I am surprised to see that so many people suggest meta-mathematical articles, which try to explain how one should do good mathematics in one or the other form. Personally, I usually find it a waste of time to read these, and there a few statements to which I agree so wholeheartedly as the one of Borel:
"I feel that what mathematics needs least are pundits who issue prescriptions or guidelines for presumably less enlightened mortals."
The mere idea that you can learn how to do mathematics (or in fact anything useful) from reading a HowTo seems extremely weird to me. I would rather read any classical math article, and there are plenty of them. The subject does not really matter, you can learn good mathematical thinking from each of them, and in my opinion much easier than from any of the above guideline articles. Just to be constructive, take for example (in alphabetical order)
- Atiyah&Bott, The Yang-Mills equations over Riemann surfaces.
- Borel, Sur la cohomologie des espaces fibrés principaux et des espaces homogènes de groupes de Lie compacts.
- Furstenberg, A Poisson formula for semi-simple Lie groups.
- Gromov,Groups of polynomial growth and expanding maps.
- Tate, Fourier analysis in number fields and Hecke's zeta-functions.
I am not suggesting that any mathematician should read all of them, but any one of them will do. In fact, the actual content of these papers does not matter so much. It is rather, that they give an insight how a new idea is born. So, if you want to give birth to new ideas yourself, look at them, not at some guideline.
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