The reasons for physical scientists and computational scientists to be excited about quantum computing might be obvious: spooky physics and the potential to solve hard problems exponentially faster than the best known algorithms on digital computers. But why should computer scientists and mathematicians care about quantum computing? In this talk, I give a computer scientist’s perspective on why quantum computing might be interesting, including the impact of topology, programming challenges, verification challenges, complexity theory, (mathematical) optimization challenges, and connections to familiar mathematical objects such as tensors, unitary matrices, probabilities, and 2-norms.