What kind of work in physics is performed by math?

About that the laws of the mathematics allow to a person

Mathematics rests more on the flight of thought, and therefore was developed faster than physics that was nourished by man-made experiments that require a lot of time and money. But gradually it became clear that the laws of nature, even the most intricate and complex, can be explained in the language of mathematics. It’s amazing that this created by man self-sufficient science has at its disposal the concepts and linking them formulas suitable to describe the independent-of-human reality, micro- and macrocosm, as if a person left there traces of their own. With the help of eigenfunctions of mathematical operators, we have formulated quantum mechanics, and metric spaces needed to describe gravity and the universe. And the exponential curve most of all proved useful. Many physical laws of the development of the very different phenomena in time and space are based on it.

Mathematics successfully describes the physical reality

The language of mathematics allows you to visualize what is not observed.

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