<p>There are actually lots of applications of pure math areas in engineering and ndustry, for which having a math major is almost essential. </p>
<p>Finance is the one most people know about. Financial models typically use lots of measure theory and real analysis, so a math major (or most of the time, a PhD) is actually necessary to work there.</p>
<p>Computer science has lots of applications of pure math in the R&D areas. There’s some fancy geometic/topological approaches to computer vision. There’s people working on computational complexity theory using algebraic geometry. Machine learning research involves the obvious probability/statistics/linear algebra as well as things like matrix analysis. </p>
<p>Robotics also attracts lots of mathematicians. A basic idea is that you can treat the positions of a robot as points in topological spaces using product structure for different motors/joints/etc. and quotient maps for components which interact with each other, and then study how to control robots that way. In fact robotics and algorithms are two fields that really like mathematicians, since in both fields being able to prove that your robot or algorithm works correctly is essential. Imagine trying to get a robot to disarm a nuclear device. Well you can’t really use trial and error to make sure it works correctly.</p>
<p>And then there’s various things like cryptography and quantum computing that are still hot research areas.</p>
<p>If you’re interested in physics, a lot of physics uses grad level math. Quantum mechanics can be formulated using measure theory, differential topology pops up even in basic electromagnetism, string theory uses lots of algebraic topology, etc.</p>
<p>So yea, basically if you keep an eye on other areas, you can easily focus on a math major or PhD and still get a good job.</p>
<p>The other areas of engineering (mechanical, chemical, electrical, etc.) are less friendly since they mostly use 200-year-old math and physics. But there might be cool things I’m not aware of, I haven’t really looked at those areas.</p>