This is a talk by Samuel Gomes da Silva, delivered in Nov. 2013 for young mathematicians in Recife, PE, Brazil. Keeping it here to think about some questions. For example, if instead of crises I asked what were the three most interesting moments in mathematical history, would they be the ones of crises too? if not, what would they be?
I think one of the good moments was Descartes connecting algebra and geometry, which ones do you like?