I recently decided I wanted to better understand modern cryptography and zero-knowledge proofs. Although I took mathematics courses in college, that was years ago, so I began working through an undergraduate abstract algebra textbook on my own, reading and solving problems most evenings.

I made progress, but found it difficult to stay motivated without a clear external benchmark. I kept wishing there were a standardized, rigorous abstract algebra examination I could register for in advance. Something that would motivate sustained study and provide an objective measure of understanding, much like signing up for a marathon months ahead of time.

As far as I can tell, exams like this largely do not exist outside formal degree programs. That raised a question for me: why not? Would there be value in a small set of written subject matter exams, for example linear algebra, abstract algebra, or algorithms, designed to assess depth of understanding rather than speed or memorization?

I have heard and investigated the common answers, such as GRE subject tests, MOOCs, certifications, and "just build things," but none of those felt quite like what I was looking for. I may be missing something.

I am trying to understand whether this idea is fundamentally flawed, impractical, or simply undesirable. I would appreciate thoughtful feedback. Thanks.