How to become really interested in math?

Question

I'm a high school senior. What can I do to be really interested in mathematics ? I know some of my batch-mates (from meeting them at several math Olympiads) are like insanely good at math (know lots of things from college/higer math, also are really good at solving extremely hard math olympiad problems, for example can solve IMO P3/P6 routinely)

While I don't believe that your mathematical skills are genetically predetermined, those guys I know are insanely interested in math. I mean every time I see them they're working on some math problems or exploring on some thing on math they find interesting or checking whether somethings are true or not (i.e always thinking about math from pure interest and not because of fame or glory in competitions).

How do I become as intersted in mathematics like them ? I am to some extend interested, but not so much insanely interested in math. There are some topics I find interesting (eg: Graph theory), but I don't feel the "spark" or the "urge to check and find out if something is true or not" or the "urge to explore" even while reading books I find interesting (for example, Diestel Graph theory). I also feel my interest is somewhat (not too much, but to some extend) hampered because of obsessing over my scores on various math Olympiads.

Thanks everyone for your advice in advance :)

Answer 1

A few suggestions for your consideration.

Mathematicians generally fall into one of two cognitive camps (so to speak): visualizers/geometers and symbol manipulators. The former are better at geometry, topology, group theory, knot theory, and such, while the latter are generally better at number theory, analysis, differential equations, and so on. Decide which camp you best fall into, and read good popular books about those fields. Also, hang out with the math team, and others interested in math. Talk to your math teacher.

But if you don't have the passion, don't worry. There are many many fields where you'll do better if you know math: physics, computer science, electrical engineering, statistics, neuroscience, ... indeed nearly all technical fields.

So I would suggest you find your interest (full passion can come later), and approach that field with a mathematical eye, looking for math problems within the field.

My own academic trajectory was of this sort. I loved (and still love) physics, and learned math in order to do better at physics. Later, I became a visiting professor of math at a good university, but I realized I didn't love the incredibly esoteric math that dominated academic math departments.

So math has helped my career immensely, even though I'm not a full-time professional mathematician.

Perhaps this might be a career trajectory for your too.

Answer 2

My impression is that people who are interested in solving puzzles and games also tend to be interested in math, if it is ever taught to them in a way that appeals to their creativity. It seems to me there is a distinct possibility that you could potentially already be interested in math, but you are feeling discouraged because your environment leads you to compare yourself to people who are more skilled at it than you are (at least for now). This would be emotionally difficult not just for you, but perhaps for most people. If you can work on solving easier problems than Problems 3 or 6 from the IMO, but which are still difficult enough to require creativity, there may be enough enjoyment in it to motivate you to study and improve. But constantly feeling that you are in competition with people like the ones you mentioned won't help.

Remember that, although it is true that a good number of successful mathematicians participated in contest math in their youth, a similar proportion never did. So withdrawing from math competitions and focusing on learning math in a way that avoids forcing you to compare yourself constantly with others could be a way out of this conundrum, and won't prevent you from anything you might want to do later.

Nonetheless, I would leave open the possibility that you aren't terribly interested in math - that's quite all right. But if you find that you are very interested in a field that relies heavily on math, like physics or computer science, it's true that you will need to find the motivation, somehow, to become competent in math.

I would say, in that case, in addition to taking steps to make math feel less competitive for you, you could read a book like What Is Mathematics? by Courant and Robbins, to get a taste of various areas of math, presented in an accessible way. Alternatively, you could start studying math on your own in university-level textbooks (with no focus on high school contest material).

Answer 3

Speaking as a sophomore math major (who is extremely interested in mathematics), I don't think this is something you can force upon yourself, rather, curiosity finds you. I became very interested in mathematics ~3 years ago when I taught myself calculus, thought it was the most beautiful thing I'd ever seen, wanted to learn more, and never turned back.

Regarding math competitions, the first I participated in was the 2017 Putnam competition (never did high school math), but competitions have no bearing on my interest in mathematics. I care about teaching, learning deep subjects and intricate theory, and I'm just not interested in the kind of problem solving used in math competitions (this is not to say math competitions are bad, just not for me). But I'm still in love with mathematics.

Learn for yourself as much as you can, and if you love it, then that's that, otherwise it may not be for you.

P.S. If the type of mathematics they use in competitions (graph theory, discrete mathematics) doesn't interest you, then look elsewhere. Math is a HUGE subject; get an abstract algebra book, learn linear algebra, analysis, topology, number theory, differential geometry; there really is no shortage of things to choose from (though there are fundamentals to cover at your early level).