Context: As a researcher you need to read many research papers by others. In the case of mathematics, a paper consists of:
- Results (theorems, lemma, propositions)
- Proofs that consist of the technique or method by which the researcher obtaining their result.
Clearly, results can be used without learning the proof. However, understanding a proof may help you develop future results (but not necessarily always).
Ideally, it is best to learn the proof and techniques used in detail in order to fully understand the reality.
Do researchers (graduate students, professors, research fellows) in mathematics have a detailed understanding of the proofs/techniques outlined in contemporary journal papers? What is the convention in math?
Please note that my issue is not whether the proof is correct or not, I want to know what most academics do in the most of the cases when a result is published in a peer-reviewed journal paper. Do they read and understand the proof or they just skip the proof and remember the result? (provided that the proof technique is not out of the box)?
Example: I was reading Simon Singh's book on Fermat's Last Theorem, he wrote that only half dozen people understood the proof of Andrew Wiles. (The number maybe slightly erratic since I read the book long ago.) But the modularity conjecture was proved by him at the same time, I guess this is quite important. This made me think how much actually people understand contemporary work? How much it is actually important? Mathematics is a very very technical subject now a days.