http://www.norvig.com/spell-correct.html How did he solve it? Using probability theory and sets.
It's not just games, cryptography, finance, signal processing, compression, optimization, and AI that require mathematics, tons of programming does most people just don't realize it and brute force their way to a solution.
Lot's of real world problem can be solved with algebra, calculus, Boolean algebra, linear algebra, geometry, sets, graph theory, combinatorics, probability and stats. What typically happens is most programmers are giving a problem, and what do they do? They start thinking in code. How did we solve problems before computer?
Apply that kind of thinking, then solve the problem with mathematics. Your code will often be much smaller and dense. Sure, dealing with output and input doesn't require you to write mathematical code, but the core of your problem can often be solved with some mathematics.