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How Failure Has Made Mathematics Stronger
The topologist Danny Calegari discusses the inevitability of disappointment in math, and how to learn from it.
Calegari remains an avid reader — of Joyce, Dickens, Nabokov, Austen, Vonnegut, Lorrie Moore, Raymond Queneau, Anne Carson. My main disappointment had to do with work I did in a field called “stable commutator length,” about the relationships between elements in so-called free groups. Even when someone proves some famous conjecture and gets a lot of attention, the number of people who actually read the details of the proof and fully appreciate the thing that was done — it’s microscopic.
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