e.g. the whole strategy of "dynamic programming", write a recursive solution, then memoize it, then reduce the amount of memory if you don't use it anymore. This works because you have changed your perspective from what clever thing can I do to how can I solve this with a smaller subproblem.
This also applies to physical actions like walking and opening doors. Most people do these slowly, but since you spend so much time doing them, it is extremely worth it to focus on what you're doing.
Consistency check: After coming up with a conclusion, check that it's consistent with other simple facts you know. This lets you catch simple errors very quickly.
Give an example: If you've got an abstract object, think of the simplest possible object which instantiates it, preferably one you've got lots of good intuitions about. This resolves confusion like nothing else I know.
Proving too much: After you've come up with a clever argument, see if it can be used to prove another claim, ideally the opposite claim. It can massively weaken the strength of arguments at little cost.
Prove it another way: Don't leave things at one proof, find another. It shines light on flaws in your understanding, as well as deeper principles.
Are any of these satisfactory?
Dimensional analysis is in instance of type signature checking, as fully understood. Unfortunately very few type systems for existing programming languages support the type transformations necessary to implement it directly.
Let's list our ‘intellectual lifehacks’ here, i.e., elements of knowledge that have properties like. :
I don't have a proper definition other than ‘I feel like it’ to the question ‘Does this count as an intellectual lifehack?’, but I'd like to make it clear that I'm setting the bar very high. I hope you'll be able to connect the dots with n=3... Anyway, share and discuss!
Hereby, our intellectual lifehacks repo:
See: How to keep the essence of a theory by looking at the type signature, or to make progress on ontologically unsolved questions
See: How to import such intellectual lifehack in another intellectual field