You show up at a meeting with the next company's CEO, you put Exxon's severed head on the table, you say 'board seats, now' and you get them without a fight.
Programmers work mostly in a discrete world of bits, bounded memory, bounded time, function names that are full words with some hint of the function's job. Mathematicians work in a much 'wilder' world, e.g. where infinite quantities are allowed; they tend to favour shorthand, greek symbols, subscripts, superscripts etc.