The roots of โโฌ™physical mathematicsโโฌ™ can be traced back to
the very beginning of man's attempts to understand nature.
Indeed, mathematics and physics were part of what was called natural philosophy.
Physicistsโ methods were often rejected by mathematicians as imprecise, and
mathematiciansโ approach to physical theories was not understood by the physicists.
However, two fundamental physical theories, relativity and quantum theory,
influenced new developments in geometry, functional analysis and group theory.
The relation of Yang-Mills theory to the theory of connections in a fiber bundle discovered in the early 1980s
has paid rich dividends to the geometric topology of low dimensional manifolds.
https://www.springer.com/gp/book/9781848829381