People metaphorically run parts of the code themselves all the time! Its quite common for people to work through proofs of major theorems themselves. As a grad student it is expected you will make an effort to understand the derivation of as much of the foundational results in your sub-field as you can. A large part of the rationale is pedagogical but it is also good practice. It is definitely considered moderately distasteful to cite results you dont understand and good mathematicians do try to minimize it. Its rare that an important theorem has a proof that is unusually hard to check out yourself.
Also a few people like Terrance Tao have personally gone through a LOT of results and written up explanations. Terry Tao doesn’t seem to report that he looks into X field and finds fatal errors.
As a grad student it is expected you will make an effort to understand the derivation of as much of the foundational results in your sub-field as you can […] It is definitely considered moderately distasteful to cite results you dont understand and good mathematicians do try to minimize it.
Yeah, that seems like a feature of math that violates assumption 2 argument 1. If people are actually constantly checking each others’ work, and never citing anything they don’t understand, that leaves me much more optimistic.
This seems like a rarity. I wonder how this culture developed.
People metaphorically run parts of the code themselves all the time! Its quite common for people to work through proofs of major theorems themselves. As a grad student it is expected you will make an effort to understand the derivation of as much of the foundational results in your sub-field as you can. A large part of the rationale is pedagogical but it is also good practice. It is definitely considered moderately distasteful to cite results you dont understand and good mathematicians do try to minimize it. Its rare that an important theorem has a proof that is unusually hard to check out yourself.
Also a few people like Terrance Tao have personally gone through a LOT of results and written up explanations. Terry Tao doesn’t seem to report that he looks into X field and finds fatal errors.
Yeah, that seems like a feature of math that violates
assumption 2argument 1. If people are actually constantly checking each others’ work, and never citing anything they don’t understand, that leaves me much more optimistic.This seems like a rarity. I wonder how this culture developed.