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Short version of my question: What are good and motivating working habits for a mathematician?

Note that, there are similar questions to mine: see this (reading books) or this or this. But none of these explains my question. Also I know the standart answer: Develop your own working habits. But I feel that I am not so efficient and fast enough, so I will try to improve these habits themselves.

Long version of my question: I like mathematics because I like to solve puzzles. But, for me, when reading a highly theoretical book, it is quite possible to get lost and become demotivated. This is because sometimes there is no enough motivation to read complicated definitions and study full proofs again and again (sometimes full proofs are not available, definitions are fuzzy or 'advanced' etc.).

I would like to ask that if there are some 'gamification' tricks that converts boring-looking (since I know they are very rarely boring) things into the enjoyable puzzles. Also reading advices are more than welcome. Because the problem can be my reading strategy: May be there is a more efficient reading strategy that keeps things alive and attractive.

To sum up, I would like to ask your strategies to deal with serious mathematics study and convert them enjoyable puzzles if they aren't itself looking much attractive.


Note also that, there are a plenty of advices to work for exams and these advices are not even close to a potential answer to this question. Because working for exams, by definition, is equivalent to working or memorizing boring things to pass the course and get the grade. In a course setup, usually there is nothing about motivation for real learning. I am not asking about motivating studying mathematics for a course or exam, but I am asking about your habits to motivative thinking itself about complicated things which seem not much meaningful at the first look given the one's background.

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Those books more often than not have exercises. When delving into new theory I need to start working on them after at most a chapter or two. Otherwise I get lost. Some need to do it sooner, some later. I also always try to "ground" the theory I'm learning to as many other theories I have learned earlier as possible. This helps in building the bigger picture. Sometimes this doesn't help (say the first time I tried to read Hartshorne :-). This is a sign that you aimed too high and need to strengthen your background in some area(s). Do whatever works for you! – Jyrki Lahtonen Apr 28 '13 at 13:20
Jyrki Lahtonen, thanks, you are right. I discovered that, reading a book in a linear fashion, chapter by chapter, theorem by theorem, is rarely working for me. When I skip something, I generally find the real motivation for working on it in later sections. I suppose, this is itself a good strategy (and may be it is a well-known fact I do not know). I am just try to construct a general strategy for myself. :-) Thanks again. – oeda Apr 28 '13 at 13:27

2 Answers 2

Henri Poincaré had a good way of working. He'd work for a couple of hours in the morning, and a couple of hours in the evening, and the rest of the time he'd let his subconscious work on it. I find that works for me too :-).

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This may help. "HOW TO Solve IT" by G. Poyla. I don't know if it's still in print. Princeton University Press was or is the publisher. Good Luck.

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This does not answer OP's Question. – user45099 Apr 28 '13 at 14:08

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