r/math • u/Fmtpires • 1d ago

Feeling like you skipped steps

I'm currently working on my master's thesis. I took a course in C*-algebras, and later on operator k-theory, and chose the professor that taught those courses as my thesis advisor. The topic he gave me is related to quantitative operator k-theory and the coarse Baum Connes conjecture.

I know a master's thesis is supposed to be technical and unglamorous, but I can't help but feel that I skipped many steps between the basic course material and this more contemporary topic. Like I just now learned about these topics and now I had to jump into something complex instead of spending time gaining intuition beyond the main theorems and some examples.

Sometimes I get stuck on elementary results, and my advisor quickly explains why something is true or why the author of the paper did that. Most of the times those things seem like "common knowledge", except I feel I didn't have time to gain that common knowledge.

Is it normal to feel like this?

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149

u/DamnShadowbans Algebraic Topology 1d ago

Congratulations, you are learning mathematics the way a professional researcher does! If you get good at it, your Ph.D. will go very smoothly.

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u/matagen Analysis 1d ago

"Don't compare your beginning to someone else's middle." Things seem like common knowledge to your advisor because they have the advantage of having thought about those things for possibly decades longer than you have. Forget about trying to look smart and start asking questions. Tell your advisor where you're struggling, or where you need details filled in, because as smart as they are, I assure you they're not some sort of mind-reading wizard that will figure out where you're struggling for you.

Contrary to the common saying, there are stupid questions - but more importantly, there are those who ask them and those that don't. Those that do, get enough stupid questions answered that eventually they start asking smart questions. Those that don't, go on to be people that still don't know answers to stupid questions. You're in a rare phase of your life where asking dumb questions is not only allowed, it's expected of you. Ask all your dumb questions now, so that you don't have to ask them later.

9

u/sentence-interruptio 14h ago

gonna make it a quote.

"stupid questions are mother of smart questions."

25

u/ThreeBlueLemons 1d ago

Yeah this is how it was for me, my dissertation topic was 999999999999999999x harder than any other course I did, with an infinite sprawling chasm of a knowledge gap. Plus all my advisor ever said was "it's rather subtle". Suffice to say it went awfully. Hope it doesn't for you.

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u/numice 10h ago

I know nothing about C*-algebra. Is the course a dedicated course on this topic or it's a topic amongst other topics in an algebra course?

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u/Fmtpires 6h ago

It's more related to functional analysis than to algebra. Usually it's studied in its own dedicated course, as it's a vast topic.

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u/numice 6h ago

Thanks for the reply. I took a course on functional analysis but it didn't touch anything on this only Hahn Banach, uniform boundedness. I guess it's more of an advanced course

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u/Lexiplehx 8h ago

Good god, I hate that feeling. I actually studied the exact same topic, but only for how it intersects with optimization. I can’t prove the general Jensen-Choi-Davis inequality, except I can use Tsuyoshi Ando’s trick in to tackle all of the functions I care about. In a paper I recently wrote, I write it as a proposition and pretend to use that gigantic hammer to prove all the results I need, but in my personal notes where I prove everything in excruciating detail, it’s Ando’s trick all the way down.