THE HISTORY OF MATHEMATICS

CHAPTER 1 – INTRODUCTION

“Mathematics is a study of size, shape or position (of anything) symbolically be it a change in size, shape or position or factors (like temperature, forces etc) affecting size, shape or position”

“Anything we see, do or feel has mathematics in it”

“Mathematics is a science of counting, forward or backward”

Mathematics is HOW MUCH of anything.

CHAPTER 2 – HISTORY

1. Language and Numbers

Well! We all know! Early humans were nomadic and wild-kind, according to some theories. But as the intelligence of humans started to increase, they started to describe everything through body signs and sound signs. Those body and sound signs of an area were called a language, which differed from area to area, giving rise to many languages that we see, hear and speak today. For a language, to write it down, signs and symbols were introduced by the noble men of that particular area or language, which we call as SCRIPT in English.

According to “Ehnologue” there are approximately 7,117 languages spoken today (Dated 04.04.2020) of which 540 are institutional, 1,549 developing, 2,102 vigorous, 1,944 in-troble and 982 dying languages.

To describe or express the QUANTITY OF THINGS they pocess, they want, they gave etc. etc., different body signs, sound signs and/or symbols were made/introduced in every language, which we call as NUMBERS in English. The process of determining the number (quantity) of anything (be it social or economical data such as number of members, prey animals, property or debts) was termed COUNTING. That was the start of Mathematics.

Every number is indicative of the number of single things or the number of units of something, somewhere. For example “1” symbol indicates there is one single thing, “2” symbol indicates two single things and so on.

2. Addition and Subtraction

Every next number is the sum of that number and one. When we are counting upwards we are literally summing one with each consecutive number/thing and stop at the last thing/element, which will give us the total number of things/elements.This summing up of numbers is named ADDITION (i.e. joining). And counting downwards is termed subtraction SUBTRACTION (i.e. removing)

To make it more logical, when we add 54 and 68, we are taking 54 ones and adding one to make it 55, one to 55 to make it 56 and this process we are repeating 68 times, which will give us 122 finally as total.

3. Mulitplication

When numbers exceeded some limit, addition and subtraction became more complex to them as they did not have the CALCULATORS. To ease the addition an intelligent person amoung them invented a new way to add things easily i.e. by grouping.

of repeated equal numbers, multiplication was introduced by an unknown person. MULTIPLICATION is just the repeated addition of equal numbers (2+2+2+2+2=2*5=10. Here 2 is added 5 times to itself. In general, if there are five digits if we count from number one we will end up to number ten). The symbol used is ( * ), when this symbol is used we can say in above example “adding two, five times”.

The main problem they faced was distribution of their assets, fruits, vegetable etc. among themselves, i.e. when there were 150 people and they had 300 apples, the equal sharing of the apples seemed to be difficult because they didn’t have any device. So, what did they do, They first distributed one apple to each person and again one to each and this process of distribution was termed as division (dividing something with respect to something, in the above mentioned example, dividing apples with respect to people). A person among them observed that this is just the reverse of multiplication and to ease the division process the use of multiplication to divide numbers started.

In-line with the development to ease calculations abacus was invented by an unknown person which made addition and subtraction of larger numbers easy, though it had limited beads, it was used for a very long time as a calculator until (and even after) the development of logarithms by John Napier, who used hit and trail method for its calculations.

Before going to logarithms,

While doing multiplication A person thought that instead of adding repeated numbers each time, why not he prepares every number’s addition-table once, to use it as a reference to solve multiplication problems. It was easily seen in those tables that division is just the opposite of multiplication or in other words division is inverse of multiplication, for example, and thus division, therefore, tables were tabulated by some person.

While observing these tables, someone working on shapes found that if 10 units are arranged in a row and if that row is repeated 10 times as column, a shape with equal sides is formed with 10 units at each side, that shape was named as SQUARE (square of 10 units consisting of 100 units in it, here 10 units is root from where that person started to prepare a square shape of 100units), he found that any number of units can be arranged in a row but the row should be repeated the number of times, the number of units used in the row, to get square shape. This was correlated with the multiplication tables, it was found that this is exactly as same as multiplying a number to itself, the resultant number after multiplying by itself was named as SQUARE, and the number which was multiplied to itself to get square was named as ROOT OF SQUARE or SQUARE’S ROOT now we say it as SQUARE ROOT..

To write it in an easier way, instead of writing “ 2*2=4 ” it was written as “ 2² =4 ” in this 2 represents the root of square which was given name as BASE or ROOT and superscript ² represents the number of times the base is multiplied to itself, in this case two times and was said as POWER and 4 represents the square. The form 2² was given name as EXPONENT

Oh my GOD! What’s logarithm now?

Its just a method to solve multiplication and division easily. When napier in _________ was doing astronomical calculations, he experienced serious problems in calculations because astronomical calculations consisted of very huge numbers. When he was observing