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posichttp://mathoverflow.net/questions/155632/advice-on-planning-organizing-and-executing-a-serious-mathematics-research-proj
The question again, with all its parts clearly stated.
In general:
Could you share advice on planning, organizing and executing a serious mathematics research project?
In particular:
0) What are the fields of mathematics that would be of particular interest given the kinds of topics I am interested in pursuing?
1) What are the community's suggestions for a possible process to follow in order to form a research topic out of my interests and the relevant fields? Should one first try to read general survey papers in order to get a bird's eye-view? Get involved in discussion with people who are involved in the field? Cold-call professors involved in the field?
2) What are some worthwhile heuristics for evaluating one's progress?
3) Given a field of mathematics, how should one chart a self-learning plan in order to efficiently "cut to the chase" (i.e. get to the point where you can start answering the questions you are interested in)?
4) How should one interact with the mathematics community in order to become a 'serious member' of established 'research circles'?
Мой коммент:
The question is indeed interesting in that it opens a view of how outsiders imagine mathematical research and discoveries being done nowadays. It also serves to prove the point opposite to what the OP suggests in an above comment, namely, how important it has become to dedemocratize the process of becoming a professional mathematician, and how urgent such a task may indeed be, given how far the democratization process has gone by now. This is also the reason why I think this question will be deleted soon.
The question again, with all its parts clearly stated.
In general:
Could you share advice on planning, organizing and executing a serious mathematics research project?
In particular:
0) What are the fields of mathematics that would be of particular interest given the kinds of topics I am interested in pursuing?
1) What are the community's suggestions for a possible process to follow in order to form a research topic out of my interests and the relevant fields? Should one first try to read general survey papers in order to get a bird's eye-view? Get involved in discussion with people who are involved in the field? Cold-call professors involved in the field?
2) What are some worthwhile heuristics for evaluating one's progress?
3) Given a field of mathematics, how should one chart a self-learning plan in order to efficiently "cut to the chase" (i.e. get to the point where you can start answering the questions you are interested in)?
4) How should one interact with the mathematics community in order to become a 'serious member' of established 'research circles'?
Мой коммент:
The question is indeed interesting in that it opens a view of how outsiders imagine mathematical research and discoveries being done nowadays. It also serves to prove the point opposite to what the OP suggests in an above comment, namely, how important it has become to dedemocratize the process of becoming a professional mathematician, and how urgent such a task may indeed be, given how far the democratization process has gone by now. This is also the reason why I think this question will be deleted soon.
