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**Veering Away from "Mechanical Thinking"**

I'm a current high school student aspiring to become a mathematician. I am doing pretty well in my math classes, taking college level math here and there. However, I'm afraid that continuing to do the math that I'm taking right now leads me further and further into the path of "mechanical thinking" - procedural approach to math that pretty much uses plug and chug. I figured that it probably has to do with the way teachers nowadays teach math - teach the "procedure" on how to do it, and then assign routine problems at the end of each chapter.

This approach loses the abstractness of math that I enjoy, and it makes me less and less able to think outside the box - say, doing proofs, solving olympiad problems, etc. I read advanced level math, I study the procedures on "how to do it", but the beauty of the theorem and their proofs in the process.

I want as much as possible to stay away from this procedural approach of doing math. I'm not really sure what kind of "question" I should ask, but I guess general advice would be really helpful.