Below are a few good quotes relevant to physics, mathematics and our research interests. Many come from the paper Quantum Theory in the Rigged Hilbert Space - Irreversibility from Causality.
The miracle of the appropriateness of the language of mathematics for the formulation of the laws of physics is a wonderful gift which we neither understand nor deserve.
---E.P. Wigner from ``The Unreasonable Effectiveness of Mathematics in the Natural Sciences'' in Symmetries and Reflections, (Oxbow Press, Woodbridge, Conn., 1979), p. 237.
Physical causality can be traced directly to the existence of a simple initial condition of the universe. But how does that initial condition enter into the theory?
---Murray Gell-Mann in The Quark and the Jaguar, (W.H. Freeman, New York, 1994), p. 216.
There does not exist...a rigorous theory to which these various methods can be considered as approximations
---Maurice Levy referring to the Wigner-Weisskopf approximation and theories of resonances in Nuovo Cimento 13 (1959) 115.
I would like to make a confession which may seem immoral: I do not believe in Hilbert space anymore.
---John von Neumann in a letter to G. Birkhoff, quoted in G. Birkhoff, Proceedings of Symposia in Pure Mathematics, Vol. 2, ed. R.P. Dilworth, (American Mathematical Society, Providence, Rhode Island, 1961), p. 158. The letter is dated 13 Nov. and Birkhoff believes the year was 1935.
A role of rigorous mathematics in physical science is to make sense of heuristic ideas (i.e. find the `correct setting') - not to assert they are nonsense.
---M. Fischer from talk ``What's Mathematical Physics to Physicists? Some Examples from Past, Present and Future'' at VIIth International Congress on Mathematical Physics, Boulder, Colorado, August 1983.
When in the 18th century Euler discovered those formulas which today still delight the mathematical phantasy, he seriously stated that his pencil was more clever than himself. This impression that mathematical structures can include a kind of self-determination concerns me at this time...Mathematics and Philosophy attack the world's problems in different ways. Only by their complementary action do they give the right direction.
---E. Kaehler, translated from original German by A. Bohm with stylistic input from N.L. Harshman.