Mathematics as a pure science is the sane everywhere. It can also be claimed that, for several hundred years, mathematical education in Europe has had some kind of unity. For a variety of reasons, including political ones, this unity has been a characteristic of mathematical education both in Europe and even beyond its frontiers. But since the early 1960s this picture has changed completely. The launch of Sputnik in 1957 also marked the launch of a new diversity in mathematical education and it is iirgued here that since then the field has split into two major schools, that of the East and that of the West. Nowadays it is largely accepted that, for commonplace historical reasons, Russia can be regarded as the main representative of the Eastern school and the USA of the Western. But with the onset of political changes in Europe in the late 1980s, there has been an impact on both schools which continues to the present day. The present argument considers that where changes have occurred in the West, they are likely to be of benefit to mathematical education, whereas the ongoing changes in the East are likely to prove to be rather more problematic both for the teaching of mathematics and for mathematics itself.