These days it’s more like math departments under CS departments (which are seen as highly important, as a CS degree is more fashionable than a maths one and mat

These days it’s more like math departments under CS departments (which are seen as highly important, as a CS degree is more fashionable than a maths one and mathematics is seen as an abstruse academic pursuit in the worst sense and a financial sink rather than a source). It’s true that (almost) every proof is built on top of others, but this is not the way mathematicians learn their craft — you do have to start at the bottom. The average programmer, on the other hand, has never been anywhere near the hardware or, these days, the software near the bottom.