4 Answers

  1. Pay attention. The question is set in the topic “Psychology”. This means that the answer to the question is not limited to the sum of knowledge, but also affects the nature and motivation of scientific activity. As for the amount of knowledge, Gavriil Serov lists mathematical tools, which are still only tools. I agree with Serov that it is necessary to plunge into the history of science and carefully understand the messages underlying the theories. Without a philosophical theory of knowledge, probably, can not do. In physics, with the light hand of some authorities, a disdainful attitude has developed towards both philosophy and people who call themselves philosophers. There are a great many philosophical trends that have developed, but the theory of knowledge is only one or two in its composition… Indeed, philosophical movements of a particularly idealistic type have a lot of things that are aimed at winning minds, gaining influence in society, and supporting their own elitism. The naked eye can see that ego-motives are dominant. But this is not a reason to reject philosophy as a whole from the threshold.

    To make new discoveries and put forward revolutionary theories, you need to “stand on the shoulders of giants”. This is not enough, in order to see far away, you need to sharpen your eyes, i.e. carefully review what humanity has developed, whether we are sitting in a deep hole. A reliable reference point is the principle of continuity in science, when a new theory does not negate the previous theory developed by practice, but includes it as part of a new one, outlining the scope of applicability.

    The road will be mastered by the walking person. In a good way.

  2. It is not necessary to have academic knowledge for revolutionary theories and discoveries. You have to have talent. But if this talent is multiplied by theoretical knowledge, then the efficiency increases significantly. Knowledge of mathematics, first of all, and physics is necessary for conducting your own routine calculations. But the Genius sees the whole problem without going into details. An idea requires talent. Implementation – necessary technical knowledge.

  3. Even in order to simply master quantum physics (not to put forward your own, but only to understand what has already been done before you decades ago), you need to have a good command of such sections of mathematics:

    • standard analysis,
    • functional analysis,
    • tensor analysis,
    • spinor analysis,
    • linear (spectral) theory,
    • integral forms,
    • generalized functions,
    • partial differential equations,
    • group theory.
  4. Well, if you really need “revolutionary scientific theories”, and even in the phys-math profile, then you need to go to the MIPT website and find “Programs for candidate exams in the specialty…”. There will be such a weighty list of directions, choose the most interesting for you and read. There is also literature by the way. If you find it completely incomprehensible, find undergraduate programs on the same site and take a look at them)

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