2.1 Mathematics as “Language of Physics”

Physics (Greek ϕυσικ ,,the natural”) researches the fundamental interaction in nature. Already the natural philosophers of antiquity thought at a deep level about the phenomena in the cosmos as well as in nature as it surrounds us and their methodology was mostly of a qualitative, descriptive and often speculative nature.

The large progress of physics in modern times is due to capturing the natural phenomena via measuring them quantitatively, and comparing the results of measurements with assumed relationships (hypotheses). This process allows via the interaction of experiments and hypotheses the evolutionary development of original hypotheses to physical “theories” that are applicable in ever larger generality.

Thus theories are well-tested hypotheses for relationships in nature, that are formulated in the language of mathematics It is an initially startling result of the interaction over hundreds of years between experimental and theoretical physics, that a plethora of individual phenomena can be described in terms of a unified theories, whose mathematical formulation only require a few symbols or lines of symbols. We list here the Schrödinger equation as fundamental equation of quantum mechanics, Maxwells equations of electrodynamics and the Naiver-Stokes equation of hydrodymanics.

Numerically difficult or even sometimes close to unsolvable only becomes the specialization of the fundamental equations to the concrete individual case and the development of the huge variety of phenomena, that are included in the theoretical founding model.

However, a large number of phenomena of practical importance can be described by very simple mathematical models, which are also easily applied to the individual cases. These include nearly all those phenomena, that are important for engineering and its effect on our daily life

Using a suitable level of abstraction of the theories, one can model an ever larger variety of phenomena in a single theory – it is for a reason, that the word formula, from which all theories for parts of physics can be derived is the always desired but not yet attained goal of theoreticians.

It is an unanswered questions of epistemology whether “the book of the universe is written in the language of mathematics”, as expressed by Galileo Galilei, i.e. that physical theories describe the reality of nature, or whether, as formulated by the positivists among the natural scientists, “physical theories are models of nature, that are applicable insofar, as they are confirmed via the experience in the individual case”. The first school of thought includes the natural philosophers of antiquity and among the modern scientists Einstein and Schrödinger as examples; for the second school of thought names such as Born, Bohr and Heisenberg are characteristic. Math

In any case mathematics provides physics with a powerful tool 1 . On the one hand, the corresponding methods were developed directly when studying physical questions as calculus was via Isaac Newton (1663 - 1727) and Gottfried Wilhelm Leibniz(1664 - 1716) while studying the movements of planets. On the other hand physics, when studying new questions, sometimes makes use of methods, that have been developed in the frame of mathematical and logical reflections, such as in the case of the general theory of relativity that made use of the non-Euclidean geometry developed by Georg Friedrich Bernhard Riemann (1826 - 1866).

The strict formulation of mathematical relationships in the highly specialized language of mathematics appeals to the expert with its convincing stringency, transparency and terseness. To the beginner this kind of presentation seems however confusing and to complex. In this text we will choose as far as possible a concrete description and otherwise refer to the specialized textbooks and internet links.