*Reference: Course on Subject Clearing*

## Introduction

**In this video we are going to look at what mathematics is. Let’s start with a quiz.**

**We all have studied mathematics. Do you know what the word MATHEMATICS means?**

**The word MATHEMATICS comes from a Greek word, máthēma, which has the concept of “learning” or “knowing”. “Knowing” is very different from memorizing. You get the sense of “knowing” when you learn to ride a bike.**

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**We all had to study mathematics in school. What is the real reason for studying mathematics?**

**You study mathematics to develop the ability to think systematically. It is much more than learning to avoid being shortchanged.**

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**How does one learn to think systematically with mathematics?**

**The basic concepts of mathematics like numbers and counting make you think systematically when solving problems. Solving math puzzles is a great way to practice math creatively.**

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## Examples

**Here is an example of thinking creatively with numbers.**

**A man gave his son the following riddle. “Take a 5-gallon and a 3-gallon bucket down to the lake and bring back exactly 4 gallons of water.” How will you solve this riddle?**

**SOLUTION:**

*Fill the 3-gallon bucket and empty it in the 5-gallon bucket.**Fill the 3-gallon bucket again and pour it till the 5-gallon bucket is full. You will have 1 gallon of water left in the 3-gallon bucket.**Empty the 5-gallon bucket back into the lake and pour 1 gallon of water into it from the 3-gallon bucket.**Fill the 3-gallon bucket and empty it in the 5-gallon bucket.**You now have 4 gallons of water in the 5-gallon bucket.*

** 3 + 3 – 5 + 3 = 4 gallons (Answer**)

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**Math teaches you to visualize the problem when solving it. Here is an example.**

**A waterlily doubles itself in size each day. From the time its first leaf appeared to the time when the surface of the pond was completely covered took forty days. How long did it take for the pond to be half covered?**

**SOLUTION:**

*During the last and fortieth day the pond which was half covered becomes completely covered – just doubled in one day.**Therefore, the pond was half covered the previous day – the 39th day.*

*So, it took 39 days for the pond to be half covered. Answer*

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**Math teaches you not to assume anything about the problem when solving it. Here is an example.**

**There are three books, each one inch thick. They stand side by side in order – Volumes I, II, and III. A bookworm starts outside the front cover of Volume I and eats its way through to the outside of the back cover of Volume III. If the worm travels in a straight line, how far does it travel?**

**SOLUTION:**

*Check out 3 books on a bookshelf. The outside of the front cover of Volume I is actually in contact with Volume II, and so is the outside of the back cover of Volume III.**So, the worm travels only through the thickness of Volume II.*

*The worm travels one inch. Answer*

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## Check your Understanding

**Why should you study mathematics?**

**You study mathematics to improve your ability to think systematically.**

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**See if you can solve the following puzzle:**

**If it takes 6 minutes to saw a log into three pieces, how long will it take to saw that log into four pieces?**

*It takes 2 cuts for 3 pieces; therefore, each cut takes 3 minutes. It takes 3 cuts for 4 pieces. 3 cuts will take 9 minutes.*

*It will take 9 minutes. Answer*

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## Final Thought

**Hope you now have a better understanding of what mathematics is.**

**The key take away is that mathematics has to do with KNOWING and not memorizing. It helps you develop the ability to think systematically.**

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