Here are a few brief remarks on possible trends in mathematics for the coming decades.
Classical mathematics is a quest for structural harmony.
And similar mathematics appears once again on a less fundamental level, e.g., in crystals and quasicrystals, in selfsimilarity for fractals, dynamical systems and statistical mechanics, in monodromies for differential equations, etc. As the body of mathematics grew, it became itself subject to a logical and mathematical analysis. This has led to the creation of mathematical logic and then of the theoretical computer science. The latter is now coming of age. It absorbs ideas from the classical mathematics and benefits from the technological progress in the computer hardware which leads to a practical implementation of theoretically devised algorithms.