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It seems possible to go from soft sciences to hard sciences. For example one professor in my philosophy department initially did math as an undergraduate. So I am wondering can you go the opposite way, for example from psychology to maths (maybe because Maths seem to be more fun).

(Sorry if I'm asking a repeat question)

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    Maths isn't a science, hard or otherwise. I think your question is built on somewhat of a false premise.
    – MJeffryes
    Mar 18 '15 at 10:00
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    Whether or not math is a science is a bit controversial (en.m.wikipedia.org/wiki/Mathematics#Mathematics_as_science), e.g. Gauss might disagree with the above commentor.
    – Aru Ray
    Mar 18 '15 at 12:49
  • Regardless of whether we call it a science or not, would you agree there is something about maths which is not like the [other] sciences? I think almost all scientists would say their work requires mathematics, whereas I don't think many mathematicians working only on mathematics would say the same of the [other] sciences.
    – MJeffryes
    Mar 18 '15 at 21:15
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I think what you know and how strong your recommendation letters are the most important factors during the application process. Usually people need to take several foundamental courses to have a solid background before conducting research in math. And you also need to have some undergraduate research experience. So a degree in math is the most efficient way to get this. But it can also be achieved even though you don't have a degree in math. My undergraduate degree is business administration but I have taken around 20 math courses including 10 analysis courses and several algebra and geometry courses during my undergraduate study. Currently I am going to start a research master program in pde and applied analysis and I hope I can do research in math in the future.

So yes, you can. But you need to make extra effort to fill up the gaps.

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