If you like numbers don't just study math - study tuning systems in music! Music theory has cool names for individual numbers, like the 'schisma', which is 32805/32768.
Lots of people say they don't like math because they don't like numbers. In reaction, many mathematicians say that math is not really about numbers. Indeed, I don't spend most of my days messing with numbers: I spend a lot of time thinking about shapes, abstract structures, ideas from physics, and so on.
But some mathematicians *do* love numbers and spend a lot of time on them. I love them as a kind of hobby. The properties of the number 24, for example, are utterly mind-blowing, connecting higher-dimensional spheres to lattices and string theory.
The study of tuning systems offers humbler fun with numbers. If you go up a fifth you multiply the frequency of your sound by 3/2. Do this twelve times and you *almost* go up 7 octaves. But you're off by a factor of
531441/524288 ≈ 1.01346
This is called the 'Pythagorean comma' - a glitch in the Pythagorean tuning system.
There's also a tuning system called 'just intonation', based on simple fractions as shown below. In this setup if you play the sequence C G D A E C you don't get back where you started: you wind up higher by a factor of
81/80 ≈ 1.0125
This is called the 'syntonic comma' - a glitch in just intonation.
In the 6th century, Boethius noticed that these two commas are close but not quite the same - a kind of meta-glitch between glitches! He called their ratio the 'schisma'. It's
(531441/524288)/(81/80) = 32805/32768 ≈ 1.00113
It's also the ratio between 8 justly tuned perfect fifths plus a justly tuned major third and 5 octaves.
I find this fun!