Textbooks Hide the True Beauty of Mathematics

Last week I shared a post complaining that the way in which we teach mathematics hides the beautiful creative process that makes mathematicians love their craft.

The latest 3Blue1Brown video explains the way in which mathematicians themselves obscure that creative process when they clean-up their mess and share only their theorems and proofs. It gives the impression that progress in mathematics requires divine inspiration, making it unattainable to those among us who dont have access to that special phone line to god.

Hint: it’s not how it happens. Quoting Grant Sanderson:

Often in math you should see the definition not as a starting point, but as a target. Contrary to the structure of textbooks, mathematicians do not start by making definitions and then listing a lot of theorems and proving them and then showing some examples.

The process of discovery in maths typically goes the other way around. They start by chewing on specific problems, then generalizing those problems, then coming up with constructs that might be helpful in those general cases and only then do you write down a new definition.