Studying Mathematics Thread

[polymath257]

IMO, regardless of one's skill level, a student of mathematics will encounter concepts and ideas that are challenging: it seems that, for the time being, there will always be problems to solve and statements to prove. Hence, for any students who are interested in studying mathematics, please don't get discouraged when you hit a bump/boulder in the road: you are not alone.  Like so many mathematicians and students of mathematics before you, embrace the fact that you are being challenged, ask questions, and allow yourself to grow from this experience, regardless of whether you are successful or not.

I'll paraphrase something that I read many decades ago, "Before anything was done using a computer, you could tell a working mathematician by how many pieces of paper were in the waste basket."

That "guess and check" method you learned in grade school has its provenance in that.

I just want to say that this is still very much true today. Computers help some with computations. They are good for writing up results. But the *real* ideas happen on paper or the black (marker) board. Reams of paper are used before the first key on the computer is hit.

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IMO, regardless of one's skill level, a student of mathematics will encounter concepts and ideas that are challenging: it seems that, for the time being, there will always be problems to solve and statements to prove. Hence, for any students who are interested in studying mathematics, please don't get discouraged when you hit a bump/boulder in the road: you are not alone.  Like so many mathematicians and students of mathematics before you, embrace the fact that you are being challenged, ask questions, and allow yourself to grow from this experience, regardless of whether you are successful or not.

Absolutely. If you are studying math to any level you *will* come across ideas that are hard to wrap your mind around. When that happens, read other books, ask people who might know, play with a hundred examples. Do whatever it takes because it will  be *worth* it. Pushing through the hard stuff is much more rewarding than skimming through the easy stuff.