How Calculus Worked and Effects of Technology

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Math has been strongly applicable to many people’s daily life for centuries. To a majority, math is considered a technical and developmental skill, where answers are to be considered functionally correct in order to be useful. When I think of math, I think about how humans are capable of solving the hardest numerical problems and how it applies to their work. We’ve grown from doing simple calculations into finding the motion of physical objects, figuring out time, and locating directions through navigation. However, I have come to realize that we underestimate our origins and evolution of mathematics. Through its historical roots and intelligent creators, mathematics holds a long story of what it has become today. So the big question here is, when and where did math appear in the first place?

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Mathematics first started when humans had to first begin counting, but counting wasn’t as easy as it seems. In order to expand numbers that were more than ten, a numeric counting system had to be developed; this system was created by Ayrabhata of Kusumapura Northeast India, which was later adopted by many other cultures. One of the most prominent cultures that refined this method by building another numeral system was the Babylonians and ancient Sumerians, who were centered between the Tigris and Euphrates rivers, southern Mesopotamia. Using numbers, they used clay tablets to write out multiplication and division. 

They named their system as “sexagesimal,” which used the number sixty as their base. Derived from the Babylonians, we now use their system and applied it as sixty seconds in a minute, sixty minutes in an hour and so on. Through their earlier discoveries, the Babylonians also created linear and quadratic formulas, then formed the mathematical constant pi, a value approximated to 3.14. From this point, this is where the shift of basic algebra becomes more complex; it’s geometry.

What advanced after simple algebraic was known as geometry. In the sixth century B.C during the Hellenistic period, geometry began to originate from Greek mathematicians who resided near the eastern Mediterranean. The Greeks played the largest and longest role in shaping geometry because they not only integrated shapes in math, but they were able to strengthen the idea of proof to approve theorems rather than repeated observations that the Babylonians used. A famous Greek mathematician and philosopher named Pythagoras of Samos were heavily influenced by the Babylonians’ math achievements; thus drove him to invent a new concept in math, geometry. 

One of his accomplishments is commonly known as the Pythagorean theorem, a fundamental relation showing that the square of the length of the hypotenuse equals the sum of the squares of the lengths of the other two sides. This theorem is well known for its application on navigation, for example, it created two-dimensional navigation that helped build compasses and drawing out maps. The Greeks delved into math as a means to introduce logical reasoning and proof in order to make theorems. After these geometric discoveries, many countries began to take every information in and translate it into their own language. It wasn’t until after a few centuries that two men were able to take math onto a whole new level and called this revolution as calculus.

Up until the 17th century, there was a period known as the Scientific Revolution, it began after the Renaissance period. Between 1665 and 1666, calculus was invented by a famous figure we all recognize today. Across Europe and somewhere in England, a prominent mathematician named Isaac Newton was trying to figure out the speed of a falling object. In doing so, he realizes that with each second that passes, the speed increased. With that, he needed to prove his theory so he began to put himself working in a field that was highly focused on gravitation and motion. Newton started finding the rate of change, at the same time, he was formulating the laws of motion and the universal gravitation. 

After figuring out how calculus worked, he was able to answer plenty of questions related to planets, space, time, and gravity. It took him around eight years on his research about calculus. Cautious about what the people would think about his discovery, Newton worked with Gottfried Wilhelm Leibniz to publish their book. Leibniz then helped Newton by providing calculus notations such as the limits and integrals. Calculus in simple terms is an integrated and differential level of math that studies anything involving rates and changes. Calculus has become an essential and foundation of physics because, without calculus, physics would be much more difficult to understand. That is why both subjects are so dependable on each other today.

Ultimately, the origins of math are quite complicated but understandable at the same time. Math did not appear out of thin air, it has been developed for a very long time and will keep getting more advanced in the future. The Babylonians have built the foundation of simple counting, leading to basic addition, multiplication, subtraction, and division. The Greeks contributed to a huge chunk of the history of math because they specialized in building theorems, which is important to the math we use today. Isaac Newton brought forward calculus in which algebra and geometry are blended together to determine motion that consists of speed, velocity, and acceleration. From simple to complex, mathematics has evolved in ways we never would have expected. We have enabled ourselves to take advantage and dive deep into the depths of mathematics, as well as find a way to apply it to our everyday modern life. 

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