By Nosherwan Khan – Team Research
If someone asks the question, who discovered America, we all know the answer that it was Columbus. But if they ask, “Who invented America?” we would all either be confounded or rightfully point out that the question is wrongly worded. The word discover is for something that already exists, but we haven’t seen it yet and after we do, we say it has been discovered, for example America was already on Earth but Columbus was the first man to go there and so it was discovered. On the other hand, invention is something that never exists but we, humans make it and so it is invented. For example, the invention of airplane by Wright brothers.
But this was about something we can physically touch, e.g. the aero plane or land. What if I ask you about the subject that we study? Was it discovered or invented? This might sound a little confusing in start but if we dig deeply we can find that yes, these 2 words exist in subjects like science as well.
Let’s talk about something theoretical. What If I ask you if math was discovered or invented? Now this might sound very odd, but you’ll be surprised to know the reality.
Discovered or Invented?
We all know the famous quote of Albert Einstein, “God does not play dice with the universe.” Why did he say that? Well, in answer to quantum mechanics, or chaos theory, Einstein said that the universe works on Mathematical principles and facts – they can never change. Not by any means! Once a mathematical statement is true, it’s true everywhere. Let’s explain this with simple examples.
If I say that 1+1 = 2, no one can say that it’s wrong, because everywhere in nature, one plus one makes 2, and that’s a fact, and by no means can these two numbers give another number other than 2. Unless! Unless! We say that 1 is 1.1 or some other finite number, which means we change them, but the value of 1 is always 1 and not anything else. So the statement 1+1 = 2 is always correct, there is no randomness or probability involved.
Let’s talk about the falling of bodies. Why does everything fall with 9.8 ms-2? Why not 10? Why not 12? Why not 16? Why does it fall with 1.6 ms-2on moon? And the answer is simple again. Our Universe is coded with the language of mathematics. If you are on Earth, and you try to jump, the Earth is coded to attract you with 9.8 ms-2 acceleration and it’s also coded, that farther away you are from Earth, the lesser will be the value of g.
Analyzing these two statements proves enough that Mathematics is discovered. Don’t worry if it’s hard to digests, I’ll explain it.
Well before you were born, the earth was still attracting everything with an acceleration of 9.8 ms-2 everywhere, and after you were born, you just felt it. Now it was there already, but after some mathematical calculations and experiments, we found the value, just like Columbus discovered America for the first time. Similarly, we found for the first time, we fall towards Earth with an acceleration of 9.8 ms-2.
How about another example?
Universal Constant, Pi
We all see circles, but what about those who first saw a circle? A perfect circle, which can only exist when the circumference of the circle is a multiple of a constant called Pi. Now how on earth, do all the circles have this property? And if it does, you find it for the first time, but it was already present before us. Before you were born, someone would have seen a circle shape, now who made it? Who made it is not important at the moment but how can it have a mathematical constant involved which we found later, is important.
So the mathematical constant Pi is another thing coded in the working of the universe.
How About Parabolas?
Now this is something interesting because no one had seen a parabola, but we found it after figuring out the quadratic equation and by watching the motion of objects in two-dimensions under gravity. Suppose you ask a physicist about the distance covered by a ball you hit. They can either take a tape and starts measuring, or they will use mathematical calculations and give you the correct answer without going anywhere after the ball.
Why is it true? Why will you get the correct answer?
Because nature works on these mathematical principles. Nature knows that a parabola’s distance equation will always work no matter what. Gravity will always work on that ball no matter what. Everything is working perfectly fine in universe, Physics is doing its job and Mathematics is doing its own Job. So, you will never get a random answer. If you use the precise calculations, you’ll get the exact answer!
Triangles
Seeing a triangle shape and knowing it’s a triangle is a different feeling, but actually knowing its mathematical nature has its own deep satisfaction which only few have. Now how come, the sum of all the angles in a triangle must be 180o? Again, the universe is coded with this. What we see is a physical triangle shape but what we can relate to it mathematically or by discussing it in language of universe, we’ll say it has 3 angles, their sum is 180o i.e., by describing its properties.
Pythagoras Theorem
Let’s put everything aside, let’s just think about the famous statement of Pythagoras, that the sum of base squared and perpendicular squared is equal to the hypotenuse squared for all right-angled triangles.
If you are a coder or doing Software engineering, you will know that when you tell a software to do something, it will do it only if that condition is true. Similarly, the universe will work in the way it’s coded.
So Mathematics is discovered. That’s for sure. It was always there, we just found it.
Invented? Or Not?
Now it’s known that it was discovered, but there is more to it. It is discovered but, by the principles that humans have described, it is known to be invented.
Let’s take examples.
Compound Fractions
Let’s take a bottle of honey and add into it, another half bottle of honey, we get one and a half bottle in total. Now one can’t just get up (or at least shouldn’t have to) and try this by themselves to know whether the statement is correct or not. But Mathematicians have invented a method to prove it without actually getting a bottle of honey, which means that this method was not known before. Rather this was invented.
Now to describe a phenomenon like the gravitational acceleration, the constant pi, addition of bottles of honey, we use some symbols or equations or some logic to describe how they work and so these methods or techniques are invented to describe a phenomenon. Hence, Mathematics is also invented.
The Infamous Calculus
We all know that changes happen due to various reasons, for example the vertical motion slows down due to pull of gravity and it exists all the time.
Now to show these changes, or show changes of any other activity Mathematicians, Newton and Leibnitz, invented a method called Calculus – a branch of mathematics. The phenomena was change. We discovered it and described it with a method or mathematical tool called calculus which we invented.
So, what’s the verdict? Mathematics is both invented and discovered.
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