Range

Freeman Dyson styled it this way: we need both focused frogs and visionary birds. “Birds fly high in the air and survey broad vistas of mathematics out to the far horizon,” Dyson wrote in 2009. “They delight in concepts that unify our thinking and bring together diverse problems from different parts 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 a time.” As a mathematician, Dyson labeled himself a frog, but contended, “It is stupid to claim that birds are better than frogs because they see farther, or that frogs are better than birds because they see deeper.” The world, he wrote, is both broad and deep. “We need birds and frogs working together to explore it.”