To elaborate on this more, we need to define the terminology first. Discovered is the thing always exist. Someone found it. Invented is the thing did not previously exist. Someone created it. What about mathematics? Mathematics is a tool, a model. It is something that we can use to describe or model parts of reality, or any other system based on quantifiable things. So, is mathematic being created or discovered?

People have debated about this over the years and even now. Some people say that mathematic is being created and some say that people discovered math. As math is a model to describe things, and a model is created, so is math. Mathematics itself did not exist before the first mathematician. But, from this can we concluded that math is ultimately being created? I don’t think so. I do think mathematics is also discovered.

Looking at this example might trigger our mind to think more about it. Eclipse is the example. Have you ever thought how human being can determine when eclipse is about to happen very precisely? By using a set of statistic and also calculation, mathematicians are able to predict when the next eclipse would occur. The idea to calculate the eclipse comes from the existing phenomenon. My point is, mathematicians are able to invent a model to describe the reality by observing the existing situation, which is being discovered. So, I believe mathematics is invented but the discovery of new things help it to be invented. Mathematics is both invented and discovered.

...“Is mathematicsdiscovered 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...

...Knowledge: Invented, Discovered, or Both?
One cannot say with certainty that specific areas of knowledge are invented nor can one say with certainty that areas of knowledge are discovered. Two areas of knowledge that deal with this topic are mathematics and natural science. In my opinion, I believe that mathematics is an invented area of knowledge with some discovery whereas science is a...

...History of mathematics
A proof from Euclid's Elements, widely considered the most influential textbook of all time.[1]
The area of study known as the history of mathematics is primarily an investigation into the origin of discoveries in mathematics and, to a lesser extent, an investigation into the mathematical methods and notation of the past.
Before the modern age and the worldwide spread of knowledge, written examples of new mathematical...

...that the paper itself could be a solution to the problem mentioned. Moreover, it makes the thesis more realistic.
To sum up everything that was tackled, I could say that the thesis served to have an important purpose in the current state of Mathematics Education in the Philippines. It is very informative and feasible. Since it is a small study because it only involved 6 average students, we could propose more studies rooting from this which would have a bigger scope such as...

...HISTORY OF MATHEMATICS
The history of mathematics is nearly as old as humanity itself. Since antiquity, mathematics has been fundamental to advances in science, engineering, and philosophy. It has evolved from simple counting, measurement and calculation, and the systematic study of the shapes and motions of physical objects, through the application of abstraction, imagination and logic, to the broad, complex and often abstract discipline we know...

...Discuss the claim that some areas of knowledge are discovered and others are invented
By
Olivia Emans
In my opinion an invention may be defined as a new device, method, or process developed from study and experimentation whereas a discovery is an act or process of finding something or somebody, or learning about something that was not known about before.
Another way of differentiating discovery and invention is in the following: A discovery is something...

...The evolution of mathematics might be seen as an ever-increasing series of abstractions, or alternatively an expansion of subject matter. The first abstraction, which is shared by many animals,[19] was probably that of numbers: the realization that a collection of two apples and a collection of two oranges (for example) have something in common, namely quantity of their members.Evidenced by tallies found on bone, in addition to recognizing how to count physical objects,...

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