When proving theorems for my research, I often take time to consider the weakest conditions under which the desired result holds—even if it’s just a relatively unimportant and narrow lemma. By understanding the weakest conditions, you isolate the load-bearing requirements for the phenomenon of interest. I find this helps me build better gears-level models of the mathematical object I’m studying. Furthermore, understanding the result in generality allows me to recognize analogies and cross-over opportunities in the future. Lastly, I just find this plain satisfying.
When proving theorems for my research, I often take time to consider the weakest conditions under which the desired result holds—even if it’s just a relatively unimportant and narrow lemma. By understanding the weakest conditions, you isolate the load-bearing requirements for the phenomenon of interest. I find this helps me build better gears-level models of the mathematical object I’m studying. Furthermore, understanding the result in generality allows me to recognize analogies and cross-over opportunities in the future. Lastly, I just find this plain satisfying.