Here are readable sources concerning biography and work: Pierre Cartier 2001, "A mad day's work: from Grothendieck to ..." http://www.ams.org/journals/bull/2001-38-04/S0273-0979-01-00913-2/home.html
--is there anybody who claims to understand that? You know, R.P.Feynman once was unable to communicate his excellent ideas about path integrals and the foundations of QED, even though Schwinger apparently was able to communicate his (considerably harder to use) ideas... which RPF explained by remarking that "his machines came from too far away." Well, looks to me like Grothendieck's machines come from still further away. The Cartier piece does not mention a single application, and apparently neither do any of the sources in his bibliography. But there is a lot of handwaving about how maybe this is somehow floating around in a lot of places that might have something to do with applications someday. That are really really profound, so profound as to be unable to connect to anything concrete; that would merely diminish its profundity. In particular (just to issue a random provocation) Simon Plouffe, who started all this about Grothendieck and speaks his language, strikes me as a far more concrete guy and I'd guess that therefore he's unable to comprehend Grothendieck. And in my case, perhaps it is a defect of my mind, but in order to motivate me to put in the work to understand an area, I need to have some evidence it does something I'll find useful. Where is that evidence?