With my full philosophical rucksack I can only climb
slowly up the mountain of mathematics.
Have you ever wondered what Philosophy and Mathematics have in common?
To answer the question we have to go back to the past.
Since ancient times, Mathematics has been one of the main themes on which most philosophers concentrated: many of them in fact used Mathematics to solve practical problems, such as Eratosthenes, who calculated the Earth circumference, or Talete, who measured the height of the Pyramids using their shadows.
Pythagoras’s community, in Crotone, was one of the first schools which formulated a teaching based on numbers and reality; this scholar is presented by legends as possessing magical powers and he has been considered, till today, a man whose life is surrounded by mystery because he didn’t write anything and we have very little information about him. However, he was the founder and, first of all, the only teacher in this community. Pythagoras and his disciples thought that numbers were the origin of nature and of whatever is around us, because many real experiences such as music, the cycle of seasons and the movement of the stars can be traced back to them; they believed the world had a geometrical order which could be represented through the “Holy tetrad” or “Tetractys”, a triangle in which each side was made up of 4 points (for a total of 10, that was considered for this reason, the perfect number) arranged like this : 1+2+3+4, where the 1 symbolizes the point, number 2 the line, number 3 the surface and finally 4 the solid.
So these scholars, who didn’t have technological instruments to prove their theories, just used their intuition and attributed to each number a particular meaning.
But apart from Pythagoras’s school, many other philosophers kept on studying mathematics, each conceiving this science in a different way…
The Greek Plato, for example, felt a large admiration for Mathematics because it gives us proved certainties ( 2+2 = 4 is always true and no one can prove that it is false) and he was inspired by Pythagoras’s teachings.
Aristotle instead inquired into reality without formulating any mathematical rules.
In the Middle Ages, scholars preferred to deal with other themes rather than this topic, which was studied again during the Renaissance.
In the period around 1600, we can’t forget Galileo Galilei who was the protagonist of a true scientific revolution and the inventor of the “experimental method”: he studied Maths and Physics but he was a great philosopher, too. He affirmed the presence, in our reality, of things that we can quantify (which are studied by Mathematics) and things that we cannot, which he avoided considering.
In the same age, Rene Descartes (best known as Cartesius, the creator of the Cartesian coordinate system, which was given his name) gave Mathematics a new importance and joined it to philosophy because he said that “one wouldn’t have its value without the other”.
He was the first to promote the use of the mathematical method in different contests of our daily life.
Many others, after these philosophers, have drawn inspiration from them and reflected on this topic… so which is the difference between Philosophy and Mathematics? Of course Philosophy tries to answer the most difficult questions of our life while Mathematics wants to solve practical problems, so they have different purposes… but at heart they are really similar: both aim at finding a solution in a coherent and rigorous way which will lead us to think logically and to consider everything from its deepest point of view; it’s not a fortuitous event that excellent philosophers were also great mathematicians and scientists.
Thanks to their discoveries we live a better life.