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Mathematics enters the period of change unprecedented in its history, perhaps even a revolution: a switch to use of computers as assistants and checkers in production of proofs. This requires rethinking traditional approaches to mathematics education which is struggling through a crisis of its own, socio-economic and political by its nature. The mathematical community faces Pandora's box of problems, which, surprisingly, are not usually discussed in any connected form. The present paper attempts to address this issue in a bit more joint and cohesive way.