# The Connection Between Mathematics And Logic

- Sep 01, 2016
- Sudipto Das

Logic is the foundation of mathematics. It may look from the hindsight that a particular math problem can be done through the implementation of a memorized formula, but that’s not even the truth. That’s mainly because students do not even think of where the formula came from. It didn’t appear out of thin air, did it? The formula didn’t just appear out of nothing and got its place in the text books. The formula is derived from real life examples through logical reasoning and is believed to be universally true because it is proved to perfection. That’s the only reason due to which mathematicians are so crazy about proofs.

**No math topic is a part of the fiction**

Students need to realize this especially those students who have just made the transition from primary schools to middle schools and are introduced to overly-abstract topics like algebra and set theory.

They have to realize that a simple formula like (a+b)^{2} = a^{2} + b^{2} didn’t appear out of thin air and landed on their textbooks. This formula is derived from real life examples as we said before. This derivation is done through logical reasoning. The students are just applying the same formula to calculate sums accordingly.

So however abstract it might appear to be, one thing’s certain that it isn’t. The wrong notions are developed among students due to the lack of a back-story concerning a particular math topic.

**Math has its foundation on a bed of logic**

We will explain this with a simple example of the Pythagoras’s theorem that says:

In a right angled Δ,

Hypotenuse^{2 }= Perpendicular^{2} + Base^{2}

As per the fig above,

c^{2} = a^{2} + b^{2}

The formula above is derived logically in this manner:

The figure above has 4 triangles from which we are going to derive our Pythagoras’ theorem.

*Calculating the area of the whole square (yellow+blue)-*

Length of each side= a + b

Area1= (a + b) (a + b)

* Calculating the area of the pieces inside-*

Area of the smaller yellow tilted square= Area2=c^{2}

Area of the 4 triangles= Area3= 4(1/2 ab)= 2ab

So total area of the pieces inside should be Area2+Area3= c^{2} + 2ab.

Now according to logic you can easily say:

Area of the whole square= Area of the pieces inside

(a+b)(a+b)= c^{2} + 2ab

=> a^{2} + 2ab + b^{2} = c^{2} + 2ab

=> a^{2} + b^{2} = c^{2}

So you can easily see that the formula is based on logic, and so the application. Similarly, each and every formula in mathematics is derived logically from real life problems.

Mathematics and logic have to go hand in hand. If you didn't see the logic in a problem, you would not be able to solve your math sums. If you are good in logical reasoning, you should be able to comprehend math concepts quickly and more efficiently. Therefore, it is important to start off early. And if your children do face some trouble in the subject, it should never be ignored. Professional math tutors can handle the situation on your behalf. That should be all for now. Hope you had a good read.

### Sudipto Das

Sudipto writes technical and educational content periodically for wizert.com and backs it up with extensive research and relevant examples. He's an avid reader and a tech enthusiast at the same time with a little bit of “Arsenal Football Club” thrown in as well. He's got a B.Tech in Electronics and Instrumentation.

Follow him on twitter @SudiptoDas1993

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