Higher Math Meta: Breadth

Want to compile "viewquakes" (a la Hanson), like Mathoverflow: a-single-paper-everyone-should-read. To quote Tobias Hartnick:

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. [Own note: see also Wikipedia: Furstenberg boundary]
• 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.

See Wei Ho's nice generals advice.

See Persiflage, Exposition is not underrated. In particular:

I don’t think this issue is really about finding a balance between research and education. It’s about individuals wanting to be rewarded professionally (tenure, salary, etc.) by writing expository articles which neither make a contribution to the corpus of mathematics nor (outside exceptional cases) to the education of the next generation of mathematicians. The language of the debate also seems to ignore the fact that the web is flooded with more expository material than would even have been conceivable thirty years ago, from Wikipedia to MathOverflow to math blogs to online course notes (this is, mostly, a good thing). Many mathematicians have a desire to explain their ideas, and it’s not clear to me that anything profitable can be gained by skewing the incentives. (If you want to argue that teaching should be taken more seriously when it comes to hiring/tenure decisions, that is another debate.) I find myself in agreement with the comment you quote from Dan L: “I also do not believe that your hypothetical “great storytellers of mathematics” really exist, in the sense that I do not believe that a person can achieve that level of mastery over a field without being a successful researcher.”

I view this post as a call to focused action. It means we should think hard about what is likely to be most useful to current and future generations. The context of level and audience are quite important.