Here I will post some collected quotes that influenced my opinion on how learning, inference, and science should be.
One thing Grothendieck said was that one should never try to prove anything that is not almost obvious. This does not mean that one should not be ambitious in choosing things to work on. Rather, “if you don’t see that what you are working on is almost obvious, then you are not ready to work on that yet,” explained Arthur Ogus of UC Berkeley.
Patterns and solutions
A mathematician, like a painter or a poet, is a maker of patterns. If his patterns are more permanent than theirs, it is because they are made with ideas. … The mathematician’s patterns, like the painter’s or the poet’s must be beautiful; the ideas like the colours or the words, must fit together in a harmonious way.
A good solution improves the balances, symmetries, or harmonies within a pattern — it is a qualitative solution — rather than enlarging or complicating some part of a pattern at the expense or in neglect of the rest.
Theory, method, and applications
A method is more important than a discovery, since the right method will lead to new and even more important discoveries.
We’re against complexity. We believe designing systems is a fight against complexity.
We’ll accept to fight the complexity when it’s worthwhile but we’ll try hard to recognize when a small feature is not worth 1000s of lines of code. Most of the time the best way to fight complexity is by not creating it at all.
Learn to stop
Rather than filling it overfull, better to stop in time.
Sharpen it to a point, the edge won’t last forever.
Gold and jade may fill the house, but no one can retain them.
Boasting of wealth and virtue, brings trouble on oneself.
Reticence when the job is done, is the Way of heaven.