*This is an edited version of the winning article in the ages 16-19 category of the 2017 BSHM schools writing competition. You can also read the winning article in the 11-15 category.*

Mathematics originated not because humans wanted it to, but because it had to. Simply put, without mathematics the human race would have achieved very little. Maths is found in almost everything we do; from the simplest things, such as counting or telling the time, to more complex ideas such as computer technology or architecture. The first known demonstration of mathematics dates to the prehistoric era when our forebears made slits on bones to aid basic counting. Tally marking — one of the most primitive forms of counting — dates to around 30,000 years ago. Today almost everyone has access to computers with vast memories. The average school student in the 21st century has access to equipment any early mathematician would have given their left arm for.

The Parthenon. Photo: Steve Swayne, CC BY 2.0.

The language of mathematics, like many modern languages, originated to a great extent in the ancient civilisations of Greece and Rome. Whilst Greece was much more advanced in terms of pure mathematics, both civilisations heavily relied on applied maths. Impressive feats of architecture such as the Colosseum in Rome and the Parthenon in Athens, were built using precise calculations which have enabled them to stay standing until this day. The famous Roman aqueducts required careful planning to ensure a constant shallow gradient to allow gravity to transport the water across great distances.

The Romans, however, were much better known for their feats of engineering in war. The Greeks were one of the first civilisations to invent large-scale weapons, but the Romans took these simple designs and developed them carefully to create efficient and effective war machines. The *onager*, arguably one of the most famous Roman siege weapons, applied physics and maths to create a formidable contraption. While still out-powered by bows, it required immense forethought and calculation to launch large, flaming projectiles over walls during a siege. Working out the correct arc needed to ensure the ball of flames did not fall short and injure their comrades, but was certain to still connect with the enemy must have been a health and safety priority.

### Archimedes

Ancient Greece was home to many famous mathematicians, but perhaps the most famous was Archimedes. Contemporary GCSE and A level maths students rely heavily on his work in geometry, including, for example, a method to estimate the value of π. Archimedes also invented what is now called the *Archimedes screw*. Initially designed for pumping out water of *The Syracusia*, which may have been antiquity's largest ship, the screw is still in use today for moving granulated solids such as grain.

We can also thank Archimedes for the *Archimedes principle* which helps us measure the volume of irregular objects. It states "the upward buoyant force that is exerted on a body immersed in a fluid, whether fully or partially submerged, is equal to the weight of the fluid that the body displaces and acts in the upward direction at the centre of mass of the displaced fluid." This fact allows us to measure the volume of an irregular object as its volume is equal to the volume of water displaced.

### Fibonacci

Leonardo Fibonacci c1175-1250.

One of the most influential mathematicians of the middle ages was Leonardo Pisano Bigollo, better known as Fibonacci. He spent much of his life in the Arab world and on returning to Italy published his book *Liber Abaci* in which he described the Hindu-Arabic numerals we use today. This decimal system was incredibly beneficial to the advancement of mathematics, using a universal and simple system for quantifying things (fond out more here). In his book Fibonacci also described the "rabbit problem", which led to the now famous Fibonacci sequence.

### Isaac Newton

Isaac Newton is another pioneer of mathematics. His most famous scientific work is *Philosophiæ Naturalis Principia Mathematica*, a three-part volume on various mathematical principles. The first book (1687) focuses mainly on the motion of objects in the absence of resistance and attractive forces of different bodies. Book 2 (1713) includes the idea of resistance in different forms. Finally, the third book (1726) combines the ideas of the two and applies them to the solar system to get orbital patterns of different planets and moons.

In this book Newton laid the foundations of calculus. In the eyes of a layman, however, Newton is more famous for his universal law of gravitation. According to legend Newton was sitting in his garden drinking tea when he noticed an apple falling to the ground and realised it must be affected by an attractive force. The law of gravitation has been revolutionary in modelling a huge range of phenomena, from collisions and explosions to the motions of planets and moons in the solar system.

### Albert Einstein

Albert Einstein in 1904.

A more modern physicist and pioneer of mathematics was Albert Einstein, known for his theory of relativity, which gave rise to one of the world's most famous equations, *E=mc*^{2}. The theory of relativity is made up of two parts; general relativity and special relativity. General relativity describes the behaviour of massive objects such as stars and planets and the gravitational force they exert on each other (find out more here), while special relativity concerns the relationship between space and time (find out more here).

In his work on the photoelectric effect Einstein introduced the idea that light, which had previously been thought of as travelling in waves, could also be viewed as made up of particles called *photons*. This *wave particle duality* was later also applied to matter, and is essential in the theory of quantum mechanics, which describes the world at very small scales.

### Where would we be without maths?

Mathematics is an intricate language that has taken millennia to evolve and through the work of generations of mathematicians. It enables us, not only to count and measure, but to describe the physical world around us, achieve engineering feats, and develop the electronic gadgets we all now rely on. Maths is driven by two main needs: our desire to live a comfortable and easy life, and our yearning to know more about the world in which we live. These two goals have combined to create the dynamic, comfortable and creative world around us.

### About this article

This is an edited version of the winning article in the ages 16-19 category of the 2017 BSHM schools writing competition. You can also read the winning article in the 11-15 category.