Math & Faith – 1. Blind Faith

CONSULTANTS Florin Ghetu
SPECIAL THANKS Andreea Paun, Irina Anghel, Florin Ghetu, Aritina Barculescu, Cristian Magura, Cristina Cuncea, Mihai Bolonyi, Costin Banica, Petrica Cristescu, AnaMaria Lupu, Dorin Aiteanu
CAMERA/LIGHT/SOUND EQUIPMENT provided by Speranta TV
SCREENWRITER & DIRECTOR Attila Peli
COPYRIGHT SPERANTA TV 2018

And all forms of religion I have encountered to that date confirmed that hypothesis. So I stuck to science, especially mathematics, also known as the science of sciences. And rightly so, because math is the basis of all sciences. For a long time I lived with the idea that science and faith are diametrically opposed.

However, there was a moment when I realized that things were not quite so.
In this series I will try to suggest something counter-intuitive, namely: that mathematics and religious belief are two systems that have the same type of structure and are just as legitimate. Let’s begin!

You see on the screen, the well-known tree of math, with its main branches: algebra, geometry and analysis, and their sub-branches. Somewhere in the trunk area we see Number Systems and below that, Set Theory, and everything is based on the logical thinking. It’s a suggestive drawing, but the designer forgot to draw something very important: the root of the tree, which is axiomatics. What is axiomatics? An axiomatic system is a set of unprovable propositions, accepted as true by the scientific community.

So, mathematics rely on a number of unprovable propositions that we must believe and accept? Obviously, they emerged from the observation of the material world, as we would say, they are “common sense”.

Let’s take, for example, geometry, which we all met in high school. I remember the surprise I had when the teacher began to write on the board the Axioms of the Euclidean geometry that you see on the screen. He then explained that the axioms are not provable, and that they must be accepted by faith and are based on common sense, on intuition. For example, if we take the first axiom, it is intuitive, common sense tells you that any two points define only one straight line.

However, I was still shocked. I knew that math was the opposite of faith, that everything had a proof, that nothing could be questioned. Later, studying in the faculty of mathematics, I got used to the idea, seeing that any branch of mathematics is actually based on axiomatics. An entire logical construction is built on these unprovable propositions, in which true sentences necessarily lead to others of truthful value.

Thus, if we were to reconstruct the tree, we would have axiomatics or common sense / intuition at the root, the trunk would be the logical construction, and the crown would be the fields of mathematics, with their various applications. For more than two thousand years, Euclid’s common sense has been good enough for everyone. So his axiomatics became truth, simply because no one contested it.

But, in the nineteenth century, two mathematicians had a different idea of „common sense”, a different belief, a different intuition, which shook the infallibility of mathematics. But, to take a look at this sujbect, join me for the next episode.