Without it, we simply don't improve ourselves, and things don't improve for us. Personally, that's what I myself hope to do with teaching. Sure, I love working with the more fundamental aspects of math and physics, but teaching students how to think their ways around corners is a big part of math and science education. That's the misinterpretation that so many people have made concerning education in these areas today. Don't be alarmed when your kids occasionally bring home math homework that doesn't involve numbers, because numbers only constitute a part of mathematics.
Logic is where math and philosophy converge.
It's the basis for critical thinking, and yet numbers don't really play a part in thinking logically, at least not in a traditional sense. Well, there's my manifesto. Mail me and tell me if I'm right or wrong, and thank you for playing.