Well unfortunatley i don't have enough points on Math Overflow to make a comment. This is in response to Pete L. Clark's answer, especially the line
There is also something "organic" in the work of both Siegel and Shimura which naturally bristles a bit at the "Bourbakistic" influence of the French school(...)
at the start of the last paragraph.
Here is a nice little tidbit from the German Wikipedia http://de.wikipedia.org/wiki/Carl_Ludwig_Siegel#Siegels_Standpunkt_zur_Entwicklung_der_Mathematik
To finish here is my own translation of that:
The position of Siegel towards the development of math
Like no other mathematician of the 20th century Siegel was critical of the increasing abstraction and axiomatization of math. The bourbaki-project was for him the pinnacle of this "catastrophic development". For him the clarity of Gauss and Lagrange were still aspirations, just as the investigation of concrete mathematical objects.
Disclaimer: this is a best-effort translation of that Wikipedia bit from myself and it does not reflect my opinion.
EDIT: here is the reference for that Wikipedia bit in english Letter from Siegell to Louis J. Mordell, 3 March 1964