It's a little hard to tell what you're really asking, so forgive me if this isn't what you're looking for. Worrying about algorithms in the "mathematical whiz k

It's a little hard to tell what you're really asking, so forgive me if this isn't what you're looking for. Worrying about algorithms in the "mathematical whiz kids" sense is extremely important when you have to be worried about speed and resources. Take databases, for instance. Their search and compression algorithms are extremely optimized (by mathematical whiz kids), and they yield phenomenal results. If everyone had always been satisfied with a simple, straightforward solution, Google would be devastatingly slow and require an enormous amount of space more than it already does. I've had to look into the efficiency of my algorithms when doing batch processing on massive XML files - I managed to cut run-time by 80% by paying more attention to my algorithm's efficiency. On the other hand, if I'm just sorting 5 entries alphabetically for some table, it's better to implement a quick-and-dirty algorithm that will take an extra 2 milliseconds to compute, than for me to spend half my day worrying about it's efficiency. So generally speaking - people designing low-level systems are very worried about their algorithms, with good reason: If their code is slow or wasteful, their platform can't be used. If you're designing a web app, you'd probably waste more time than it's worth if you delve into that. It's just a question of priorities.