0. Introduction (what we talk when we talk about math)

0 – 5: Water is a chemical compound with the chemical formula H2O. A water molecule contains one oxygen and two hydrogen atoms that are connected by covalent bonds. Water is a liquid at standard ambient temperature and pressure, but it often co-exists on Earth with its solid state, ice, and gaseous state, steam (water vapor).

That is a definition for water. Does it motivate anybody to learn swimming? Definitely no. The best way to define swimming is jumping in water. You can find many definitions for math throughout Internet, but they are not as attractive and mesmerizing as solving a math problem. So instead of defining math, I’ll try to portray it.

Mathematics is a language in which we speak of quantifiable problems. It has its own words, sentences, grammar and punctuation. The big difference between English and math is if you made mistake in an essay, it would probably result in a weak essay, not a wrong one; however in math, your solution would be certainly wrong. We can analogize communicating in English and math to driving a car and an airplane respectively; if airplane pilot made a minor mistake, it would end up in a deadly accident. That’s why math is the most challenging subject for majority of the students.

The second aspect of this portrait is the elegance and efficiency of math in order to solve problems. If solving a problem can be analogized to a journey between two places, math is the aerial travel. In this analogy, land is the reality or the physical approach, and sky is the realm of mind.

Imagine that you’re asked to count the number of planted trees in a land. You could count them one by one and if there were 50000 trees, it would take a long time (if you could count one tree per second, it would take 15 hours approximately). However, if you could find a pattern (such as grid plantation), you would need to count the rows and columns (say 500 by 100) so instead of tallying 50000 tress you’d need to count 600 trees, then your brain could process the numbers (in the sky!) to find the answer (it would roughly take 10 minutes)

Without science and math as its language, who would trust to get on an airplane? If an engineer announced that this plane had been designed and manufactured after 1000 experiments (without applying mathematical approaches), would you trust them?

So, wherever we talk about a quantity, we can see math, coming along.