2.1.1 Mathematical Physics and Theoretical Physics
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The term ‘mathematical’ physics is also sometimes used in a special sense, to distinguish research aimed at studying and solving problems inspired by physics within a mathematically rigorous framework.
Mathematical physics in this sense covers a very broad area of topics with the common feature that they blend pure mathematics and physics. Although related to theoretical physics, ‘mathematical’ physics in this sense emphasizes the mathematical rigour of the same type as found in mathematics.
On the other hand, theoretical physics emphasizes the links to observations and experimental physics which often requires theoretical physicists (and mathematical physicists in the more general sense) to use heuristic, intuitive, and approximate arguments. Such arguments are not considered rigorous by mathematicians.
Arguably, rigorous mathematical physics is closer to mathematics, and theoretical physics is closer to physics.
— Wikipedia
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2008.06.03 Tuesday