... Earth's crammed with heaven,And every common bush afire with God; And only he who sees, takes off his shoes— The rest sit round it and pluck blackberries. —Elizabeth Browning
Descriptions of Mathematics
From the inability of non-theistic assumptions concerning the nature of mathematics to account both for its unity and its involvement in the natural sciences, comes surrender in the battle to define mathematics. James R. Newman delineates the problem when he says,
There are two directions of mathematical inquiry. It can either penetrate into the other sciences, making models, maps, and bridges for reasoning; or it can mind its own business, cultivate its own garden. Both pursuits have been enormously fruitful. The success of mathematics as a helper to science has been spectacular.
Then, as always, comes the unanswerable. "How," Newman asks,
is this universality to be explained? Why has mathematics served so brilliantly in so many different undertakings—as a lamp, a tool, a language; even in its curious, ape-like preoccupation with itself? What, in other words, is the mathematical way of thinking?
Caught up on the same twin horns, von Neumann wrote, "There is a quite peculiar duplicity in the nature of mathematics. One has to realize this duplicity, to accept it, and to assimilate it into one's thinking on the subject."