This essay sample on Math Is Discovered Essay provides all necessary basic info on this matter, including the most common “for and against” arguments. Below are the introduction, body and conclusion parts of this essay.
“Is mathematics discovered or invented? ” To commence with this essay, we must first understand a few key words used in this statement and question. ‘Mathematics’ is generally believed to be the body of knowledge centered on concepts such as quantity, structure, space, and change, and also the academic discipline that studies them.
Whereas ‘discover’ and ‘invent’ means to find information, a place or an object, especially for the first time and to design or create something which has never been made before respectively.
Therefore this question can be rephrased. The body of knowledge centered on concepts such as quantity, structure, space, and change is being found or created? Actually, this is a great philosophical question. Mathematics is like a religion. Though it appears to be a very precise and concrete subject with many proofs to support with, for example like the Pythagoras’s theorem to support the a relation in Euclidean geometry among the three sides of a right triangle, it is not always how it seems.
We never know whether the so called proof is correct.
What if one day somebody simply proved this theory wrong? There could be many fallacies behind. Generally, there are two streams of people who believe in different sides of mathematics. One believes that there are universal principles that just “are” and what we as humans are doing are to discover them one by one.
And obviously the other one believes that mathematics is invented. Actually, personally I think there is no definite answer for this question. The answer is uncertain because mathematics is genuinely being discovered and also invented.
Back to the very basic, mathematics itself did not exist before there was somebody who literally studied mathematics, who worked on mathematics etc. it is us, human being who grouped the concepts such as quantity, structure, space, and change into mathematics. Therefore, we can say that we invented the subject mathematics. However, concepts such as quantity, structure, space, and change have always been existed. Nobody is ever going to invent any mathematics that was not true. For instance, we all know that 1+1=2 and there is no room for argument.
This is not something that we invent as 1+1=2 is always the truth that exists. Before the plus and minus sign was discovered, people might understand the concept through counting tangible objects. People would know there were two rocks in total when they saw the rocks and counted them. The quantity part of this equation has always been known. However, what we discover about this equation is the ‘+’ or ‘=’ sign that we use. It’s often said that in order to create any body of mathematics, you first have to have the right notation, and then the rest just comes without much effort.
So, mathematics notation, which is a human construction which isn’t necessarily inherent in the math (like concepts of quantity) itself has a huge impact on what we perceive as mathematics, and what math gets created. So in this sense, mathematics might be called “things that are true” or “things that are provable. ” Tracing back to the counting tangible objects part, indeed, there are not any rocks on the ground without someone’s having ‘invented’ mathematics to tell me that. I would certainly see two rocks on ground; but what appears in my mind would not be a number ‘2’.
Apparently I would know there was something on the ground, but the quantity seemed unknown to me. Consequently, I cannot make the discovery about the number of rocks, but what I know and what is are distinct for me. Another good example to explain this philosophical question is gravity. When Newton saw an apple drop from an apple tree he had come up with the concept of gravity. Even though no one before him had ever thought of gravity, it doesn’t mean that gravity doesn’t exist. Indeed, it had always existed and had always made apples and even all objects on earth drop to the ground.
It was a given fact that if you drop an apple from a tree it fell down until something stopped it. What Newton “discovered” is a force that has been existed since the earth was created and what he did is to put a name to the concept of an object being pulled towards the earth. All in all, he did not “invent” gravity. It is only the concept being ‘invented’. But gravity wasn’t “invented”, just as math wasn’t “invented”. He didn’t create the force but rather just discovered it by observation. And he put them in written form for our benefit.
In short, math is kind of like science. Its fundamental concepts and elements have always been there, we discover them and we have evolved a means of putting them on paper, that is called invention. In sooner future where technology is more advanced, computers can basically do everything for us. At that point, perhaps there would be some interesting questions raised. Like are books invented or discovered? Scientists could write a computer program that given enough time, it could generate every possible sequence of characters and plots.
This sounds very abstract. But in a sense, every possible book that could be published is just waiting to be found by computer programme! So can we possibly determine whether a book is being ‘created’ or ‘discovered’? The answer is NO. In reality, I think there is nothing precise. If you look at the perspective of a reader, certainly the book is an invention or creation of an author, or more like a computerized author. However, as a scientist, he/she will certainly think that the book is merely a discovered product of the computer programme.
Everything new book that is being published is nothing but a new-generated-computer-formula-product. Everything differs if you look at different perspectives. The same thing applies on this philosophical question ‘is mathematics discovered or invented? ’ if you believe that the fundamental concepts of mathematics have always existed, then mathematics is certainly discovered. You may have the sense that there is some huge body of mathematical knowledge that is just sitting out there and partially discovered, waiting patiently for people to come along and discover it, just like how human discover oil underground.
They are waiting to be dug out. Yet, if you believe that everything that we now learn about mathematics is only made up by human beings (they might be true after proofs, but initially they are just being invented), then of course mathematics is invented. Although there are great contradictions between beliefs of mathematics is being invented or discovered, I think both sides cannot know the answer by proving themselves correct anyways. There is just unlimited knowledge to be learnt through different ways.
Maybe in the future the human brain will be so developed that each truth is seen without questioning. However, up to this point, we are still limited by our abilities. So, to conclude, what has been proven throughout this essay is that mathematics is being discovered and invented. Mathematics itself was invented. Yet, how to use mathematics was discovered and it is a symbolic representation that used to help describe the world around us.