ABSTRACT
This chapter lays out some historical facts and views of mathematics. It interludes with Kant, pointing out some of his claims and insights in aesthetics, and some aspects in mathematics that one might think he overlooked or underestimated. The chapter brings out some aspects of higher mathematics that one might show are similar to art. These aspects are in the doing and creating of mathematics, not in the finished theories. They are usually not found in textbooks. The chapter shows that a researcher in mathematics is like a painter or composer, exploring and creating. To see this, one has to adopt a first-person perspective. In this way one shows that aesthetics plays a role and leaves its traces also in mathematics. Kant claims that in mathematics one can "make" everything "entirely intuitive", so that others can "follow it". He says Newton could make "all his steps" intuitive and that he "had to take" them.
