a generation earlier.
Standing on shoulders
None of them worked from nothing, since every great discoverer stood on the shoulders of earlier giants. Still, in mathematical theory there was almost always some nub of hard work, some leap of genius, that belonged to one person alone. The dream of becoming that person was surely part of what drew people into the field.
Why did verifying Perelman's proof take years?
Grigori Perelman posted his proofs of the Poincaré conjecture to the arXiv preprint server in 2002 and 2003 rather than submitting them to a journal. The papers were terse and left many steps for readers to fill in. Several teams, including Bruce Kleiner and John Lott and also John Morgan and Gang Tian, wrote out the details over the following years. Morgan and Tian published a book-length account in 2007, and the Clay Mathematics Institute announced its prize for the result in 2010.
How did Wiles work in secret for seven years?
Andrew Wiles began his attack on Fermat's Last Theorem in 1986 and worked on it largely alone in the attic of his Princeton home. He told almost no one, and he let colleagues think he was still producing the usual small papers. He announced the proof in a lecture at Cambridge in June 1993. A gap turned up during refereeing, and Wiles repaired it with his former student Richard Taylor in 1994, with the final paper appearing in the Annals of Mathematics in 1995.
How did Newton's discoveries reach the world?
Newton developed his early calculus in the 1660s, but much of it sat unpublished for decades. In 1684, the astronomer Edmond Halley visited him at Cambridge to ask about the orbits of planets, and Newton said he had already worked it out. Halley urged him to write it up, and when the Royal Society had no money for printing, Halley paid for it himself. The result was the Principia, published in 1687.
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