"When will I ever use this in the real world?" I remember hearing this question from my students on a weekly basis as a math teacher. And, honestly, it's hard to answer when you're teaching asymptotes.
Of course there are many applications in engineering, computer science and other STEM fields, but not every student will take on a STEM career. So I had to think more deeply about my response. I thought back on the advanced math I learned in college. Abstract Algebra, Real Analysis, Vector Spaces. I couldn't remember much of that stuff, let alone claim I'd been needing it in my day-to-day life.
Eventually, I came to understand what I consider the biggest benefit of learning math: critical thinking skills. Doing math builds brain muscles that help in countless applicable-to-real-life ways. Now as a small business owner, I use those same critical thinking skills to solve problems on a daily basis. Choosing whether to rent, build or buy a home requires critical thinking skills. Managing time effectively, solving problems in relationships. The impact of being able to analyze a problem and find a path forward is immeasurable.