Mathematics is so frequently put into the same category as the sciences that students often assume that it is one of the many scientific disciplines, just like physics, chemistry and biology. This can become a problem when students try to understand the reason for studying mathematics. Most students can immediately see that biology is the study of living organisms and the immediacy of that subject makes it both instantly appealing and comprehensible. In mathematics, however, as soon as the studied objects become sufficiently abstract and far removed from everyday experience, students fail to see their significance. As layers of abstraction are added, visualizing mathematics becomes even harder than picturing microscopic cells.
When confusion arises about the nature of mathematics, it can be helpful to introduce a few ideas from the philosophy of mathematics. That is exactly, what the following PBS Idea Channel video does. The question of whether mathematics is a science that studies objects that exist in this universe or is a mental construct that is aesthetically elegant and just happens to be the best language we know for describing nature, remains unanswered, but the discussion is important. Without it, students may never suspect that mathematics plays a unique role in human history and that it spans almost all disciplines. For those who want a deeper take on the nature of mathematics, Eugene Wigner’s classic paper on The Unreasonable Effectiveness of Mathematics in the Natural Sciences will provide much more food for thought.