While the Greek mathematician Pythagoras may have been brilliant, he also possessed certain interesting "eccentricities," in keeping with the times.

There are many things in this world which have interesting or unusual origins which befuddle the mind and drive a stake into our perceptions of humanity itself… but one wouldn’t generally expect mathematics to be one of them. After all, doesn’t mathematics by its very nature attempt to transcend all the metaphysics and oddness that so often befall human beings and explain things rationally? Shouldn’t it be a relatively certain discipline, unarguable in its results and relatively devoid of controversy? Shouldn’t it be free of the bias and ideological derision so prevalent in the ancient histories of other sciences?

One would thinks so… but alas, history has proven otherwise.

Pythagoras and the Soul of Mathematics

Pythagoras was in many ways the very founder of modern day mathematics. He developed the theorem which bears his name (remember it? a² + b² = c²) and founded one of the very first schools devoted entirely to the study of numbers and mathematics. And this is where all the trouble starts.

For Pythagoras, in addition to being a certified mathematical genius, also seems to have been a bit caught up in the Greek superstitions of the day (and then some). Even for his time (that is, sometime during the 6th century, B.C. in Greece, when some superstitions were a dime-a-dozen), Pythagoras was something of an eccentric.

Pythagoras’ genius was great enough that the school he established in Croton, Italy became a veritable hot-bed of mathematical activity, the brainstorming hub of the Greek world. But Pythagoras was in charge of it all, so nothing about it could be normal. Pythagoras was obsessed with the “deeper meanings” behind numbers; the spiritual and metaphysical meanings of their relationships with each other and their transcendence beyond the universe at large. In Pythagoras’ mind, number theory transcended even God himself. If the world had never been created, numbers would have remained, he thought. It was a mathematical cult, to say the least.

It is out of this quazi-religious atmosphere that modern mathematics was practically born. In addition to thinking about math, Pythagoras demanded that all of his students at the school - called the Pythagorians, naturally – refrain from eating all types of meat (in fact, until the word vegetarianism arrived rather recently, this practice was known almost exclusively as pythagorianism). In addition, he refused to allow them to eat beans, which, indeed, does not seem to make much sense.

Taking Math to the Extreme

When Pythagoras finally developed his most famous theorem, the celebration was so great that 100 bulls were sacrificed to the gods in thankfulness. That is what many would call commitment. With today’s many advances in mathematics, it’s a good thing such practices have ceased.

But Pythagoras was not all genius.

His mathematical skills were severely shrouded by his personal biases. In Pythagoras’ opinion, all numbers in mathematics had to be either whole numbers or simple fractions of whole numbers. In his mind, no other number could exist because such numbers couldn’t possibly represent any form of reality, for this is exactly what numbers were, representations of the real, tangible universe. Numbers had to be able to be divided into either even numbers or odd numbers – the even to some representing all that is female and the odd representing all that is male. In this way, Pythagoras believed that every tangible thing in the world could be described using only numbers, and he viewed it as his job to find out exactly how.

Unfortunately, these beliefs severely detract from his stature as the first great mathematician.

Just ask Hippasus, one of his many pupils. Actually, this is impossible, because Hippasus is dead. As the story goes, Hippasus found himself excitedly working on a proof of a very peculiar problem – specifically, the definition of √2. What he and others had found was that the solution to this problem was one which was infinitely reducable – that is, if put into fractional form, it could be divided an infinite number of times without end. In this sense, it is clearly an irrational, non-existent number.

Hippasus was very pleased with himself to have discovered this answer, but Pythagoras was most certainly not. He argued against the very existence of irrational numbers, but when he realized that he could not defeat Hippasus’ flawless logic, he had him executed by drowning.

And that is the legacy of Pythagoras. Tortured Greek genius whose mathematical skills changed the world forever.

One must be both grateful to this phenomenal mathematician for his many gifts to the scientific community, but thankful at the same time that such times have since passed, and that mathematics have evolved to a point where logic has trumps superstition.

References:

“Pythagoras.” The Internet Encyclopedia of Philosophy.

“Pythagoras.” Stanford Encyclopedia of Philosophy.