The Science of Math

Are you wondering why have I got this weird looking spiral image in this post? Well, this is an image of a very interesting sequence of numbers. Before we go into this deeply, answer this question: does this image look familiar to you in some way?

Observe this numerical sequence:

1

1 + 1 = 2

1 + 2 = 3

2 + 3 = 5

3 + 5 = 8

5 + 8 = 13

8 + 13 = 21

1, 2, 3, 5, 8, 13, 21...

Is there a pattern in these numbers? Well, there is. Each number is equal to the sum of the previous two numbers. For example, 13 is the sum of 5 and 8 which are the numbers that come before 13 in this series. This is what the above diagram is trying to represent in a pictorial format. This is what the westenners call Fibonacci Sequence. 

But to the Indians or the Bharatiya, this concept was already known at least a millennium before. Alas, the repeated attacks and invasions on this subcontinent for over one and half millennium has forced us to lose the invaluable treasure hidden in the Ancient Indian Science. That is a story for another time.

Back to the topic. 

This kind of pattern is seen in galaxies, snail shells, conch shells (शंख ), etc. Here have a look.

As you can see from the above images, these two images are slightly similar to the image at the top. This makes the Fibonacci Sequence a very unique kind of number pattern.

Mathematics, is one of those subjects that can fascinate and amaze us to start thinking about it more and more. It contains wonderful things and properties like these that tell us about how this universe functions. It has always been in this universe, and will always be. 

Many students tend to dislike mathematics. They don't like the mathematical ideas because they can be very hard brainteasers. They can trick you into believing something, and disprove you right this instant. Mathematics is something that most students try to hesitate studying, but once someone starts studying it, then that person can get amazed of mathematics and its properties.

Srinivas Ramanujan, A.P.J Abdul Kalam, these two people always come two our mind whenever we think of mathematics. It is because they did not study math, they lived in math. Anything and everything in this universe can be associated with mathematics. 

Another important thing about mathematics is that it lets us think freely and experiment. If you learn math, then you will learn to think scientifically and stop building random beliefs without experimenting them. Mathematics teaches us that anything that is correct can be achieved in several methods. There are many methods to solve questions in mathematics which teach us that there are many methods to find answers to problems.

Mathematics is much more realistic than you think it is. You might think that mathematics is just merely problems in your book that you need to solve and get marks in the examination. But, mathematics is much more than just a set of questions that you are asked to solve. Mathematics tells us how the universe functions. Just like the Fibonacci sequence, there are many different number patterns in mathematics that you can find out yourself. 

If you have studied mathematics closely, then you might find that everything is interconnected; especially in the geometry part. Points are connected with Circles, Squares are connected with Nonagons, in some way or the other. 

Patterns are a very big part of mathematics. Almost everything in mathematics shows a pattern in its existence. Moreover, patterns help us to understand how can we relate things and solve problems using those relations. These patterns are called properties in mathematics. If you see the topic of Integers as an example, then there are properties like commutativity, associativity, distributivity and closure. And if you go in an even higher level, you will study about rational numbers that also have these properties.

Is there an algorithm to solve problems in mathematics?

Like discussed before, there are patterns in mathematics. And patters technically are algorithms. This is the algorithm to solve problems in mathematics:

1. Question analysis: First, see what the question is asking you. This is the first step in solving a problem in mathematics. Try to understand the problem first.
2. Finding patterns: To get to the answer, this is the second step. Try to see if there is a pattern in the problem that can help you to find the answer.
3. If the pattern in the problem fits your hypothesis, then you can experiment this by answering the question according to the hypothesis. 
4. If you get the correct answer, move ahead. If not, try again until you get the correct answer.

These are the four steps that help you to solve your problems in mathematics. This is the algorithm that will help you to solve your problems in mathematics. Use this algorithm to solve your problem.

Learning mathematics is much more than just learning to solve problems in the book. Hope you got an idea about math's wide range of science, thank you for your time.