The best programmer I know personally, who hooked me on Perl originally (When I asked if there was a good Basic or Lisp for Irix =), is a Philosophy Major, a fine swordsman, and a maddened redheaded redneck. The other programmers I work with were working on Chemistry and Graphic Arts degrees. Two others are in non-science related fields, like History and English. All are exemplary programmers.

What is missing isn't "Maths and Science" but a foundation of critical thinking. They have learned to break up problems into patterns and sub units. My boss is the Graphic Artist and his approach to problem solving has been described as "brutal". He can rip a problem apart faster than anyone I know. He often sees the issue while we are still asking the question. While he is a real genius, I've seen plenty of computer types who weren't brilliant but had a critical capacity for breaking down problems and spotting patterns.

Programmers build up a toolkit of problem solving techniques in their head. The best ones don't keep hitting everything with the hammer, they whip out the jigsaw and Vise-grips. =)

--
$you = new YOU;
honk() if $you->love(perl)