Ah yes - I used to love reading Euclid's proofs [1]. Wonderful descriptions. He used such poetic phrases too - things like describing a line as 'a length withou

Ah yes - I used to love reading Euclid's proofs [1]. Wonderful descriptions. He used such poetic phrases too - things like describing a line as 'a length without breadth.' As wonderful as it is, mathematics needs notation, and lots of it. You can express incredibly complex ideas in mathematics, totally unambiguously, through a collection of symbols. Not to mention that they're universally recognised. The reality is that mathematics is 100% about thought. You'll struggle to put together the concepts in your mind long before the notation is the real issue. Once you have a clear picture of the abstract space you can use the notation you've learned to communicate the world you've created to others. What could be more wonderful? [1] http://aleph0.clarku.edu/~djoyce/java/elements/bookVI/propVI2.html http://aleph0.clarku.edu/~djoyce/java/elements/bookVI/propVI...