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Mathematicians need to be metamathematicians
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What can a lower bound say about potential proofs of the upper bound?
If you are getting stuck, then try to prove rigorously that your approach cannot work
Mathematicians need to be metamathematicians
Which techniques lead to which kinds of bounds?
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Littlewood-Paley heuristic for derivative
Geometric view of Hölder's inequality
Diagonal arguments
Finding an interval for rational numbers with a high denominator
Try to prove a stronger result
Use self-similarity to get a limit from an inferior or superior limit.
Prove a consequence first
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