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General problem-solving tips
Don't start from scratch
If an argument looks promising but needs a hypothesis, assume the hypothesis for now but try to remove it later
If you don't know how to make a decision, then don't make it
Look at small cases
Mathematicians need to be metamathematicians
Prove a consequence first
Simplify your problem by generalizing it
Think about the converse
Think axiomatically even about concrete objects
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Recent articles
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Littlewood-Paley heuristic for derivative
Littlewood-Paley heuristic
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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