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It is important to note that (in the Terry Tao's opinion) the 'more' comes only after being very thorough on the rigor and proofs,

He identifies three sequential stages in learning mathematics - the pre-rigor/intuitive handwavey stage, the rigorous 'axioms and proofs' stage and the final post rigorous stage (quoting from the article) .

'in which one has grown comfortable with all the rigorous foundations of one’s chosen field, and is now ready to revisit and refine one’s pre-rigorous intuition on the subject, but this time with the intuition solidly buttressed by rigorous theory. "

Many interesting thoughts on the transitions from one stage to the next. Great post.

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