Note: I am sorry this is late but I had a crazy day!
I am writing this post after having slaved away on a mathematical logic assignment for the past bajillion hours. It's long sometimes tediously boring work but it becomes worth for those brief moments when that mathematical logic reveals something truly beautiful. In this case it was coming to the realization that the divisibility lattice of any number that is a product of non-repeating primes (ie: 3*5=15 but not 60=3*3*5) is a boolean algebra. But that's just one really specific example. Mathematical beauty occurs EVERYWHERE in math and it's part of why I enjoy it so much.
In fact, one of my all time favourite blogs is proof that math is beautiful, which is a great source for some examples you can appreciate fairly easily. But it can only scratch the surface because much of the beauty in math cannot be enjoyed unless you truly grok the concepts.
My love of math had waned while in university mostly due to my continued struggles with calculus. My theory is that I didn't understand so I didn't enjoy so I didn't bother to take the time to understand which might have let me enjoy... in a viscous cycle. Two factors contributed to starting this cycle though.
First of all there are huge wholes in my understanding of calculus and solving increasingly complicated with a weak foundation is a recipe for unpleasantness. There is a great analogy that Salman Khan makes in his TED talk about Khan Academy about being taught how to ride a bike. Once you know 60% of bike riding they hand you a unicycle... It makes learning hard if you don't have a solid foundation.
Second, I don't find that a 300 person calculus class is a good environment to teach math. I think this is more a personal issue, but learning math has always been a very 1 on 1 or small group learning process.
Anyway, to leave you with a quote from the Mathematical Beauty wikipedia article
Mathematics, rightly viewed, possesses not only truth, but supreme beauty — a beauty cold and austere, like that of sculpture, without appeal to any part of our weaker nature, without the gorgeous trappings of painting or music, yet sublimely pure, and capable of a stern perfection such as only the greatest art can show. The true spirit of delight, the exaltation, the sense of being more than Man, which is the touchstone of the highest excellence, is to be found in mathematics as surely as poetry.
- Bertrand Russell