Mathematics is a (or, probably, the only!) language that enables ideas about physics be communicated between people across different generations and across different cultures.

Inevitably, it ”suffers” from approximation and abstraction compared to physical reality. A bit like an impressionist painting reflects the real picture.

The question is what and how much is sacrificed here.

One test of whether the sacrifice is acceptable or not is in the way how people, while using mathematics, can build physical objects such as airplanes, cars, bridges, radios, computers etc. If they can and at a reasonable cost, then the language is adequate to the purpose.

For example, it seems that the mathematical language of Heaviside’s operational calculus is sufficient for the purposes of designing and analysing electrical circuits of good quality and in an acceptable time.

Another example, the language of Boolean algebra is sufficient to design logic circuits if we clock them safely so that they don’t produce any hazards. If, however we don’t clock them safely, we need other ways to describe causal relationships between events, such as Signal Transition Graphs.