Most mathematicians (people who actually work in the field of mathematics) are not mathematicians. They are teachers, professors, statisticians, actuaries, accountants, topologists, algebraists, geometers, engineers, etc. They use mathematics in their work, but not the entire field of mathematics. They are specialists with the field of mathematics. Mathematics itself is really too broad a field for any one person to be an expert in all of it.
I used to call myself a “Free Range Mathematician” to describe what I did in mathematics. I was free to wander about in the field of mathematics to partake in its delicacies as I wanted, and not to wander into other fields of mathematics that I did not enjoy.
But that is not how it started. I started just like everyone else: having to learn basic arithmetic in elementary school, and expanding into geometry, algebra, trigonometry and calculus in high school. I eventually went to college and studied engineering. I would not use the term “math nerd” or “mathematical badass” to describe myself back then. I could do enough math to get through my classes, but I would not say that I enjoyed it. It just did not have anything that really caught my attention.
I really think that math in general is not taught in an interesting way. It is almost always taught in a manner to give you enough mathematical skill to move on to the next class, or to do a certain job – but all the fun stuff was taken out. (It’s kind of like the cafeteria food – before they served it they ran it through a machine to remove the flavor. I doubt if that is really true, but many people swear by it.).
Even when I was a school teacher I tried some stuff to make math classes more interesting – but I still had to spend most of our time teaching mathematics that few of us find “inspiring”.
I spend my time in mathematics much more efficiently now. I don’t waste time of mathematics that I don’t enjoy, and don’t need.
Now I spend most of my time studying recreational mathematics (wait! I’ve already heard all the jokes about how there is no such thing as recreational mathematics – it’s just an oxymoron.) It is mathematical for sure, and some people (including myself) find it very recreational.
Now I describe myself as a Mathematologist – someone who studies mathematics and everything related to mathematics such as: the history of mathematics, the tools of mathematics, the psychology of mathematics, mathematical music, mathematical poetry, mathematical humor, the relationship between mathematics and religion, mathematics and literature, mathematics and … well … everything.
More specifically (since nobody can know everything about mathematics, they also can’t no everything about everything related to mathematics) I now use the term “Recreational Mathematologist”.
(You may not be familiar with the term “mathematologist”, and you may have problems finding it in the dictionary. Don’t worry. I made the word up, so it means whatever I want it to mean. That’s not a big deal – all words are made up by somebody.)