## The History of Mathematics and its role in Human Progress

In humanity there are two kinds of people. Some are philosophical and use philosophy as a means of reaching conclusions and justifications whereas others use logic and facts to counter different situations. Mathematics and mathematicians fit under the latter category and it’s important for us to know how this, very frequently used subject, changed and developed over time. Due to this we will take a glance into the Qur’an, Hadith as well as different time periods in human history and try to follow the journey of mathematics.

## A Mathematical Miracle in the Holy Qur’an

Some people are mistaken in thinking that the Holy Qur’an is just full of words and nothing else. Upon closer analysis, we can see that the structure of the Holy Qur’an is filled with a copious amount of mathematical codes which are far beyond human mind to comprehend let alone fabricate. For example what could’ve been the chance of the word month being used in the Qur’an for a specific number of times? Whether you regard this as a coincidence or a proof of the Qur’an being divinely sent from Allah the Almighty the fact is that the word ‘month’ in its singular form has been mentioned in the Qur’an exactly twelve times. There references are as follows:

[2:186](twice), [2:195](twice), [2:198], [2:218], [5:3], [5:98], [9:37], [34:13](twice), [46:16], and [97:4]

(These are only those areas of the Qur’an where the month is mentioned in its singular formaccording to the Arabic lexicon. These may however have a plural translation in order to fit the context.)

I believe that it’s nothing short of a miracle that the Qur’an , which contains 86,430 words , used the word month exactly 12 times (as there are 12 months in a year)

Another astonishing point worth mentioning is that the Qur’an even uses mathematics to express the similarities between Jesus ^{as}abbreviation for "Peace be upon him" and Adam ^{as}abbreviation for "Peace be upon him". This is done by mentioning Prophet ^{as}abbreviation for "Peace be upon him" Jesus and Prophet Adam ^{as}abbreviation for "Peace be upon him" exactly 25 times. In addition, these 25 appearances are all in different areas of the Qur’an. I.e. there is only one verse in the Qur’an where Jesus ^{as}abbreviation for "Peace be upon him" and Adam ^{as}abbreviation for "Peace be upon him" appear together and in every other case they appear in different verses. By doing this, Allah is using mathematical coding to prove that Jesus ^{as}abbreviation for "Peace be upon him" is an ordinary prophet like every other and the theory or claim of him being the son of God is baseless.

Places where Adam ^{as}abbreviation for "Peace be upon him" appears in the Holy Qur’an:

[2:32, 34, 35, 36, 38], [3:34, 60], [5:28], [7:12, 20, 27, 28], [17:62, 71], [18:51], [19:59], [20: 116, 117, 118, 121, 122] and [36:61]

Places where Jesus ^{as}abbreviation for "Peace be upon him" appears in the Holy Qur’an:

[2:88, 137, 254], [3:46, 53, 56, 60, 85], [4:158, 164, 172], [5:47, 79, 111, 113,115, 117], [6:86], [19:35], [33:8], [42:14], [43:64], [57:28] and [61:7,14]

This mathematical composition of the Holy Qur’an is nothing short of clear proof that no worldly being could’ve fabricated this divine book.

## Mathematics in its beginnings and its journey:

We can’t exactly say that mathematics is an invention, thus the question of who invented maths is unanswerable. A more suitable and appropriate question would be, who discovered maths and what is its earliest human record?

### Babylonian Mathematics

Records show that the first use of mathematics was in the prehistoric era. During this time, people started recognising that everything has a quantity. They would know that there are “one”, “two” or “many” apples on the table. The Babylonian era was split into two time periods: The first few hundred years of the second millennium BCE (Old Babylonian period), and the last few centuries of the first millennium BCE (Seleucid period). The earliest record of written mathematics was found in this period (Ancient Sumerians) , from 3000BCE, they started developing a complex system of metrology and roughly 500 years later, they had the means to design multiplication tables on clay. This was a vital stage in human history because multiplication is a pivotal calculation in our current lives.

### Egyptian Mathematics

Then came the Egyptians. This era could be described as the back-bone for modern mathematics. Many advanced mathematical calculations and systems formed a base due to the Egyptians. The Egyptians used different symbols to form different numbers and through this system, any number could be formed as long as you use the correct symbol. A practical example which can help us appreciate their high level of understanding mathematics is the construction of pyramids. The fact that the pyramids are so stable and visually all exactly the same proves that mathematical thought was put into building these pyramids. Building them would have required extreme levels of trajectory and precision and this wouldn’t have been possible without a deep understanding of advanced mathematics. As well as introducing division and all other mathematical operations, they also devised the decimal point. Despite having the minds and brains to build extraordinary things, they lacked the mind of understanding. They failed to recognise the true prophet of Allah and instead followed Pharaoh and that was the cause of their ruin.

إِلَى فِرْعَوْنَ وَمَلَئِهِ فَاتَّبَعُوا أَمْرَ فِرْعَوْنَ وَمَا أَمْرُ فِرْعَوْنَ بِرَشِيدٍ“To Pharaoh and his chiefs; but they followed the command of Pharaoh, and the command of Pharaoh was not at all rightful.”

The Holy Quran (11:98)

This verse from the Holy Quran is emphasising the point that although Pharaoh was wrong and committed wrong deeds, his people were equally at fault because despite being given the knowledge to come to their own conclusions, they made the wrong decision (by following Pharaoh) and rejecting Prophet Moses ^{as}abbreviation for "Peace be upon him". This shows that despite the Egyptians having the capability of designing incredible monuments, they didn’t focus on what truly mattered which was recognising and accepting the divine light.

### Greek Mathematics

Following this was Greek mathematics. This started from around 600BCE. People called this era the start of ‘sophisticated mathematics’. An example of what this means is that before the Greeks, the earlier cultures used repeated observation to draw conclusions for different situations. The Greeks however used a system of deductive reasoning which meant that they used logic to derive suitable conclusion and this shows us their advanced level of thinking as well us understanding of mathematics. The Greek’s time was home to some of the ‘founders’ of mathematical concepts. For example, Thales, one of the Seven Sages of Ancient Greece, who lived on the Ionian coast of Asian Minor in the first half of the 6th Century BCE, presented the guidelines for the abstract development of geometry. Today this is known as the ‘circle theorem’. Over 2000 years ago, a man in Greece, with limited resources, came up with a concept involving parallel lines, circles and triangles which laid the foundations of our modern mathematics. Surely there must have been a divine light or power behind these people who guided them to discover what they did.

Another Greek who is controversially regarded the ‘legend’ of mathematics is Pythagoras. Many people know, or rather believe, that he invented Pythagoras’ Theorem, but because there is no written record found with regards to him, speculation is raised whether or not he really was the father of mathematics. Giving him the benefit of the doubt, we can look at some of his practices and discoveries. As well as Pythagoras’ Theorem, he discovered triangular numbers, square numbers and found out that two right angles equals 180°. Pythagoras believed that ‘God is Number’ and some evidence suggests that he worshipped numbers. He believed that every number has its own individual meaning. For example, the number one was the generator of all numbers; two represented opinion; three, harmony; four, justice; five, marriage; six, creation; seven, the seven planets or “wandering stars”; etc. Odd numbers were thought of as female and even numbers as male. All this just goes to show that however much worldly success one gains, if he is not on the right path in religious terms, logic even starts to deceive him. Such an intelligent person like Pythagoras was making illiterate comments and all this was a result of him not believing in The True God.

### Roman Mathematics

The Romans tightened their grip on the Greek empires by 1 BCE and continued their legacy of mathematics. They did not have any specific mathematicians of note nor did they discover any specific mathematical method. One of their discoveries commonly used today were the Roman Numerals. This is a system with many flaws. One being that it doesn’t involve the number 0 and when you start reaching big numbers, it becomes too complicated. This makes it inefficient and not very useful.

## Islam’s contribution to mathematics

Muslims can be regarded as the founding fathers of Algebra in Mathematics. Muhammad Al-Khwarizmi was an early Director of ‘the House of Wisdom’ in the 9th Century (set up in Baghdad around 810CE), and work started almost immediately on translating the major Greek and Indian mathematical and astronomy works into Arabic, and Al-Khwarizmi was one of the greatest Muslim mathematicians. Al-Khwarizmi’s biggest contribution was in the discovery of numerals used today (1-9 and 0) and this was a basis for revolutionising Islam and later Europe. Moreover, he introduced the fundamental algebraic methods of “reduction” and “balancing” and provided an exhaustive account of solving polynomial equations up to the second degree.

Another famous Muslim mathematician of the 10^{th} century was Al-Karaji. His role in mathematical history was the extension of algebra and freeing it from its early geometrical heritage. He also introduced calculus and was the first mathematician who used induction to prove his results. This means that if the first statement in an infinite sequence is true, if any other statement is also true, so is the next one. He also used this method to prove the binomial theorem. A binomial is a simple type of algebraic expression with just 2 terms and the co-efficient needed. When a binomial is expanded it forms a symmetrical triangle called Pascal’s Triangle.

## Importance of Mathematics:

Just imagine our lives without mathematics. Mathematics literally means counting something so without mathematics, we wouldn’t know the time, how many people are in our family, how much of something we own and many more things. In short, without mathematics, our lives wouldn’t run as they should.

فَاسْلُكْ فِيهَا مِنْ كُلٍّ زَوْجَيْنِ اثْنَيْنِ وَأَهْلَكَ إِلَّا مَنْ سَبَقَ عَلَيْهِ الْقَوْلُ مِنْهُمْ

The Holy Qur’an (23:28)

“Take thou into it two of every kind, male and female”

Without mathematics, Noah ^{as}abbreviation for "Peace be upon him" wouldn’t have been able to obey this command of Allah. Likewise, there are many references to numbers in Qur’an and Hadith and without us having any knowledge of mathematics, we wouldn’t even know how many times a day we should pray and at which specific times.

In a spiritual sense, mathematics can be very useful as well. This is because a lot of reflection and thinking takes place when trying to solve a problem. That increases a person’s patience and concentration levels. Both these qualities are vital in spiritual and religious environment.

## Role of mathematics in the development of society:

Mathematics is at the heart of areas such as science and technology. It’s used when designing and building infrastructure and a major part of NASA’s success. It’s used in cases such as pre-natal scanning. When ultrasound is used, a mathematical calculation determines how big the child is. The time it takes for the ultrasound to reflect off a surface and return determines the size of the child. The longer it takes for the ultrasound to return, the smaller the child. Some mathematics used in NASA’s case is:

- During the building of a new space shuttle
- Determining various things in outer space.

**1: **When building the space craft, we need to be aware of the centre of mass of the shuttle as well as its different motions when it’s flying and orbiting planets.

**2: **Maths is used to calculate the rotational period of various planets that astronauts might be observing. When satellites send 2-dimensional pictures of planets geometry is used to interpret them and create models of them. Logarithms are used to understand how radiation is observed by the Earth’s atmosphere.

As you can see, the world has come a long way since the first discovery of mathematics and numbers. Where once upon a time mathematics was used for counting, now it’s used on an immense scale which would’ve been unimaginable even 200 years ago.

وَإِذَا قِيلَ انْشُزُوا فَانْشُزُوا يَرْفَعِ اللَّهُ الَّذِينَ آمَنُوا مِنْكُمْ وَالَّذِينَ أُوتُوا الْعِلْمَ دَرَجَاتٍ وَاللَّهُ بِمَا تَعْمَلُونَ خَبِيرٌ“And when it is said, ‘Rise up!’ then rise up; Allah will raise those who believe from among you, and those to whom knowledge is given, to degrees

The Holy Qur’an (58:12)of rank. And Allah is Well-Aware of what you do.”

“It is the duty of every Muslim man and woman to seek knowledge.”

Sunan Ibn Majah

From this Qur’anic verse and Hadith, we can clearly see how much emphasis Islam puts on seeking knowledge, and the reward for people who have more knowledge is greater than those who do not seek to gain knowledge. This knowledge has grown in the case of mathematics for humans and we will continue to make advancements and progress. There is no tangible number in the world which is tantamount to the favours and blessings Allah has bestowed on us. Eventually all this and everything else in the world will lead us to God and show us that He really does exist and is the Knower of all things and The One Who possesses most knowledge. Insha’Allah.