I may be slightly biased here based on A Levels alone, but I'll detail my maths story (FM, M, Ph, Chem)
For me it ended up being a language thing, when I was less proficient at English, numbers, math, was in any case, the language that both me and my peers could both grasp firmly, it ended up bridging the gap between us and in a sense brought us closer together.
My initial love of mathematics began with (to my current self's dismay), a slightly empiricist approach
"Mathematics is the gate and key of the sciences. ... Neglect of mathematics works injury to all knowledge, since he who is ignorant of it cannot know the other sciences or the things of this world. And what is worse, men who are thus Ignorant are unable to perceive their own ignorance and so do not seek a remedy."
Whilst the last part is a tad edgier, Mathematics is the gate and key of the sciences resonated strongly with me, as someone young, and curious about the world around me, especially in one lied around us, beyond us, mathematics just seemed like the right path to help me achieve that.
Eventually you come to appreciate mathematics' beauty for what it really is, and begin to appreciate it for its own merits, as opposed to its beneficial use elsewhere in science (although I still appreciate that). Within it are some of the most beautiful and complex conceptions one can conjure. Which takes me aback when many tell me that Mathematics is not 'creative' field, when you take a look at the works of Euler, Newton, Leibniz, Euclid, Archimedes, Taylor, who spearheaded new phenomena in mathematics seemingly out of nowhere, you realise that to really call yourself a Mathematician you need a lot of thought.
However it is understandable for people to say that, and for people who grew up under the British education system, it really isn't surprising. Given that Mathematics as taught in schools has largely been stripped away of the awe and wow factor that inspired young mathematicians generations ago, now being reduced to just memorising rote techniques, discouraging thinking outside the box, critical thinking, and problem solving (GCSE 9-1 is a step in the right direction though but more needs to be done). These latter kinds of skills are what to me makes a mathematician.
Would just like to end on a quote from Hilbert, in response to when one of his pupils dropped out to pursue a career in poetry: "Good, he did not have enough imagination to become a mathematician".