The French Mathematician

/, Literature, Blesok no. 52/The French Mathematician

The French Mathematician

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– Geometry, announces Vernier.
In three weeks of arithmetic his voice has never risen above a dull drone, and now he introduces the new topic as though it is the title of an epic poem he is about to recite by heart. For the first time since my demotion, I sit up and take note. Geometry. The word has a certain resonance. Or is it just Vernier’s enthusiasm coming through? His words strike a chord within me, stir me, make me quiver with wonder. At times, for minutes on end, as he paces and gesticulates, I forget the shadow of the window’s grille falling obliquely on my bare hands, forget the anxiety and frustration that has unsettled me during the past year, forget my demotion. During these moments I neither love nor hate, neither fear nor hope. Drawn from the emotional chaos of recent months, I feel at ease in the order and certainty of geometry.
– Euclid’s Elements, Vernier continues.
He is about thirty, with black hair fringed across his forehead and spectacles made of circles, lines, and arcs. He wears gray gloves to prevent chalk dust irritating his dermatitis. As he raises the book high above his head, its image is skewed in the lamp’s concave reflector.
– The Book of Books, gentlemen. The most influential text ever written, more so than the Bible. It has leaped across centuries, nations, languages, religions. Its relevance is timeless; its nationality, universal; its language, logic. Truth, gentlemen! Absolute, transcendental truth. You have done your exercises in arithmetic: You have added, subtracted, multiplied, divided, and extracted roots. Well and good, all very useful. I would be the last to deny the usefulness of arithmetic. It goes hand in hand with money, and, as we know, coins make the “world go round. It is vital to examiners, bankers, and generals. It determines pass and fail, measures profit and loss, counts life and death.
– But, gentlemen, despite its prevalence in the affairs of the world, arithmetic has nothing to do with the spirit of mathematics. That spirit finds its first expression in geometry. The spirit, gentlemen! Think about it. A spirit not unlike the Holy Spirit, and just as the Holy Spirit cannot be apprehended merely by attending church regularly on Sundays, dropping a coin on a collection plate, saying one hundred Hail Marys and two hundred Our Fathers, so the spirit of mathematics cannot be grasped by the repetitive exercises of arithmetic. Many are called, gentlemen. Some are chosen to serve in schools, and others at higher institutions such as our Polytechnic, but few, perhaps a handful in each generation, are chosen to become initiates, to partake of the mysteries, to serve the spirit in the inner sanctum.
I am entranced by the brown book whose binding has frayed, its gold lettering faded. And when, looking directly at me, Vernier asks “which of us” will be among the chosen few, my heart leaps. I want to know more about Euclid.
Is absolute truth possible in these confusing times, when countless groups claim to have the truth, and the world seems on the brink of chaos? Royalists, Republicans, Bonapartists, Socialists, Saint-Simonists, Anarchists, the reemerging Jesuits—they are all active among students, all seeking to make converts to their particular truth. There seems no end to it, especially when combinations of some groups produce new truths. Perhaps Euclid, having stood the test of time, might dispel the chaos churning inside me and help make sense of the world. My attention is caught by Vernier’s gloved hand —the book’s truth is too pure to be held by naked flesh.
– Since 1482 more than a thousand editions have appeared in print, he continues, “walking “with measured strides between our desks. We know Euclid compiled the work in thirteen books covering the geometry of triangles, circles, and various quadrilaterals; the theory of proportion; number theory; irrationals; solid geometry. As for geometry, which will be our main concern, we know that he based everything on twenty-three definitions and ten axioms, five of which he called common notions, the other five propositions. From all this, we know the mind of Euclid, but what of the man?
– I put it to you, gentlemen: Does the man matter in the dazzling light of this creation? Beyond the fact that Euclid taught in Alexandria around 300 B.C., probably summoned there by Ptolemy, little else is known about him. We do not know where and when he was born. We do not know his nationality. Some maintain he was not Greek at all, but Egyptian. We do not know how he felt about the gods of the day; whether he was kind or cruel; whether he was fond of wine; or whether he had children. The personality does not matter, gentlemen. For most of us it disappears without trace in four generations, let alone forty. What matters is the idea, the ideal, truth. But the truths in this book are not easy to grasp. There is no royal road to geometry. It will require hard work and concentration. Some of you will fall by the wayside early, but those who persevere will see a world more dazzling than Alexander’s conquests, one that withstood the might of Imperial Rome and outlived the shadow of the Dark Ages. A world to which our French mathematicians have contributed greatly since the time of Descartes.
– The call has gone out, gentlemen. Who will heed it? Who will serve the spirit? Who wall deny themselves for the sake of truth?
My hand shoots up involuntarily. The room explodes with laughter, which once again proves their stupidity. They are insensitive to the spirit of mathematics, unable to grasp the subtlety of Vernier’s words. Let them laugh. It confirms that I am smarter than them.
How can Vernier tolerate them? He should threaten them with detention. Why is he smiling faintly, rubbing the lenses of his spectacles, squinting as he holds them up to the light? When the laughter finally subsides, he picks up another book and holds it up to the class.
– Euclid has been excellently interpreted and presented by Adrien-Marie Legendre in his Element’s of Geometry, a text written for the purpose of teaching the subject in a modern way, and from which I will be drawing heavily. Open your books, gentlemen, and let us commence.
Held firmly in his gloved hand, the chalk scuttles quickly across the blackboard, striking at periods, scratching in underlining, sometimes screeching in its haste. From the back of the room, straining to read the board (my eyesight has always been weak, but it appears to have deteriorated in the past few months), I do my best to keep up with Vernier and copy in my book the definitions, propositions, axioms, and theorems. One idea leads to another, naturally, effortlessly, like the notes that combine to form a pleasing melody. As Vernier erases the restrictive board (the night sky is not wide enough to accommodate the possibilities of geometry), I contemplate the first definition: A point is that which has no part. It seems that a point is and is not. If I represent it on the page, it is no longer a point. If I try to grasp it in thought, it vanishes. I imagine a point moving at a great speed; at that instant it is both a point and a line, a particle and a process. If I grasp the line, I lose sight of the point. If I focus on the point, the line proves an illusion. Astonishing that something so intangible should be the basis of all geometry! In a flash, I see the indivisible point as the seed of creation. Perhaps the universe exploded from the primal point. Perhaps God is the primal point. Perhaps the soul is nothing more than a point.

AuthorTom Petsinis
2018-08-21T17:23:10+00:00 February 20th, 2007|Categories: Prose, Literature, Blesok no. 52|0 Comments