Very often, I get stunned by something unexpected and feeling unable to do anything about it. The solution is often a healthier mindset.
As I’ve written before on getting yourself unstuck, whenever I see a maths problem that I have no idea on it’s very easy for me to get stunned by it. Whenever that happens, I need to remind myself that it’s okay to not have any idea on a question, that it’s very likely due to lack of some sort of pre-requisite knowledge / experience, and that I’m going to get over it if I spend some time working at it. Then I need to find ways to be productive by beefing up my fundamentals, trying different angles of attack, asking someone about it or just forgetting about the question for now.
This is especially bad in an exam setting. It’s easy to start blaming your past self for not revising hard enough which is of no benefit to my performance in the exam. Time is also limited so you generally need to get out of that state fast.
Usually I cope by looking at some other questions first and doing all the easy parts first. This gives me some time to subconsciously think about the difficulty of the problem / recall my memory. Completing easy parts also assures my ability is of a certain standard at least.
Somehow this feels less bad when I’m programming. Perhaps being confused / googling for answers is just such an ingrained part of modern programming that I expect myself to get stuck some where along the way. I hope I would incorporate more of that mindset into mathematics.
Edit: When I’m learning an abstract theorem, I find it helpful to “run the proof” on a specific example to see how the proof actually works. It’s similar to when you learn an algorithm (e.g. sorting), it’s helpful to actually run the algorithm on a concrete example.Previous personal post
All personal posts