# History of Mathematics and How It Is Used in Military

Mathematics is a science that deals with the logic of shape, quantity, and arrangement. It is a science that is all around us, in everything we do. It is the foundation for everything in our daily lives- electronics, engineering, military, sports, and even art are just some of the fields it is used. Since the start of recorded history, mathematic discovery and innovation have been at the forefront of every civilization and was in use even in the most primitive and backward of cultures in one way or the other. The need for mathematics arose based on the wants of society. The more complex and advanced a society, the more complex the mathematical needs. Backward tribes needed little more than the ability to count but also relied on mathematics to calculate the position of the sun and the physics of hunting.

Several civilizations-in China, India, Egypt, Central America, and Mesopotamia- contributed to the mathematics as we know it today. The Sumerians were the first to develop a counting system. From which later arithmetic, which includes basic operations, multiplication, fractions, and square roots developed. This system passed through the Akkadian empire to the Babylonians around 300B.C. Six hundred years later, in America, the Mayans devised complex and elaborate calendar systems and were skilled astronomers. It was also around this time that the concept of zero was developed.

As civilizations developed, mathematicians began to study geometry, which involves computation of areas and volumes to make angular measurements and has lots of practical applications. Geometry is used in many things from construction to fashion and interior design. Geometry went hand in hand with algebra, which was invented in the ninth century by a Persian mathematician, Mohammed Ibn-Musa-Al-Khowarizmi. He developed quick methods for multiplying and dividing the number, which are called algorithms.

Algebra provided civilizations a way to divide inheritances and allocate resources. The further development of algebra meant mathematicians soon began solving linear equations and quadratic equations. They started delving into positive and negative solutions and also began studying number theory. With its origins in the construction of shape, number theory delves into figurate numbers, the characterization of numbers, and theorems.

Mathematics saw extensive development under the Greeks who used the earlier studies as building blocks for the development of a model of abstract mathematics through geometry. Greek philosophers and mathematicians were role models for most innovators until modern times. Several schools of thought evolved in Greece such as the Ionian school, the Pythagorean School, the Eleatic school, the Sophist school, etc. After the Greeks, the development of mathematics came under many other civilizations, which led to the ushering of a new era in mathematics. Over the past few centuries, mathematics has developed into what it is today and embedded itself into our daily lives.

People often wonder what purpose mathematics serves today. In contemporary world, applied mathematics is crucial. It is a branch of mathematics that is involved in the study of the physical, biological, or sociological world. Technology is changing rapidly and the basis for many of these developments is mathematics and logic. It also has extensive applications in the military. From the counting of the number of soldiers to radio communications to navigation in ships, it has a multitude of uses.

It is used by artillery observers to give firing solutions to the artillery batteries. It is used by weapons developers to make new weapons and by soldiers to count the number of bullets they have left in their rifles. It is also used extensively in planning logistical routes and schedules. It is also used by the air force to calculate the trajectory of aircraft or missiles. The navy uses it for navigation and detection purposes such as using it in radar and sonar. It is also used by engineers, pioneers and sappers in their operations, which generally include the construction of defensive emplacements and lines, laying and removal of minefields and explosives, demolition work, and repair of damaged and malfunctioning armoured and non-armoured vehicles.

The supplying of troops in different parts of the country and world and troop movements involve extensive logistical planning which includes calculation of travel schedules, amount of supplies or number of troops to be transported, calculating the number of vehicles required. Mathematics is also involved in meteorological studies which help in operational planning. A good example of this would be the planning of Operation Overlord, the largest amphibious invasion of occupied Europe on 6 June 1944. It involved extensive study of weather which lead to its success. During the current times, mathematics is also used extensively in electronic and cyber warfare, which is an integral part of the modern battlefield.

In addition to providing the framework and foundation for the designing and invention of new technologies and weapons to be used in the field of battle or for battlefield support, such as solutions to logistical problems like the transportation of soldiers, weapons and food, mathematical models are used to develop and simulate complex and detailed military tactics and strategies. These simulations might involve statistics or probability, and game theory, which is a theoretical framework for conceiving social situations between competing players. In some aspects, game theory is the science of strategy and optimal decision making of independent and competing actors in a strategic setting. The key creators and pioneers of the game theory were mathematicians John Von Neumann and John Nash as well as an economist named Oskar Morgenstern.

Mathematics also plays an extremely important role in cipher warfare which has become increasingly important, for intelligence gathering and counterintelligence, industrial espionage and sabotage. Organizations like NSA, RAW, MI6, GCHQ, etc. constantly develop and attempt to break secret codes. A very good example of cipher warfare was the breaking of the German cipher known as Enigma during the Second World War by the allies, which lead to them to victory in the battle of Atlantic. Other battles were also won due to the intelligence provided by these transcripts which were codenamed ‘ULTRA’. Mathematics is thus an integral and crucial part of the battlefield and military as much as it is in our daily lives.

-Ashwin Karthik (One of the Prize Winners of Article Writing Competition in the 13-24 Years Age Group)

Picture Credits: afcea.org