Feynman’s greatest strength as a problem solver was bringing a different set of mathematical tools to a problem. Even if bringing along a big fat stack of examples is the best way for you to solve a problem, I fully expect some prominent mathematicians to solve problems from building a theoretical framework. If for no other reason, they’ll be successful at the problems that framework-building is the best strategy at and earn respect for solving those problems, even while the majority of problems get done easier with examples.
In other words, I expect framework building to be good at solving at least some problems that example-pulling are bad at. That’s enough for a mathematician to earn success by having a mind that’s particularly well suited for the former method. This success and kind of mind are completely independent of your best research strategy.
Feynman’s greatest strength as a problem solver was bringing a different set of mathematical tools to a problem. Even if bringing along a big fat stack of examples is the best way for you to solve a problem, I fully expect some prominent mathematicians to solve problems from building a theoretical framework. If for no other reason, they’ll be successful at the problems that framework-building is the best strategy at and earn respect for solving those problems, even while the majority of problems get done easier with examples.
In other words, I expect framework building to be good at solving at least some problems that example-pulling are bad at. That’s enough for a mathematician to earn success by having a mind that’s particularly well suited for the former method. This success and kind of mind are completely independent of your best research strategy.