most recent 30 from http://mathoverflow.net 2013-05-20T12:10:43Z http://mathoverflow.net/feeds/user/28032 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/112298/math-research-guide Raphaël Hythlodée 2012-11-14T14:27:29Z 2012-11-14T14:27:29Z

I have a math undergrad, and am currently doing grad work in the social sciences. In the social sciences methodology is a big topic and there are full books dedicated to even tiny subtopics of it. I realize in pure math that there is no research in the formal sense (preforming surveys, collecting data, etc.) but there must still be some sort of method followed to go from nothing to a publishable work. The sort of questions that need to be answered are: What constitutes a "worthy" research question? How do you go about refining that question into something coherent?

http://mathoverflow.net/questions/112298/math-research-guide Raphaël Hythlodée 2012-11-14T13:59:22Z 2012-11-14T13:59:22Z

The book would not give a recipe, it would explain what it means to be a rigorous proof (establish a criteria), and also possibly give tips as how to begin a rigorous proof. The book is a best practices book, not a how-to book. Certainly when a grad student shows a prof his work, the prof will preform some sort of verification; the same goes for peer review. The verification is not only for correctness but also for "rigour".

http://mathoverflow.net/questions/112298/math-research-guide Raphaël Hythlodée 2012-11-14T13:36:49Z 2012-11-14T13:36:49Z

If that is the case then such a guide in mathematics would be about how to produce rigorous mathematical proofs. To reformulate the question then, are there books which explain how to produce rigorous proofs of publishable questions?

http://mathoverflow.net/questions/112298/math-research-guide Raphaël Hythlodée 2012-11-14T05:30:41Z 2012-11-14T05:30:41Z

In regards to " How does one build an academic career" this is not something that will ever be treated in a research guide. The purpose of the guide is to encourage and treat best practices, as well as create a framework in which research can be done in a consistant manner. Such a guide would not be about how to be a mathematics professional, but rather how to do mathematics in an academically sound way.