Mr. delta says
P.M. Dirac on the relationship between mathematics and physics. I’ve noticed this, in my abortive attempts to read mathematical physics books— namely, they seem more abstract than most abstract math books—, but wouldn’t know how to put it quite so elegantly.
The steady progress of physics requires for its theoretical formulation a mathematics which get continually more advanced. This is only natural and to be expected. What however was not expected by the scientific workers of the last century was the particular form that the line of advancement of mathematics would take, namely it was expected that mathematics would get more and more complicated, but would rest on a permanent basis of axioms and definitions, while actually the modern physical developments have required a mathematics that continually shifts its foundation and gets more abstract. Non-euclidean geometry and noncommutative algebra, which were at one time were considered to be purely fictions of the mind and pastimes of logical thinkers, have now been found to be very necessary for the description of general facts of the physical world. It seems likely that this process of increasing abstraction will continue in the future and the advance in physics is to be associated with continual modification and generalisation of the axioms at the base of mathematics rather than with a logical development of any one mathematical scheme on a fixed foundation.
Paper on Magnetic Monopoles (1931)
Makes me want to be a physicist… wait, no, it makes me want to be a mathematician.
Another quote from P.M.:
I consider that I understand an equation when I can predict the properties of its solutions, without actually solving it.
Quoted in F Wilczek, B Devine, Longing for the Harmonies
So obviously, I have a long way to go.
Possibly relevant posts:
- Physical Semantics (7/2/2002)
- Twilight zone for book ordering (8/15/2006)
- More On Installing Software (11/15/2003)