Mathematics

“God ever geometrizes.” –Plato, 4th Century B.C.

Mathematics has a special relationship to God. Mathematics is, in itself, universal, invisible, infinite, immutable, omnipresent, and eternal. These are attributes that are most often heard with reference to God Himself, but they apply just as well to mathematics. Think for example of the number 2. Has there ever been a time when there was not this number? Will this number ever change? Does it apply differently to angels, elephants, and atoms? But the same holds for shapes, functions, surfaces, solids, multidimensional figures and so forth. This is why we speak of mathematical discoveries, and not inventions. It is—and was—there all along, but we have come to knowledge of it only recently, in the last three or four millennia, and especially in the last five centuries.
Mathematics is, then, coeternal with God, though our understanding of it is, no doubt, limited by our symbols, history, and the idiosyncrasies of our cultures. Perhaps the human mind in its current form is unable to deal as directly with mathematics as we would like. But in the Eternal City of God, to which any human being may attain, mathematics has a high place and will forever hold that place.
Thus we might say that mathematics is a school in which we can learn about God’s properties—and especially those of His mind. As God comprehends all of Himself and his kingdom in one great eternal gaze, mathematics must be at the forefront of his thought—hence Plato’s statement above.
On earth however, one of the most important attributes of mathematics is its close relationship to philosophy. To that we must now turn in order to see its true dignity. Tradition has it that Plato’s Academy had over the door the words, “Let no one ignorant of geometry enter here.” Whether the story is historical or apocryphal, one might say that this is a worthy statement about the field of philosophy as a whole. For this reason it is said that no book next to the Bible has wielded a more powerful influence on the human mind than Euclid’s Elements. The precision and elegance of mathematical proofs the single most important training for a philosopher.
Beyond the precision and logic, we should keep in mind that mathematics deals with all things, including the universe as a whole (“uni” = one). This is precisely what philosophy attempts to do, though certainly with greater ramifications for human well- being. For it is philosophy’s job to come to grips with the whole of human life, and provide a direction grounded in knowledge. Pythagoras, Thales, Plato, Aristotle, Augustine, Aquinas, Descartes, Leibniz, Frege, Husserl, and Russell all shared a deep respect, even reverence, for mathematics. And for the person today seeking to escape the bewildering flood of ideas in our world, mathematics provides an essential part of the way out.