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Thread: Research Mathematicians

  1. #1 Research Mathematicians 
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    How do two or more mathematicians work together in terms of mathematical research? Do they start off with a basis of research and each add onto each others musings until they have something worth publishing, or do they sit down and discourse on a particular problem together? Are mathematicians even able to work together while researching, or is every individual contribution the work of a single mathematician?
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    Quote Originally Posted by Ellatha View Post
    How do two or more mathematicians work together in terms of mathematical research? Do they start off with a basis of research and each add onto each others musings until they have something worth publishing, or do they sit down and discourse on a particular problem together? Are mathematicians even able to work together while researching, or is every individual contribution the work of a single mathematician?
    Some research is the work of a single individual, and some work is the result of collaborations.

    It is pretty simple. Mathematicians talk to one another all the time, and quite often a comment from one can trigger a useful idea from someone else -- that is not usually enough for dual authorship by any means. But when two mathematicians find a problem that interests them, their combined insights are often synergistic and the final result is simply the result of two minds. The collaboration can take place face-to-face at a chalk board, via telephone or internet, or in older times even by mail.

    You have only to look at the literature to find many examples of multiple authorship, and many examples of papers with a sigle author. Unlike papers in big experimental physics projects, however, you do not find author lists that approximate the Manhattan phone book.

    Sometimes, when the two collaborators are sufficiently powerful the result is a blockbuster theorem as in this example. Michael Atiyah and Isadore Siinger are two of the most powerful mathematicians ever.
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    Also, when a person makes recommendations for what type of research should be funded, as you have in the past, what exactly is one funding in terms of mathematics? Because mathematics only seems to require pencil, paper, and a competent mind, are they paying for that person's time?
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  4. #4  
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    Quote Originally Posted by Ellatha View Post
    Also, when a person makes recommendations for what type of research should be funded, as you have in the past, what exactly is one funding in terms of mathematics? Because mathematics only seems to require pencil, paper, and a competent mind, are they paying for that person's time?
    I do not recall any recommendations of that sort, beyond the fact that I stated that I was not opposed to research in string theory (which is NOT mathematics) and though that there should be some funding for it.

    Mathematics research is commonly funded by any of the branches of the armed forces, the National Science Foundation, and some private sources. Generally funding covers time, travel, publication expenses, often funding for summers, etc. Mathematics grants to individuals tend to be smaller than grants in the sciences because, as you note, the research is usually not as expensive.

    There are also, or at least used to be, block grants to large institutions that fund sevreal people, or perhaps fund meetings of significant size.

    Mathematics research proposals are not much differenet from proposals in anything else. One proposes to do researc to pursue some question or questions in some area. That is the same thing that one does in physics, biology or chemistry. Only the questions or methods differ.
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