Not only am I a mathematical realist, I go one step further by stating that mathematical structures are all that exist (mathematical monism). This is epitomised by Max Tegmarks mathematical universe hypothesis (MUH).
For me, this belief arose from constantly thinking in terms of immutability, which eventually lead me to think of spacetime as an immutable object with time as another dimension.
Additionally, we keep discovering mathematical regularities in spacetime, so it would seem that spacetime isn't just some randomly configured object - but rather a mathematical structure. Max Tegmark has described this really elegantly.
This philosophy has gotten me interested in physics again, however, if I do get into physics it would have to be timeless physics just as when I when I do programming it has to be declarative programming. Mathematics will definitely continue to be my primary area of study because it is intrinsically declarative.