As of this moment, I’m in my second year of undergraduate studies in physics. Therefore, I’ve seen a bunch of classical topics (electricity and magnetism, mechanics, wave motion, elementary astrophysics) while only seeing a snippet of “modern” physics (special relativity, mostly in the form of time dilation). I haven’t taken any classes on quantum mechanics, so I’m definitely a novice there.
On the mathematics side, I’ve taken the usual classes of calculus, linear algebra, and differential equations. In a sense, I’m still learning the techniques before actually applying them to topics such as topology.
As you can see, I’m just starting to really dip my feet into my mathematics and physics training.
However, this hasn’t stopped me from pushing my boundaries and learning about other topics. I follow a variety of mathematics and physics blogs that I try and keep up with while reading. Additionally, I watch many video series which are part of the new swath of educational videos, such as PhysicsGirl, Infinite Series, 3Blue1Brown and PBS Spacetime (probably the best channel that I’ve found online). I also read books here and there that push my comfort zone in terms of physics and mathematics.
The point is that I don’t back down from being completely bamboozled. In fact, I want to find those places where I’m baffled, because they point to new opportunities to learn, which is always exciting. I also think that while I may not understand everything I read or watch, it can spark my curiosity to learn about it some more. Sometimes, it’s good to just have your head explode from not understanding.
At the same time, don’t just ignore what you can’t understand and move on. Instead, think about the problem and what’s fuzzy in your mind, and you’ll usually be able to form a plan to figure out what you need to learn. From there, you can give yourself a boost in your education without necessarily waiting for the appropriate classes at school. This is even more relevant when studying topics that aren’t part of your field, since self-study is the only opportunity you will usually get.
Take advantage of the wealth of information available to you (much of it free), and learn. It’s probably the best investment of time you can make.