On the surface, it would seem as though that the two human activities that would be the greatest distance apart from each other are mathematics and war. On one end, you have the utter violence and destructive and chaotic force that is war. Its main objectives are to kill people and destroy things, as well as ultimately bringing one nation’s or group’s military (or often times, their whole society) under the control of another. On the other hand there is mathematics, which, by contrast, would seem as a path of human achievement and enlightenment. Mathematics describes the world around us with a clean precision, in angles, lines, and equations. You might wonder how, of all things, the peaceful study of math could possibly have an influence over the brutish nature of war. For the answer, you need only to examine the various tools and plans that have been developed and used in warfare throughout history. It can be seen that advancements in mathematics and technology throughout history has had a profound effect on what kinds of weapons, from axes and metal swords to Intercontinental missiles, warfare has been fought with and what strategies have been used to fight wars and maintain armies.
Part I: Weapons
The most obvious thing that comes to mind when you think of war is weapons. From wood and stone clubs to laser guided missiles and tanks, the overall purpose of weapons has not changed at all since the time of our ancient ancestors, but they have indeed changed and evolved to go with the times, to better suit the needs of the societies using them. Underneath it all, mathematics and technology have always been the driving forces behind the innovation of weaponry. Granted, it has been the needs of society that has pushed for deadlier, larger, and more innovative weapons, but math has always been the biggest driving force in getting to those goals. There is proof that Prehistoric humans had been using primitive weapons for thousands of years to hunt and fight, with little to no changes in how they were developed or used. Cave paintings in Spain that date back from 10,000 to 5,000 BC even show men fighting with bows while similar cave paintings in Africa from 6,000 BC shows men armed with some form of wooden clubs. As creative as they were, these early weapons were still rather basic in their design and purpose. They were simple extensions of the force that a person could exert with their own bare hands, with only slight modifications such as extended reach with spears and bows, and increased force with clubs and stone axes. During these early periods, swords were not an effective weapon since they could not be made flat enough to a point where they had adequate cutting power to go through an opponent and his armor. It wasn’t until civilizations learned how to better make things from metal that the sword saw a distinct rise in manufacture and use. The rise of swords is also owed to the discovery of iron, as well as the knowledge of working it and making weapons out of it. Before iron, bronze was the metal used to make many weapons and armor. It was difficult to make as it required that two separate metals, copper and tin, be smelted together and poured into a cast. This limited its use dramatically. Iron, however, only required just the element itself to be smelted down and cast, and also had the advantage of being malleable enough to be beaten into shape. This allowed for a much stronger and sturdier metal. It’s strength, combined with the fact that iron ores were far more easier to come by than either tin and copper ones, allowed ancient armies to keep readily available supplies of weapons at hand whenever they needed, and also made effective weapons available to more soldiers. Historically, it revolutionized warfare for centuries as iron swords became standard on battlefields, being a much more effective weapon for cutting through an opponent’s armor at close range than clubs and axes. From a mathematical perspective...
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