The dark side proof is that most mathematical problems are incredibly contrived. Taking a business requirement and translating it into known mathematical problems is harder than it sounds. Once you can do that, you're 90% of the way there, and people who can do that reliably are regarded as geniuses.
But most of the time, development is done without full understanding of the problem space. Usually, the problem doesn't become fully understood until you've already spent a good amount of time coding up your solution. If you wait until you fully understand the problem before starting, then you'll never start, because your brain simply can't comprehend the entire scope.
So instead, you get code bases full of sort-of well-factored code, but with lots of unwittingly reinvented wheels. This status is occasionally improved when somebody really smart happens to notice the commonality, and remembers a classic problem that it resembles, and manages to refactor the entire thing using the general solution. However, this almost never becomes apparent during the first revision.
But most of the time, development is done without full understanding of the problem space. Usually, the problem doesn't become fully understood until you've already spent a good amount of time coding up your solution. If you wait until you fully understand the problem before starting, then you'll never start, because your brain simply can't comprehend the entire scope.
So instead, you get code bases full of sort-of well-factored code, but with lots of unwittingly reinvented wheels. This status is occasionally improved when somebody really smart happens to notice the commonality, and remembers a classic problem that it resembles, and manages to refactor the entire thing using the general solution. However, this almost never becomes apparent during the first revision.