…mathematics is so rich and infinite that it is impossible to learn it systematically, and if you wait to master one topic before moving on to the next, you’ll never get anywhere. Instead, you’ll have tendrils of knowledge extending far from your comfort zone. Then you can later backfill from these tendrils, and extend your comfort zone; this is much easier to do than learning “forwards”.
Enlightening the man on the street with a beautifully simple experiment.
Before functoriality, people lived in caves.
Nothing is more fatal to the progress of the human mind than to presume that our view of science is ultimate, that our triumphs are complete, that there are no mysteries in nature, and that there are no new worlds to conquer.
Only the mediocre are supremely conﬁdent of their ability.