Why should you study mathematics?
That's a difficult question...
because I like studying mathematics, I should of course answer how many and what reasons all
speak only for mathematics, but many speak just as much for other courses of study or training. But
mathematics or the study of mathematics combines many beautiful things:
Finding suitable proofs requires creativity, just as it is desired in art, engineering courses or in some trades. The pursuit of precision and correctness can also be found in the natural sciences or law. And mathematics is useful, just as a bicycle or a hammer is.
But I can think of one thing that is unique to mathematics:
Mathematics means freedom.
I keep hearing the phrase “Mathematics investigates self-created structures” and I particularly like it because of the word “self-created”. You are free to choose which structure you look at: Manifolds, algebras, schemes, ...
And this freedom extends further than in other fields such as physics or law. Mathematics is not bound to physical laws or to society - the only restriction is that one draws logical conclusions (but this is present everywhere).
And this freedom extends to the mathematical foundation: Which axioms do I accept? Others can take other axiom systems, but we all agree: a proven theorem is proven!
But with freedom also comes the agony of choice: what should you do? There are many great options here, ranging from analysis to pure logic or set theory. I am particularly interested in geometry and category theory and feel at home there. But each area is interesting in its own right and discovering relationships between them is a great pleasure.
Alexander Dallinger B.Sc.
Graduate award winner for outstanding B.Sc. degree at the Department of Mathematics