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Two ways to crack a walnut, per Grothendieck (2025)
The mathematician Alexander Grothendieck was “considered by many to be the greatest mathematician of the twentieth century”. Somewhere in his 1000+-page autobiographical work Récoltes et Semailles (“Harvests and Sowings”), he describes two styles in mathematics: Take for example the task of proving a theorem that remains hypothetical (to which, for some, mathematical work seems to be reduced). I see two extreme approaches to doing this. One is that of the hammer and chisel, when the problem posed is seen as a large nut, hard and smooth, whose interior must be reached, the nourishing flesh protected by the shell. The principle is simple: you put the cutting edge of the chisel against the shell, and hit it hard. If necessary, you repeat the process in several different places, until the shell cracks—and you are satisfied.
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