Like programming, it really is just symbol manipulation and nothing more. I strongly disagree. Arithmetic, perhaps... but not "math." Some of the best math p

Like programming, it really is just symbol manipulation and nothing more. I strongly disagree. Arithmetic, perhaps... but not "math." Some of the best math proofs require little-to-no direct symbol manipulation. You might be able to reduce a mathematical statement down to the symbolic level (eg. using sets), but so much of the beauty is in the simple intuition. One simple example: the pigeon hole principle -- you can teach it to a 3 year old, and yet its incredibly powerful. EDIT: If you read about Lockhart's Lament (as mentioned elsewhere in this thread), he specifically writes: The cultural problem is a self-perpetuating monster: students learn about math from their teachers, and teachers learn about it from their teachers, so this lack of understanding and appreciation for mathematics in our culture replicates itself indefinitely. Worse, the perpetuation of this “pseudo-mathematics,” this emphasis on the accurate yet mindless manipulation of symbols, creates its own culture and its own set of values. Those who have become adept at it derive a great deal of self-esteem from their success. The last thing they want to hear is that math is really about raw creativity and aesthetic sensitivity. Many a graduate student has come to grief when they discover, after a decade of being told they were “good at math,” that in fact they have no real mathematical talent and are just very good at following directions. Math is not about following directions, it’s about making new directions.