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Members of the Pythagorean school
also happened upon findings they did not want.
The numbers with which people were familiar back then were natural numbers,
like 1, 2, and 3, and fractions that are ratios of natural numbers.
The Pythagorean school firmly believed that
all numbers can be expressed as ratios of integers.
The Pythagoreans, however, discovered that
they could not express the diagonal length of a square in the form of a fraction.
The diagonal length of a square, whose sides measured one each, was 1.414.
Thus the Pythagoreans found the concept of the endless irrational number.
This unforeseen discovery led them into great confusion.
For people who were so convinced that
they could explain everything in the universe with numbers,
the discovery of irrational numbers shattered their faith from the ground up.
Pythagoras was tormented by the discovery.
He eventually named his irrational number
“alogan”, meaning one cannot mention it.
Thus irrational numbers became a secret
that Pythagoreans had to guard to the point of risking their lives.
When they discovered that
the diagonal of a square, of a unit square, one by one,
was not the ratio of two whole numbers,
they were shocked,
and they didn’t want to upset their theory
that everything depended on integers.
So this is one reason probably why they kept it a secret.
But they kept most of their results secret.
They never wrote anything down,
even when they had their discoveries, they were all communicated orally.
There’s no written record of anything that the Pythagorean school has done.
There is no eternal secret.
Hippasus, a Pythagorean,
was also perplexed by the discovery of irrational numbers.
Their secret could not be kept for long.
Legend has it that Hippasus eventually broke away from the rule,
and eventually disclosed the secret to others.
Dark clouds began to gather over the fate of the Pythagorean school.
Once the world knew that there are irrational numbers that cannot be explained,
the entire Pythagorean creed that everything was made of numbers
had no ground to stand on.