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The passions do very often give birth to others of a nature most contrary to their own. Thus avarice sometimes brings forth prodigality, and prodigality avarice; a man's resolution is very often the effect of levity, and his boldness that of cowardice and fear.

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Terence Tao

Volume grows spatially slower than scaling.

Volume, Grows, Spatially, Slower, Scaling
Same Author Quotes

Ultimately you should follow advice not because someone tells you to, but because it was something that you already knew you should be doing.

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Education is a complex, multifaceted, and painstaking process, and being gifted does not make this less so.

Doe, Education, Gifted, Multifaceted, Process

Pointing out that countless great mathematicians had tried to solve the problem and failed before you came along is in particularly bad taste and should be avoided completely.

Failed, Pointing, Problem, Should, Taste, Tried

. . . it can often be profitable to try a technique on a problem even if you know in advance that it cannot possibly solve the problem completely.

Math, Often Is, Problem, Solve, Technique, Trying

At a purely formal level, one could call probability theory the study of measure spaces with total measure one, but that would be like calling number theory the study of strings of digits which terminate.

Formal, Measure, Numbers, Probability Theory, Purely, Space
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