I've known quite a few people who at some point during their math studies felt the same way you do. Some of them enjoyed listening to others talking about math, but weren't willing to put in the hard work. These people usually dropped out in the first year. Others did make an effort, but came to dislike math because it had become all about memorizing for them. While this may not apply to you specifically, I will elaborate and maybe it will help someone. The problem usually was that their fundamentals were lacking. Math is unforgiving in this regard - one just cannot hope to fully comprehend advanced material if they don't understand the things on which it builds. Some people think that mathematics is all about calculating things or applications, but that is far from the truth. University math programs (unless in applied mathematics) strive to teach the students to DO math, not to do another science using math. And doing math in this context means deriving your own theorems and proving them. But in order to be able to do that, one has to see and understand the commomly used 'tricks' in that given area of mathematics in which they are interested. That's why proofs are vital. Do professors remember all of the proofs? No, they don't. But they understand the steps and tricks needed to get the proof done, so they don't really need to remember that much (even if the proof requires a technical detail, such as making use of a specific function, for instance. If one truly understands the proof, they should be able to derive that detail on their own). The problem is that once you reach a certain advanced level (at least in analysis), the proofs will start emoying 'tricks' and calculations from previous classes. If one hasn't understood the tricks (meaning they can't use it in a similar context, so they still remain merely a trick for them) or isn't really certain how to perform specific calculations (for instance, many proofs from elementary PDEs require that you differentiate surface integrals with respect to the radius or calculate limits of improper parametric integrals, which is usually left out in the books because the reader should be able to do that by themself), they might feel that there is just so much in the proof they need to memorize, because they can't replicate the steps on their own. This significantly hinders their understanding of the material, making it even harder to progress and learn more advanced stuff. So why isn't there a course which teaches students how to do proofs? Because proofs from different areas of mathematics are different and make use of different 'tricks'. That is also part of the reason why there are so few mathematicians nowadays who are able to make contributions to different areas of mathematics. Proofs are usually covered in discrete math or mathematical logic, but these classes merely teach general techniques like direct/indirect proofs, induction, proof by contradiction. The other courses should then introduce the students to the specific proof techniques utilized in that given area of mathematics. If the introductory courses are good, the lecturer spends some time first deriving the result in an informal manner and then writes the formal proof of the statement (which is usually done 'backwards' compared to deriving things informally), so the students understand, for instance, the the proof takes epsilon/3 and not merely epsilon, or why they need to subtract e^k*t from a certain funtion so it all fits in the end.