I really like pure math, like analysis, topology, and number theory, but I also like physics. I am wondering how many applications pure math has in higher level physics, because I don't want it to leave my life. And also, would a pure math /physics double major be intuitive or a waste of my time. At this point I my best case scenario after undergrad is to go get a Phd in math or physics, and try to get a job as a professor. My second case after undergrad is to go to grad school in engineering or physics and work in industry, because I would never go to grad school in math and end up working as an analyst or acruary, I would die.