Have you ever seen a rainbow? Until recently, I had looked at many rainbows but had never truly seen a rainbow.

In his writings on faith and logic, religious scholar Bediuzzaman Said Nursi maintained that looking and seeing are two different things. In his book, Words, he says,

“The eye is a window through which the spirit looks at this world. If you use it on behalf of your carnal soul, without selling it to God Almighty, by gazing at transient, impermanent beauties and spectacles, it panders to lust and other carnal desires.”

Using Nursi’s reasoning, you might look at…

From the day I learned Calculus, I noticed that I had become obsessed with learning how certain things worked. While it is fun to understand how certain things work, it is even more entertaining to learn about how something was discovered. Furthermore, it is most amusing to learn how something works or exists on our own. For example, knowing that 2•2=4 isn’t very rewarding for a child. However, understanding why 2•2=4, demonstrating it with wooden blocks, is extremely rewarding.

That is why it is so enjoyable to come up with and read about proofs. To write out a proof takes…

In his 1969 book, The Science of the Artificial, Herbert Simon defines design as “To design is to devise courses of action aimed at changing existing situations into preferred ones.” To move away from the thing at hand to one chosen, the chosen one can’t simply be functional. It has to also appeal to the eye. We can say that things that are functional yet appealing have good design.

All of the brilliant designers I have had the opportunity to meet had vast imaginations and significant aesthetic concerns. Furthermore, all of them had interests in geometry and mathematics. Spending my…

Everyone knows about honey bees. However, the bees have known what human mathematicians didn’t know for thousands of years. A honeybee may be the most extraordinary creature in the universe. Its body is beautifully patterned, can fly wherever it wants, spends its time near beautiful flowers, produces the most delicious and incredible substance in nature, honey, and, most importantly, it is a great mathematician. The amount of knowledge they have of the world around them is comparable to graduating from the best science and engineering schools. They show us that mathematics is the language of nature and science. Aristotle was…

It was finally the weekend! After my long mathematics presentation, I came home to watch my favorite tv show, Person of Interest, to de-stress. Surprisingly, the episode was about the most famous mathematical constant, pi (π), equal to the ratio of a circle’s circumference to its diameter, commonly approximated as 3.14159. Mr. Finch (the main character) acted as a substitute teacher and wrote on the chalkboard 3.1415926535. Then he asked the students, “What does this mean?”

I answered the question in my mind, thinking, “If I have a bicycle tire with a diameter of 1, then one full revolution of…

Archimedes used calculus as a simple way of thinking that was never seen before. On the other hand, Richard Feynman held that calculus was the language that God had used when creating this universe. In reality, both are correct. Not only is calculus a form of thinking, but it is also a way to explain an unknown occurrence. If we look further into it, we can assume that they are the same thing. After all, language is the spoken form of thoughts. (Let us ignore those who talk without thinking).

Ever since Leibniz proposed calculus to the world, mathematicians and…

When I close my eyes and go back in time, I see a college student sitting in the back row and looking sad while the professor is standing next to the chalkboard, writing mathematical definitions on it with chalk. The click, click, click sound was still obvious every time the professor wrote on the blackboard. Then, the student goes into deep thought when the professor said:

“For every epsilon greater than 0 [ε>0], there exists a delta greater than 0. [ δ>0]”

Upon hearing this, the student asked himself repeatedly: What does epsilon mean? That student actually was me. Although…

On a snowy day in London, as he was lying in bed and gazing at the ceiling, Sherlock Holmes’ mind was once again at work trying to crack yet another case. It wasn’t long before Dr. Watson came knocking at the door and described to him a most peculiar murder case. Sherlock at first paid no attention to any of what Watson had to say. However, when Watson told him of the tracks from the bicycle with which the culprit had made his getaway, Sherlock suddenly turned to him and said, “well, now, why don’t we have a look at…