Lesson History of mathematics

The Pythagoreans (5th Century BC)  

Some of the earliest mathematicians were Pythagoras and his followers. Mixing 

religious mysticism with philosophy, the Pythagoreans' contemplative nature led 

them to explorations of geometry and numbers.  

The most famous result attributed to Pythagoras is the Pythagorean theorem: for a 

right triangle, the sum of the squares of the two shorter legs that join to form the right 

angle is equal to the square of the long side opposite that angle. This is one of the 

fundamental results in plane geometry, and it continues to fascinate mathematicians 

and math enthusiasts to this day.  

One apocryphal story of the Pythagoreans illustrates the danger of combining religion 

and math. The Pythagoreans idealized the whole numbers, and viewed them as a 

cornerstone of the universe. Their studies of geometry and music centered on relating 

quantities as ratios of whole numbers.  

As the story goes, a follower of Pythagoras was investigating the ratio of the length of 

the diagonal of a square to the length of the sides of that square. He then discovered 

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that there was no way to express this as the ratio of two whole numbers. In modern 

terminology, this follower had figured out that the square root of 2 is an irrational 

number.  

According to the legend, when the follower who discovered this fact revealed it to his 

peers, the idea that there could be irrational numbers — numbers that can't be 

expressed as a ratio of two whole numbers — was so shocking to the Pythagoreans 

that he was taken out on a boat and murdered by drowning.  

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