Math for math’s sake

Arguably, theorem proving and problem solving aren’t even the most important goals for mathematicians. In a famous 1994 essay, the mathematician William Thurston argued that what mathematicians are doing “is finding ways for people to understand and think about mathematics,” especially as members of a social community. Thurston gave an example from his own life. Early in his career, he quickly proved a string of “dramatic theorems” in an area of mathematics called foliations. However, because he was so successful at proving the theorems — and significantly less successful at communicating the ideas behind his proofs — other mathematicians evacuated the field. The end result was that the social structure that had supported research into foliations collapsed and the subfield died. “I had the conception that what people wanted was to know the answers,” Thurston wrote. “That’s only one part of the story. More than the knowledge, people want personal understanding.”