Thursday, March 3, 2016

astro picture for the day/ Grothendieck quote

Image credit: APEX, the Atacama Pathfinder EXperiment telescope

Quote for the day,

"I prefer to accent “unity” rather than “generality.” But for me these are two aspects of one quest. Unity represents the profound aspect , and generality the superficial." - Alexander Grothendieck

link --> How Grothendieck simplified Algebraic Geometry

As Velleman points out in his "How to do Proofs", proofs starting from conclusion are by means of reexpression(I'm not sure who first came upon this proof technique/insight actually) . . . here, we see Algebraic Geometry being reformulated many times; this cuts through and unifies much mathematical history from the 1800s up to . . . Alexander Grothendieck.



    The Notices article about how Grothendieck revolutionized 'algebraic geometry' looks to be a variant of the 'rising sea' chapter, linked in this reply.

  2. The Notices article has more history of the past 150 years, more geometry, and and less detail on Weil, Serre, and Grothendieck in the 1950s.

    1. My link to the Notices article seems to be not working. I suppose I could try to find it again. I don't like the American Mathematical Societies new Notices website design.

    2. Hello Colin,

      I thought I'd share this with you . . .

      Appears the world is about to transform . . . within a week. One could also profit by it.