How Failure Has Made Mathematics Stronger

Reading a math paper is a bit like having dinner at a nice restaurant. The entrée might taste delicious, but it doesn’t tell the full story of how it was made. Clever recipes that end up tasting funky don’t make the menu; undercooked dishes are (usually) not served to customers. But missteps in both conception and execution are important parts of the process. Danny Calegari, a topologist at the…

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