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For the professional mathematicians or the students that are getting there, I was wondering specifically what is meant by expanding one's 'mathematical toolbox' in regards to research?

So for example, if you are learning one particular subject in math, does expanding the mathematical toolbox mean just knowing more definitions, theorems and important examples or maybe approach to solving problems like heuristics?

Mat.S
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  • Feynman talked about this some in the section "A Different Box of Tools" in Surely You're Joking, Mr. Feynman. – littleO Sep 25 '13 at 03:51

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I ponder rather the second interpretation, because you are thinking not on an academic knowledge but on tools for solving problems. So it is on an acquirement (it is the best English analog of Russian word “усвоить” which can literally mean “to make it a part of you” :-) which I found) of new methods to solve problems, a brilliant form of which is a/to form a new kind of mathematical intuition.

Alex Ravsky
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