The subject of physical mathematics is concerned with physically motivated mathematics and is different from mathematical physics.
The use of the term “Physical Mathematics” in contrast to the more traditional “Mathematical Physics” by myself and others is not meant to detract from the venerable subject of Mathematical Physics but rather to delineate a smaller subfield characterized by questions and goals that are often motivated, on the physics side, by quantum gravity, string theory, and supersymmetry, (and more recently by the notion of topological phases in condensed matter physics), and, on the mathematics side, often involve deep relations to infinite-dimensional Lie algebras (and groups), topology, geometry, and even analytic number theory, in addition to the more traditional relations of physics to algebra, group theory, and analysis.
- Gregory W. Moore. "Physical Mathematics and the Future" (PDF). Physics.rutgers.edu. Retrieved 2016-04-03.
- Eric Zaslow, Physmatics, arXiv:physics/0506153
- Arthur Jaffe, Frank Quinn, ``Theoretical mathematics``: Toward a cultural synthesis of mathematics and theoretical physics, Bull. Am. Math. Soc. 30: 178-207, 1994, arXiv:math/9307227
- Michael Atiyah et al., Responses to ``Theoretical Mathematics: Toward a cultural synthesis of mathematics and theoretical physics``, by A. Jaffe and F. Quinn, Bull. Am. Math. Soc. 30: 178-207, 1994, arXiv:math/9404229
- Michael Stöltzner, Theoretical Mathematics: On the Philosophical Significance of the Jaffe-Quinn Debate, in: The Role of Mathematics in Physical Sciences pp 197-222, doi:10.1007/1-4020-3107-6_13
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