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It's the summer holiday for me right now and I've been spending a lot of time doing math problems. I've done a bunch of Olympiad questions and the like recently, and I feel like I've hit a plateau recently. I don't seem to be able to improve nearly as quickly as I did just a couple months ago. I've only recently started doing Olympiad problems and I was wondering if it is normal to feel this way. Is it possible that I am still learning a lot but not realizing it?

I wonder if you guys have any ideas on how much practice is overpractice and instead harmful for me.

Are there any other ways to improve mathematical thinking other than just doing more problems and reading up on theorems?

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To answer your bolded question, yes. Oftentimes it is only apparent later just how much your research or study in a certain area has benefited you. I would say that if you consistently practice more than 6 or 7 hours a day, then that could be harmful. It is much healthier to take frequent breaks, and stretch or eat a snack or what have you. If you have healthy habits, you can study much longer than someone who does not, and you can take in more information. That is a question that is going to generate varying answers based on opinions, so take answers to that question with a grain of salt. As for your last question, it's another resounding yes! Reading about the history of mathematics and mathematical thought through the ages has greatly deepened my understanding and appreciation of mathematics. In addition, read papers and articles about the philosophy of math, and look into recreational mathematics.

JacksonFitzsimmons
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