Known facts: Your improved solution is using a 'known fact' from other field. It often helps to know little bit about other fields to make your application faster, especially if your problem doamin involves that field. It is upto you, how do you know other facts and make efficient usage of them.

Just like your life, everybody can give 2 cents from their perspective, no matter how expert you are. They have their own perspectives to look at the problem.. (remember light bulb jokes).

Mathematics and Algorithm have heavy impact on programming. We develop libraries to solve such things in most efficient ways so that you don't have to deal with it on personal level.