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It's a physicist! No, it's a mathematician! Actually, it's a mathematical physicist.

As I see it, mathematical physics has two main areas of focus. The first is to find new applications of mathematics to physics. The mathematical methods employed in this quest tend to be slightly too esoteric to be part of the average physicist's knowledge base. One example of such a breakthrough is Einstein's General Theory of Relativity, which utilised differential geometry at a time when hardly any physicists received training in what seemed to be such a useless topic.

The second branch of mathematical physics is concerned with finding more mathematically rigorous frameworks for existing physical theories. It is interesting to note that several major branches of mathematical study have been inspired by a cobbled-together physical theory. One of the foremost examples of this is functional analysis, which finds much of its historical motivation in quantum mechanics.

It is difficult to classify scientists who lived less-recently as mathematical physicists since such fine distinctions were not drawn until the latter half of the twentieth century, but I would include the following as mathematical physicists: Albert Einstein, Emmy Noether, Paul Dirac, Adrien-Marie Legendre, George Gabriel Stokes, Isaac Newton, Lev Davidovich Landau, Julian Schwinger and Jean Fourier.

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