Maths: what matters beyond formulas
Unlike other sciences Maths does not have a face in the collective unconscious: it is generally perceived as obscure formulas on books. However these formulas came from people in flesh and blood and led to concrete results. I will not discuss about great mathematicians or real world application, it would take a book and I do not want to bore you for sure! Instead I want to tell you some concrete facts about Maths.
What I like about Maths:
You just need pen and paper and you are ready to go. Well you might also need some books from the library.
If you consider other sciences, take chemistry or engineering, a lab is necessary and the first serious one available would be in university. Even then you would be tighted to the course program and not completely free to develop your ideas.
Almost all the professors I met are great minds and, at the same time, very humble people. I never felt treated inferior or stupid despite the enourmous intelligence and knowledge gap between myself and them.
I learned to be humble myself, to limit my ego and to ask often for help.
When a researcher obtains some results he must show his work to a group of experts which examine the correctness of the proofs. Then the results are published. The need for collective review makes research in Maths unique since it is available to everyone. In this way knowledge is a public good rather than something an enterprise or a government could keep for itself to take advantage of.
What Maths can teach you
Mathematicians are known to be pedantic and extremely precise. However this attitude results to be a useful skill in team work: precision avoids ambiguity and yields faster understanding.
Another handy resource is simplifying concepts: “what are you studying?” is an extremely difficult and yet common question for a mathematician since the person asking usually does not have the necessary background for a satisfying answer.
Now think about the opposite situation where you are the one asking: you have been assigned something you reckon completely wrong on a technical point but your boss does not have your scientific knowledge to understand why it is wrong. Explain concepts at high level to make them understandable and your boss might listen to you.
You learn how to define a problem and how to tackle it. How to proceed patiently and correctly from one step to the next one, until you reach the solution.
What Maths requires
Passion and a lot of hard work.