...analysts are like samurai. They make a cut--shhh! And if it's a good cut, then they can throw a part away. Then they can find a very good formula.
(Heisuke Hironaka, Interview to the Notices, Notices AMS, 52, 9 (2005) p. 1019)
I think that when the Americans first became research-conscious
they took up the newer fields which don't require so much
background; for example, they went to algebra and topology.
In the early 1900's those were new fields. One could understand
what had been done without too much background.
One could see any number of problems that were open.
If they had chosen to go into analysis, they would have had to acquire much more extensive backgrounds before they could do original work of their own. I think that people in our country got started the easiest way at the time.
(C. Reed, Courant, p. 210 )