In one of Edna St. Vincent Millay’s sonnets, she states that “Euclid alone has looked on Beauty bare.”
If one has not worked through Euclid’s Elements, it is hard to convey what is meant here, or at least what it might imply. Millay’s poem goes on to make other claims which one may take or leave.
But of Euclid, of the measured simplicity in which one truth proceeds from and then to another, of the harmony and symmetry of shape matched with reason and reason with shape, of the wonder of the hidden being made manifest, and the improbable at times proved firm, of surpassing what can be seen by the eyes alone or their distant companion–the intuition, all of this is meant by Euclid.
All this and more for the constructions themselves accompany these discoveries and delight the imagination as well as the sense, moving step for step with truth as does a foot and its print.
And yet there is a precision which exceeds all that Euclid grasps, and much in the manner of Pascal, one might say there is a Beauty of which the Euclid knows not.
What is this Beauty?
It is that of woman who finds the right world to say, the true caress, the just reproof and says its place; it is the boy who sticks to the truth when those about him, of whom he would be esteemed, press him to drop it, and is yet a gentle lad; it is the life a man poured out for his own; it is the precision of prudence, of grasping the good, the intended word and deed which is the truth in each given moment.
No act more difficult, no other act calls for so much in man, or requires such wisdom and grace. For life is not a breathless length, and those we must act among (and the very matter of the self) is by no means inscribed by two perfectly right angles.
The complexity, the uncertainty, the dignity of this good so far surpasses that of Euclid–they are indeed not of the same kind. The mathematician is not the judge of right and wrong in this realm. And it is not the mathematician who can inherit this kingdom.
But we shall perhaps see in heaven, that what he have done in the hands of God and by his hand guiding us as does the geometer a fragile and foolish compass, will be writ with a glory that outshines any of Euclid’s constitutions or conclusions. We will then know his work for the distant foretaste which it is.
For we shall not have inscribed in us a triangle or some platonic sold, nor shall we have proved some theory or new property to our certain knowledge. But the God who circumscribes all of creation shall have inscribed himself in us in. And that child within shall write his name in our very deeds, such that what little we conform to him, trembling to his touch, yet more certain than any carpenters rule, shall be truer than any line we have yet or ever shall know.
In that Geometer’s hands, whose subject is flesh and blood and spirit, a book has been begun, a book which we are being made adequate to read. By faith, we apprehend that the proof exceeds our ciphering, and by faith we hope for the day that we shall pass into sight.