Det är någonting med de här beskrivningarna av matematikern Alexander Grothendieck som liksom kittlas. Alla andrahands-beskrivningar, eftersom jag misstänker att jag aldrig skulle förstå en läsning av originaltexter. Och att extremt abstrakta beskrivningar behöver beskrivas med analogier, metaforer och barnsliga teckningar.
Metaforer för problemlösning:
Grothendieck spoke of problem-solving as akin to opening a hard nut. You could open it with sharp tools and a hammer, but that was not his way. He said that it was better to put the nut in liquid, to let it soak, even to walk away from it, until eventually it opened. He also spoke of “the rising sea.” One way to think of this: there’s a rocky and difficult shore, which you must somehow get your boat across. There may be a variety of ingenious engineering feats that can respond to this challenge. But another solution is to wait for the sea to rise, providing a smooth surface to cross effortlessly.
En annan analogi:
Ravi Vakil told me that mathematicians sometimes describe this moment with an analogy: “It was as if, in order to get from one peak to another, Deligne shot an arrow across the valley and made a high wire and then crossed on it.” Grothendieck wanted the problem to be solved by filling in the entire valley with stones.
A functor is a kind of translation machine that lets you go from one category to another, while bringing along all the relevant tools. This is more astonishing than it sounds. Imagine if math could be translated into poetry, and somehow it made sense to take the square root of a stanza.
(I stil med “writing about music is like dancing about architecture“).
I slutänden handlar allt om språk:
Ravi Vakil, a mathematician at Stanford, said, “He also named things, and there’s a lot of power in naming.” In the forbiddingly complex world of math, sometimes something as simple as new language leads you to discoveries.
Grothendieck’s rewriting of foundations can seem complex and difficult, but only because, Ellenberg said, they were previously described in the wrong terms.
Grothendieck argued that mathematicians hide all of the discovery process, and make it appear smooth and deductive. “He said that, because of this, the creative side of math is totally misunderstood. He said it should be written in a different way, that shows all the thinking along the way, all the wrong turns—that he wanted to write it in a way that emphasized the creative process.”
Om barnteckningar/dessins d”enfants:
“He saw that the absolute Galois group acts on these drawings. And then he did something that I find so touching. He actually drew it. He drew these little drawings. Grothendieck did not do examples, of course—and here he was, doing an example, something concrete.”