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> Mathematics & Philosophy Issue: 2010-2 Section: 14-16



Mathematics & Philosophy


Many of you believe that Mathematics is very different from Philosophy. Are you sure about this? If this is true, why the most famous Mathematicians are also famous Philosophers or why the most famous Philosophers are also famous Mathematicians? In other words what is the link between Mathematics and Philosophy?


The bond between these two sciences is based on a time line from Ancient Greece to today…


Ancient Greece

In Ancient Greece, there were schools and individuals who were interesting in Philosophy and Mathematics. Thales (624-548 B.C.) was the first one who convinced Mathematics and Philosophy. He is known not only as a mathematician, but also as a philosopher, astronomer, physician and even a politician. Furthermore he is the founder of Reductio ad absurdum method.

Reductio ad absurdum method is very usual in Number Theory. In addition many use it when they want to make a decision about an issue, and they finally choose on solution from many just with rejecting the rest one after another.

Moreover, he was the first who used axioms based on logic to confirm geometrical problems.


His ideas influenced…


Pythagoreans who believed that the world has been made by integer numbers, so if they studied numbers (especially using the Reductio ad absurdum method), they could discover all the mysteries of the world. Their ideas influenced…


Plato (Please don’t get confused with the modern Plato’s Academy. In other words the nowadays-philosophy of some people who live in this area and of course is the philosophy of drinking, boring and generally doing nothing).

On the door of his Academy had written: Μηδείς αγεωμέτρητος εισίτ, which means that anyone who doesn’t know geometry or he hasn’t thought of philosophical questions in his life, he cannot enter this

Academy… On Platonists’ point of view, our world is the Idea World, which is a reflection of the Real World and the Real World have been made of Mathematics. This means that everything we live now is not real, we should find the truth. In his book, Politia (Πολιτεία), he describe his thoughts with an example as it follows:

We are in a cave, gagged and trussed up and we look the wall. Behind us there is fire and after the fire the pictures of Real World are passing, the only thing we see is the reflection of these pictures on the wall… So if we want to reach the truth we have to work our hands and legs free, pass through the fire and then to get out of this grave…

In addition, the supporters of Platonism believed that there is no infinity in the universe and the word άπειρο (=infinity) had a negative meaning.


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