Finding Beauty in the Dissonance

…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”.

– Ravi Vakil

The ideal situation occurs when the things that we regard as beautiful are also regarded by other people as useful.

– Donald Knuth

Enlightening the man on the street with a beautifully simple experiment.

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.

– Humphry Davy

Only the mediocre are supremely confident of their ability.

– Michael Atiyah in the Advice to a Young Mathematician section of the Princeton Companion to Mathematics.