Whenever I teach
- [this kind of definite integral](https://math.stackexchange.com/a/900398)
- [geometry question](https://math.stackexchange.com/a/1190038),
- [WEAK mathematical induction]( https://math.stackexchange.com/a/4677828),
many students raise their hand, and asks for the reasons behind the [Inventor’s Paradox](https://math.stackexchange.com/q/3742954). Most students reasonably reckon that a broader problem is knottier, thornier than a more specific, narrower problem – multivariable calculus is broader, thornier than single variable calculus, [abstract algebra](https://math.stackexchange.com/a/4568989) broader, more complex than [linear algebra](https://math.stackexchange.com/q/717651) that’s broader, more esoteric than [high school algebra](https://math.stackexchange.com/q/2408069).
These lists beneath just instantiate problems that become more easily solvable when generalized, but none of them explain why.
[Particular problem solved by solving a more general problem](https://mathoverflow.net/q/21214)
[Generalizing a problem to make it easier](https://mathoverflow.net/q/40005)
[When was the generalization easier to prove than the specific case?]( https://mathoverflow.net/q/323228)
[Examples where adding complexity made a problem simpler](https://mathoverflow.net/q/114383)
[What are some good low-prerequisite examples for the heuristic advice "If you cannot prove it, prove something stronger."?]( https://matheducators.stackexchange.com/q/2157)
