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Suresh Venkatasubramanian's profile photoSamuel Isaacson's profile photoPatrick Honner's profile photoJoerg Fliege's profile photo
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This reminds be a bit of the principle that it is often easier to solve a more general problem than the specific one.
 
+Patrick Honner During my candidacy exam, my advisor asked me a simple question that I could not answer. He then said "Let me ask you a harder question." I was still lost. Then he said "Let me ask you an even harder question." Then I got it. He made the question sufficiently abstract that I could recognize it.
 
Cf the theory of approximation algorithms for NP-hard problems - cant solve it exactly easily, but can get close easily, and for some problems it just gets harder and harder as you get closer and closer
 
Somewhat OT, but there is a logical resolution to your "interesting number paradox": the "proof" that all numbers are interesting assumes that there is a set of interesting numbers. However, internal set theory is a conservative extension of ZFC in which one could assume that 0 is interesting, n interesting implies (n+1) interesting, and yet non-interesting natural numbers exist! Edward Nelson has a charming introduction to this sort of mathematics in his book "Radically Elementary Probability Theory."
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