I do math for fun! That said, I'm a computational MD/PhD, so math is part of work, too.
Having gone through the preclinical years, I always tried to think about how the material would fit into an applied maths context, at least a little bit. It made the memorization easier because it made the material more fun. Making studying fun also made doing well on Step 1 easier for me; not only that, but since I had approached the material with a "problem-solving" mindset, I could more often than not correctly answer questions even if I had never seen them before. I never felt like I had enough time to think about math as much as I would have liked to, regardless. I was afraid I'd lost mathematical intuition when starting my thesis work, but thankfully it gradually came back. Now I just hope I don't forget too much medicine!
Recently I've been craving going back to the fundamentals, so I've been re-reading some textbooks from undergrad and working on the interesting problems I never got around to doing the first time. I'm currently going through Spivak's Calculus! I'm additionally liable to spend hours browsing through maths I've never studied before online. I find it very enjoyable: if you feel math is your hobby, you should totally cultivate it! Only downside is that it's not a very common hobby in any population outside of math, engineering, or computer/physical science students, so it can be hard to find people to talk about it in person. Most other people I've met in medical school have almost math-phobic tendencies, so our context as medical students doesn't exactly help in that regard...
