I have always found it difficult to handle math that is strictly numerical. I don’t have issues with the parts of mathematics focused on solving specific problems, and I am quite fast at estimations, calculating percentages, and other types of practical math. However, whenever the linguistic or visual components are stripped away—whether it was basic arithmetic as a child once the written examples stopped, or calculus now as an adult—my brain just shuts down. This also happens with computer science, coding, and basically anything involving abstract concepts that lack concrete, real-world applications to anchor them. I am working incredibly hard to absorb this material, but the progress is painfully slow. After a while, I get a literal headache and feel like I need to snack constantly just to stay focused. Are there any exercises I can do between study sessions to build up my mental stamina for this type of logic? Perhaps some non-mathematical suggestions?
It is like saying your arms ache when doing push-ups and asking how to build muscle without the discomfort. You simply need to practice more using simpler problems. There is no shortcut other than persistence. Learning to code is a good path, though. Just start with something approachable like Python.
If you start getting a headache, you should rest. You will only make the learning process more grueling by forcing yourself to continue. Aside from being in a ‘flow state,’ almost nobody can maintain deep focus on difficult topics for more than 25 minutes at a time. Mental endurance is a byproduct of becoming competent at a task, not from special hacks. You need to keep your brain’s reward system engaged. Begin every study block with simple problems to warm up, and mix in some easier ones among the difficult tasks to remind yourself of what it feels like to succeed. Furthermore, try to de-abstract your learning. Seek out any real-world applications for a specific problem type and work through those. For example, use calculations regarding speed and acceleration to understand differential equations. Practicing this way helps you develop an intuition for the process through a more natural mental model. Once you have generalized the idea, you will find it easier to apply those methods to different scenarios or pure abstractions.
Create your own practical examples. Use a strength-based approach to learning. Take a subject you already understand deeply and try to explore it further using the specific tools you are currently struggling to learn.
Actually, earning a degree in architecture really improved my ability to grasp abstractions in both math and physics.