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We attempt to discuss one aspect of relation between mathematics and physics. Well known contradictions of foundations of mathematics, contradictions in conceptions and axioms give us a lot mathematics with illogical and discrepant theories. Confidence in the mathematical accuracy and logicality gives physicists possibility to create abstract theories which are fare from Nature. We have a lot physics too: classical, relativity, quantum and different kind of alternative physics. Circle is closed by ?confirmation? of illogical theories in physical experiments, especially, in quantum experiments. We talk over also about strength and weakness of mathematics: creation of a new notion and unification, and try to formulate problem of redefinition of notions in mathematics and physics. We consider necessity to development ?open physics project? with constantly open discussion of physics' foundations and a physical methodology. We argue initial notions of space, substance and time, and a few open problems.