The article gives a tight review of the author's work dedicated to a new trend in modern mathematics called quantum computing mathematics. Quantum computing methods are interpreted extendedly as relating to quantum mathematical information (quantum mathematics). Mathematical information quanta are whole numbers (integers) characterizing principal integrity of relevant mathematical objects. This approach was applied to solving Beal's Conjecture (Generalized Fermat's Last Theorem) that allowed

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... only to prove the famous problem but unmask excessive formalism of traditional quantum theories. It was revealed also that Fermat's method of infinite descent was in fact the first case of exact application of quantum ideology in pure mathematics.