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mathematiciansQuanta Magazine
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Danny Calegari is a topologist at the University of Chicago .
He published an essay in the Notices of the American Mathematical Society about the importance of failure in mathematics.
He says failure hurts every time, but it’s not always a bad thing.
The author says mathematicians often think that no one cares about their best work.
He says that mathematicians are reluctant to change gears when they try to prove certain things wrong.
By reading through failures, mathematicians can better understand the current cutting edge, he says.
Hardy: Mathematicians don’t always appreciate the power of that.
It's hard to know what's going on inside other people’s heads in mathematics, he says.
Good writing gives you a way of seeing what it's like to be other people, he adds.
He says it's useful to introduce subtle aspects of the topic one might find confusing.
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