Mathematics is considered the model of black-and-white truth—the universal language of the world. But this is a myth.

I once taught Euclidean geometry, the most basic of all theoretical mathematics, to high school students. This geometry is based on a plane—a two-dimensional figure that stretches infinitely in two directions but has no thickness. Planes do not exist in real life, not really; neither do lines and points. A line has length but no width: one dimension. A point has neither length nor width: no dimensions. All plane figures—triangles, circles, angles, rays—are made up of these basic principles, lines and points. The study of Euclidean geometry is essentially faith in what cannot be seen. Euclidean geometry is also the foundation for the rules of engineering and physics. Therefore, it is a faith underpinning scientific facts.

I taught this faith to teenagers, who were actively working out their own understandings of truth and belief. Within the parameters of a plane, I asked them to prove statements of truth—that two angles have the same measure, for example, or that two lines are parallel—using only the definitions, postulates, and theorems of Euclidian geometry, not the tools of science—protractors, rulers, compasses. Our instrument was a two-column proof, the baby-step of mathematical analysis, in which a statement is paired with a fact that demonstrates the truth of that statement: Two angles are congruent because they are vertical angles, and two lines are parallel because a pair of internal angles on the same side of the transversal are supplementary.

>Read more of “A Proof for Truth,” The Rumpus

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