«Some mathematics are birds, others are frogs. Birds fly high in the air and survey broad vistas of mathematics out to the far horizon. 

They delight in concepts that unify our thinking and bring together diverse problems from different part of the landscape.

Frogs live in the mud below and see only the flowers that grow nearby. They delight in the details of particular objects, and they solve problems one at time.

I happen to be a frog, but many of my best friends are birds. The main them of the talk is this: mathematics needs both birds and frogs.

 Mathematics is rich and beautiful because birds give it broad visions and frogs give it intricate details.

Mathematics is both great art and important science, because it combines generality of concepts with depth of structures.

It makes no sense to claim that birds are better than frogs because the see farther, or that frogs are better than birds because the see deeper.

The world of mathematics is both broad and deep, and we need birds and frogs working together to explore it.»

(Freeman Dyson, Birds and frogs)