Perhaps after 53 lectures it’s about time that I define what I mean with mathematics?

Mathematics can be defined as the science dealing with quantities, numbers and geometrical objects in particular.

It is characterised by its logical method which consists of drawing logical conclusions from already proven results.  This chain of reasoning can then be traced all the way back to the fundamental axioms.

Kant pointed out that mathematics is a purely theoretical science.

The axiomatic system of  mathematics is independent of the physical world. Still mathematics is of outmost importance for the empirical sciences since it provides a means for constructing mathematical models able to accurately describe and predict outcomes in the  real world.