Edit: Kindly ignore this essay as it was my first and I do not consider it worth reviewing for a GRE AWA section.
The best ideas arise from a passionate interest in commonplace things.
“Eureka!” cried Archimedes as he hurtled through the streets ancient Greece. Legend has it that it was a bathtub that inspired his solution to a particularly befuddling problem. Yet another legend relates to Newton whose ground-breaking theories of gravity were preceded by the observations of falling apples. An impression I’ve gathered over hearing such stories about Newton, Kekule and Feynman is that several of their insights were founded on a keen observation of the world around them.
One day on observing my less than commendable artistic skills, my friend commented, “Did you know that every closed curve has an ‘inside’ and an ‘outside’?” I ruefully admitted to being incapable of drawing circles, but he was quick to correct himself. “No no, this is actually a major theorem in mathematics!”
Apparently, this seemingly innocuous statement about drawings has a reputation of its own among mathematicians as the “Jordan Curve Theorem”. Its proof requires a very deep understanding of the way drawings on paper behave. (And I, as a struggling artist could agree no less!) This subject is topology, the knowledge of surfaces and objects around us. The ideas developed in topology have been crucially used in to model systems in physics and chemistry.
Number theory is another important subject in math that illustrates our central theme. Mathematicians have for long occupied themselves patterns in numbers. An open problem on prime numbers that has generated great interest over the centuries is the “Twin Prime Conjecture”. It asks whether there are infinitely many pairs of primes which differ by two, such as five and seven. This remarkable simple statement subsumes within it a remarkable amount of insight into the theory of numbers. An outstanding amount of machinery has been developed in trying to understand basic patterns in numbers. This learning has lead to great technological advances in cryptography and machine learning.
Several scientific discoveries have been spearheaded by a childlike curiosity of the world in which we live. I’m convinced that a great amount of our understanding comes from asking simple questions about commonplace patterns.
(First time and I'm realising how difficult it is to generate content in 30 minutes!) Kindly let me know if this essay has too informal a writing style.