Embodied in the average blue collar workday, there are centuries of received wisdom.
Embodied in the crustiest Turing complete device you have, there are mathematical truths you wouldn't grasp from a lifetime of studying mathematics.
Computing is what happens when the subject we thought was mathematics for the past several millennia was doused with ice water and woken up from its long sleep in the ivory tower, wrestled out of the human mind and forced to get a job, to operate on the scale of nanoseconds, and to take place in finite space and time. We found that even the games we fancied infinite were obviously not. If they were, how else would they have fit in a mind or in a book? Computing is not the lesser technological cousin of mathematics. It is mathematics. Everything that ever went by the name and more.