Complex numbers and Physics (Touches to the EPR paradox)

Someone knowledgeable and witty subtly noticed that one of the major discoveries of the twentieth century physics was the discovery of a complex number. Of course, this primarily concerns discovery of the quantum world and creation of an appropriate mathematical formalism of quantum mechanics, significantly complex. The ideology of probabilities, rather complex amplitude probability, lies in the foundation of all the mathematical part of the quantum theory.
This year we celebrate the 100th anniversary of the publication of Einstein’s General Theory of Relativity (1916). But Einstein was also known to be a pioneer of quantum physics, though, having rather deterministic views, he radically disagreed with Bohr. The famous thought EPR (Einstein, Podolsky, and Rosen) experiment was invented with the aim to illustrate this determinism as well as to show the measure of incompleteness of quantum description of the nature. This experiment became a subject of discussions for physicists and mathematicians of several generations. In our time it has transformed into the idea of quantum communication, quantum information theory, quantum computation and quantum computer. Without plunging into these already very broad areas in which the speaker is not competent, we confine ourselves to the main mathematical ideas related to the content and conclusions of the EPR experiment.