Celebrating Grothendieck
FORM: Geometry and Algebra
Grothendieck’s mind, in a body-discounting fever, brought into figural salience for all to see, what someone characterized as nothing, the concepts that fit reality as given to us, and went on to name: with names befitting the thus abstracted concepts, all along being conscious of the basic character of generals distinguishing the abstract general from the particulars that it unifies (e.g., particulars: 3^2 + 4^2 = 5^2, 5^2 + 12^2 = 13^2, et al., and the corresponding general: a^2 + b^2 = c^2), and in doing so endowed his mind-made cohesive body of concepts: theories of topoi and of sheaf (cf. cohesive variation all around us, all the time, and all too visible, and yet impossible to see à la heimlich), merely to name a couple, with the thing: the soul animating greater constancy (cf. time-tested; Concepts that are historically stable tend to be those that in some way reflect reality, and in turn tend to be those that are teachable.)
Let’s discuss Grothendieck’s (i) Geometry of Forms and (ii) Figure Algebra (I’m tempted to compare and contrast with Professor F. William Lawvere’s (i) form as extensive quality and (ii) figure geometry, but that’s for another day / week / … kalpa ;)
… later gator ….