Methods of reconstruction in the history of mathematics

The first problem in the context of the title of the report is a problem of the relation between “presentism” and “antiquarism”. Presentism is a desire to talk about the past by a modern language. Antiquarism is a desire to restore the picture of the past in all its internal integrity without any references to the present. It will be demonstrated an approach to resolve the controversy in the issue of the reconstruction of the genesis of theoretical mathematics. The second problem, which closely related to the first one, is a problem of translation. The report will show that a solution to this problem is much simpler in the history of ancient mathematics than in the general historical and scientific context. Along with a reconstruction of the genesis of theoretical mathematics, discussed in the first part of the report, a special role in solving the particular problem of translation of ancient mathematical texts plays Plato's dialogue "Cratylus".