Education is a complex, multifaceted, and painstaking process, and being gifted does not make this less so.
Ultimately you should follow advice not because someone tells you to, but because it was something that you already knew you should be doing.
... 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.
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.
Unsolicited surprise requests from strangers are essentially guaranteed to be met with a negative response.
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.
Volume grows spatially slower than scaling.
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