Physical mathematics
 

The subject of physical mathematics is concerned with
physically motivated mathematics and
is different from mathematical physics.

The details of physical units and their manipulation were addressed by
Alexander Macfarlane in Physical Arithmetic in 1885.[1]

The science of kinematics created a need for mathematical represention of
motion and has found expression with complex numbers, quaternions,
and linear algebra.

Wiki

The roots of โโ‚ฌ™physical mathematicsโโ‚ฌ™ 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