A lot of people think that computer science is just a branch of maths. But when I was doing my doctorate, I was a computer scientist, and my three supervisors were a mathematician, an engineer, and a meteorologist. The difference between us was much more than the stuff we knew - it was the way that we thought, and therefore approached a problem. Supervision meetings were interesting - it very much felt like four people speaking four different languages.
On a very broad level (and I'll get loads of people disagreeing with this, because both mathematics and computer science divide further into different specialities), mathematics is primarily about proving logical truths, whereas computer science is about managing complexity. That's a massive cognitive difference, even if many of the problems the two fields tackle are the same.
On a very broad level (and I'll get loads of people disagreeing with this, because both mathematics and computer science divide further into different specialities), mathematics is primarily about proving logical truths, whereas computer science is about managing complexity. That's a massive cognitive difference, even if many of the problems the two fields tackle are the same.