#grothposting

[groupoid-cocycles]

There’s like a 45% chance that I’ll start ranting about Grothendieck whenever I get drunk.

[groupoid-cocycles]

Seriously what was up with Grothendieck’s obsession with agricultural metaphors.

[groupoid-cocycles]

Hausdoff: A space is a set X of points where each point x has a collection of neighborhoods such that.

Every neighborhood of x contains x.

If a subset of X contains a neighborhood of x then it is a neighborhood of x.

The intersection of two neighborhoods of x is a neighborhood of x.

If N is a neighborhood of x then it contains a neighborhood M of x such that N is also a neighborhood of every point in M.

Grothendieck: Anything can be a space if you believe! (◡‿◡✿)

[groupoid-cocycles]

Since then I’ve had the chance in the world of mathematics that bid me welcome, to meet quite a number of people, both among my “elders” and among young people in my general age group who were more brilliant, much more ‘gifted’ than I was. I admired the facility with which they picked up, as if at play, new ideas, juggling them as if familiar with them from the cradle–while for myself I felt clumsy, even oafish, wandering painfully up an arduous track, like a dumb ox faced with an amorphous mountain of things I had to learn (so I was assured) things I felt incapable of understanding the essentials or following through to the end. Indeed, there was little about me that identified the kind of bright student who wins at prestigious competitions or assimilates almost by sleight of hand, the most forbidding subjects. In fact, most of these comrades whom I gauged to be more brilliant than me have gone on to become distinguished mathematicians. Still from the perspective or thirty or thirty five years, I can state that their imprint upon the mathematics of our time has not been very profound. They’ve all done things, often beautiful things, in a context that was already set out before them, which they had no inclination to disturb. Without being aware of it, they’ve remained prisoners of those invisible and despotic circles which delimit the universe of a certain milieu in a given era. To have broken these bounds they would have to rediscover in themselves that capability which was their birthright, as it was mine: The capacity to be alone.

Alexander Grothendieck, Récoltes et Semailles