A good problem is something you don't know how to solve. That's what makes it a good puzzle and a good opportunity.

There is nothing as dreamy and poetic, nothing as radical, subversive, and psychedelic, as mathematics. It is every bit as mind blowing as cosmology or physics (mathematicians conceived of black holes long before astronomers actually found any), and allows more freedom of expression than poetry, art, or music (which depends heavily on properties of the physical universe). Mathematics is the purest of the arts, as well as the most misunderstood.

The only thing I am interested in using mathematics for is to have a good time and to help others do the same.

Mathematics is the art of explanation. If you deny students the opportunity to engage in this activity-- to pose their own problems, to make their own conjectures and discoveries, to be wrong, to be creatively frustrated, to have an inspiration, and to cobble together their own explanations and proofs-- you deny them mathematics itself.

There is nothing as dreamy and poetic, nothing as radical, subversive, and psychedelic, as mathematics.

Mathematics is the purest of the arts, as well as the most misunderstood.

Doing mathematics should always mean finding patterns and crafting beautiful and meaningful explanations.