"But the never ending feeling of not knowing anything takes over." That is something you need to get used to in a PhD, so you already have a good qualification. ;-)

You're doing a depth-first search. Consider breadth-first instead.

There's a reason we have libraries with well-defined APIs (application program interfaces for non-CS folks) like OpenGL. The whole idea is that if you want to build a program with some type of fancy graphics, you shouldn't have to know or care about what happens below the API. You trust that the person who wrote it understood, and you can focus on the higher-level details -- like making Half-Life 3 or designing a new piece of computer vision software for your research. (1/2)

The exception to that, of course, if if you plan to improve upon whatever is under the hood. But then there's likely some lower layer that you still don't care about -- i.e., how the transistors on your GPU are laid out. The point is, understanding how it works under the hood is fun sometimes. But don't let that distract you from the ultimate goal -- which is to write your program/paper/dissertation/what-have-you! (2/2)

You are not the only one, as you can see from this question from Maths.SE: math.stackexchange.com/questions/617625/…

Take a class. That will give you some external structure. // Very slightly related, but you might find it helpful: academia.stackexchange.com/a/78073/32436

@tonysdg You still have to know some of the underneath. You can't use OpenGL fully without understanding Vectors and Matrices or knowing about writing shaders and different kinds of lighting etc. You don't necissarily need to know everything about how these things work, but you need to know enough to know what you're doing wrong when you go wrong (e.g. understanding the layout of a vector is helpful when your problem is that you've accidentally ended up with a transposed matrix).

Why would you need probability before linear algebra.

As someone who works in the graphics industry, if your objective is to become an expert in X, you really don't need to go much further than about 10% of the way through W.

I've heard the dilemma described as the "the Conjurer vs the Scribe". A "Conjurer" just hacks bits of pieces together just to get something to work. And a "Scribe" reads and understands the docs completely before beginning. Which mode you're in and when, is completely up to you. But both are useful at times... but the final decision is all yours.

The depth-first vs breadth-first analogy is a great one. You're in the field of CS, so you're likely to understand it. In general, though, this dilemma appears not only in CS, but in other areas as well. You can also refer to this as a 'top-down' vs 'bottom-up' approach. Also coming from CS, I find I tend to spend too long in 'bottom-up mode', and just the shift in mindset to explicitly try a top-down approach (making the necessary compromises) helps stop the great descent into the bottomless pit of knowledge.

Abstraction is key. You need to be able to work with defined properties of something and trust that they hold true. For example, you don't need to know how a computer chip at all to make a website, eventhough it is ultimately executed on a computer chip (while beeing interpreted).

If you're studying purely for personal interest and have no goals, then IMO what you are doing is totally fine, if it gives you happiness. (If you don't much care where you get to, then it doesn't matter which way you go — as the Cheshire Cat said to Alice.) But perhaps you are not happy with this phenomenon, which is why you asked this question…

I did something similar when I studied Machine Learning, and then finished couple of courses online at the end of my depth-first search. It look me quite sometime.

See also: "yak shaving" (one thing leads to another ...) and "bikeshedding" (doing the fun/unimportant stuff first).

You found out it’s turtles all the way down. Good luck!