I wasn't there to see the birth of Brazilian mathematics out of essentially nothing in the 50's and 60's, but it is clear to me that its beginning was due to a handful of idealistic individual mathematicians with great talent and strong personalities. Sure, there were universities and engineering degrees where the budding mathematicians could start to learn but if these pioneers hadn't the fortitude to go abroad to get their PhD's and then come back to build it, it wouldn't have happened.
Once they came back, if they stayed at the universities of the time they would have been stifled and left (in fact the early ones kind of commuted to the US and back for a bit). It was only with the creation of IMPA (and a benevolent government that gave some money for its maintenance) that things started to pick up. There was an ambient of research and graduate studies that tried (and eventually succeeded) to emulate the institutions of the developed world. Always uncompromising with regards to quality, IMPA had open doors, a good library, courses in the summer for bright undergraduates, conferences and the Brazilian Mathematical Colloquium which besides a conference had mini-courses at various levels to spread the word.