In this post I will share my perception of relation of mathematics with other academic disciplines. All this is based on my very limited knowledge of various disciplines.
Mathematics deals with study of properties of numbers (or the symbols representing them) and geometric objects (not in classical sense, it can mean manifolds also). In my opinion, there is no partition of mathematics into “applied” or “pure”, but intersections with other subjects. The term applied Mathematics doesn’t make any sense to me. Mathematics is somehow applicable in various places. For me, mathematics is what people call “pure” mathematics (what about “impure” Mathematics??). Also now I agree with the vastly established belief that art and mathematics are similar, since both involve abstract ideas motivated but physical situations (at some point).
All experimental sciences (physics, chemistry, biology, economics) are based on statistics. Since statistics is a young discipline (only a couple of centuries old) many times we get wrong interpretation of results. As far as real life is concerned, study of statistics gives us a powerful tool for predicting future and Probability Theory acts as the connecting link between statistics and mathematics. Understanding of statistics affects us on daily basis since (effective) government policies are framed keeping statistical analysis in mind. Unfortunately, most of universities don’t have separate department for statistics.
Study of algorithms is one of the most important aspect of computer science (I am not talking about software industry…). What surprises me is that Euclid’s division algorithm is one of the most efficient division algorithm even for computers! The neglected subject of Logic, which is supposed to be foundations of mathematics, flourishes in computer science. P vs NP is another “millennium open problem“.
For me, Economics like Statistics is full of imperfections due to real life complications (so many dependencies to account for). Game Theory appears to be the connecting link between mathematics and economics.
We all know that the needs of physicists are responsible for development of calculus and study of differential equations. On the other hand, theoretical physics (quantum mechanics, string theory) depends heavily on the developments in algebra.