I would be interested in hearing from PhD students (and upwards) specializing in pure maths (in particular, the more algebraic aspects). My question is this:
When reading to learn mathematics at the graduate level (so no written exams, for example) is it the case that some of the proofs are just not important?
To give an example: chapters 1 and 3 of Koblitz's book on p-adic analysis and zeta functions are devoted to constructing the p-adic complex numbers and apart from a few niceties (such as Hensel's lemma and classification of tame totally ramified extensions of Q_p) it is just a collection of technical results and I'm not convinced that the proofs are all that important providing one understands the results, the motivation and the calculations.
I look forward to hearing what people have to say.
Many thanks!
All the proofs? Don't think you can make such a blanket statement. But I'll give my opinion.
The proofs matter, but it really depends. Is this your first time reading through a book or paper? Then maybe most of the proofs should either be skipped or briefly skimmed over until the next reading. The technical ideas can get in the way of forming the big picture in your head. But most likely you are studying math because you want to prove things yourself, so it can be really important to see how some of the big important proofs go. Maybe you get ideas about how to apply a certain technique to a specific type of problem. Or maybe a proof about existence of a certain group element gives an idea of how to obtain that element.
Of course, some proofs are really basic, reference huge computations, or consist of brute force algebraic manipulation. Your mileage may vary reading these.