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Sep 30, 2013 at 4:25 comment added Bill Johnson Grothendieck knew the Dvoretzky-Rogers theorem, which I guess is some evidence. He had another proof of an important application of the D-R theorem that motivated the discovery of the theorem (namely, that in every infinite dimensional Banach space there is an unconditionally converging series that is not absolutely convergent). Actually, these days the D-R theorem is considered the most difficult step in the proof of Dvoretzky's theorem.
Sep 30, 2013 at 1:26 comment added Igor Rivin I will need to digest this... I guess one question is: why did Grothendieck suspect Dvoretzky's theorem was true?
Sep 29, 2013 at 20:26 history answered Bill Johnson CC BY-SA 3.0