The authors present the main ideas of the computer-assisted proof of Mischaikow and Mrozek that chaos is really present in the Lorenz equations. Methodological consequences of this proof are examined. It is shown that numerical calculations can constitute an essential part of mathematical proof not only in the discrete mathematics but also in the mathematics of continua.

Jacek Urbaniec: Platonism in the philosophy of mathematics does not necessarily imply that there are links between the temporal physical world and the eternal world of mathematics..