A Mathematician's Lament

Observation and discovery are one thing, but explanation is quite another. What we need is a proof, a narrative of some kind that helps us to understand why this pattern is occurring

School has never been about thinking and creating. School is about training children to perform so that they can be sorted

it is far easier to test someone’s knowledge of a pointless definition than to inspire them to create something beautiful and to find their own meaning

the most valuable skill for a scientist or engineer is being able to think creatively and independently

Mental acuity of any kind comes from solving problems yourself, not from being told how to solve them.

We learn things because they interest us now, not because they might be useful later

It may be true that you have to be able to read in order to fill out forms at the DMV, but that’s not why we teach children to read. We teach them to read for the higher purpose of allowing them access to beautiful and meaningful ideas

Teaching is not about information. It’s about having an honest intellectual relationship with your students

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

If there is anything like a unifying aesthetic principle in mathematics, it is this: simple is beautiful