[JadeNB]

> Grothendieck and lack of machinery do not belong in the same sentence.

They most certainly do! Grothendieck’s work is heavy on definitions, but the essence of his work is that the right definitions obviate (and are seen to be right because they obviate) the need for heavy machinery. See the famous quote, taken from Wikipedia (https://en.wikiquote.org/wiki/Alexander_Grothendieck#Quotes_...) because that’s the first place I found it:

> I can illustrate the ... approach with the ... image of a nut to be opened. The first analogy that came to my mind is of immersing the nut in some softening liquid, and why not simply water? From time to time you rub so the liquid penetrates better, and otherwise you let time pass. The shell becomes more flexible through weeks and months — when the time is ripe, hand pressure is enough, the shell opens like a perfectly ripened avocado! A different image came to me a few weeks ago. The unknown thing to be known appeared to me as some stretch of earth or hard marl, resisting penetration ... the sea advances insensibly in silence, nothing seems to happen, nothing moves, the water is so far off you hardly hear it ... yet finally it surrounds the resistant substance.

[solveit]

I mean, we're arguing semantics at this point, but these definitions we're talking about are things like schemes, which pretty much everybody would call heavy machinery.