HIPPASUS : AN UNFORTUNATE MATHEMATICIAN

This is my first blog on mathematics. Mathematics is essentially the 'science' of numbers. Mathematics is the house of numbers. I personally feel that all these numbers have their own expressions, they are living entities, they are constantly used in our daily commute. 

 ''Mathematics is the Queen of all Sciences and Arithmetic is the Queen of Mathematics''

-Carl Friedrich Gauss

With the help of set theory, if the consider the universal set (U) as 'number' denoted for simplicity as N, i.e. U= N, then I can denote the elements in N in the form of a set as given below.

N={0,1,⅔,5i,√2,-3}

Here inside the set we find different types of numbers. So for better understanding the numbers are classified into many groups. Now I will introduce the different types of numbers and give an example for each by taking a number from within the set N,

Natural numbers- eg. 1

Whole numbers- eg. 0 and 1

Integers- eg. 0,1 and -3

Rational numbers- 0,1,⅔,-3

Irrational numbers- √2

Real numbers- 0,1,-3,⅔,√2

Complex numbers- 0,1,-3,⅔,√2,5i

I will explain about each of these different numbers in detail in coming blogs. 

In this blog I would like to introduce to you all a mathematician, who was very passionate about numbers which in turn killed him...

Hippasus was a very intelligent student. He studied under the great Greek mathematician and philosopher, Pythagoras. Pythagoras is a familiar name to most of us because we have been learning a quite a lot about him in our math textbooks. We are very familiar with the Pythagoras Theorem and Pythagorean triplets. Let us just recall these concepts quickly,

Pythagoras Theorem states that, 

''In a right angled triangle, the sum of the squares of any two sides of the triangle is equal to the square of the third side (the longest side) which we call the hypotenuse''

                                                                              

                                                                            

Figure-1: A representative figure to explain Pythagoras theorem

In this figure, if we apply Pythagoras theorem we find that,

                                                                a² + b² = c²

Now what do we mean by a Pythagorean triplet. It is nothing but the set of three numbers which make up the three sides of a right triangle such that the three numbers are in accordance with the Pythagoras Theorem.

For example, {5,12,13} is a Pythagorean Triplet

Because, 5²+12²=13²=169

Similarly, {1,4,√5} is also a Pythagorean Triplet.

Now let us go into the main topic,

                                                                   

Figure 2: Pythagoras

A school of thought called Pythagoreanism was existing during the period of Pythagoras. Pythagoreanism as the name suggests is a body of ideas based on the teachings of Pythagoras.

Pythagoras defined the world in terms of rational numbers. But this philosophy was about to to go down to bits.

                                       

Figure 3: Hippasus

                                                                

One day, Hippasus was studying the number '√2' and was trying to find out an equivalent fraction for it. But he soon found out that it didn't have an equivalent fraction. And since it didn't have an equivalent fraction, Hippasus claimed that '√2' must be an irrational number.

But when he presented his idea to his teacher, Pythagoras, he was terribly annoyed and worried at the same time because it questioned the very fundamentals of his theory that the world was made up of rational numbers! Hippasus was criticised for going against his teacher's idea and was drowned to death...

What a terrible life he had...whenever I do math sums involving irrational numbers I think of him, a man who went unnoticed because of the selfish behavior of his teacher and his supporters, a man who could have contributed a lot to mathematics...

''Mathematics reveals its secrets only to those who approach it with pure love, for its own beauty''

-Archimedes

Picture credits:

Wikimedia Commons: Figure representing Pythagoras Theorem, image of the bust of Pythagoras, and the image of Hippasus.

Information credits: Books like 'Tell Me Why' which I used to read in my childhood and even continue to read.