The meaning and difference between ‘Discovered’ and ‘Invented’ is the first knowledge issue that comes up after reading the title. How do we categorize something as being discovered or invented? Are all inventions discoveries; or all discoveries inventions?

The word discovered means to gain knowledge or awareness of something not known before, whereas invent means to create or produce something that did not exist before.

The areas of knowledge are mathematics, natural sciences, human sciences, history, arts and ethics. But due to the word limit constraints, it is difficult to take all areas of knowledge into account. So, I will take 2 areas of knowledge and discuss them.

First let’s take history into account. The past is fixed; immutable and absolutely certain. Nothing we can do can change it. Therefore, we hold up history as the model for truth and certainty. BUT!!! This is what we think. We do not take into account the bigger side of this. How can we be sure what the historians tell us is right? How can we be sure that this is what definitely happened in the past?

All the above sayings tell us one thing that history is completely different from what we consider it to be. This is because all historians research the past with certain interest or questions in their mind, pick out only the pieces that are relevant to their investigation, and assemble them in different ways.

All historians are selective and they select on the basis of their own paradigms. All historians are humans and their history is based on their own particular interest, which probably are dependent on their own culture.

For example, if we consider a situation where people plant bombs maybe in an attempt to force the government to make some changes according to their wishes; now in this situation, I and probably most of the people will call it terrorism as it is killing innocent people. BUT, some people will probably call it freedom- fighting. This situation probably has arisen in history many times, but as I said before, all historians will portray this situation according to what they believe. This obviously means that history is altered according to different historians. A proof of this maybe found in two different history books where one historian might have portrayed the above situation as terrorism and the other as freedom- fighting.

So, the conclusion to all the above arguments leaves us with the belief that history is invented according to different historians, what they believe and what they think about the situation. BUT, as being a TOK student, the second side of the arguments also has to be explored.

People say that history is constructed by biased historians working with biased sources which are why there is no such thing as historical truth. But just because their work is selective, it does not mean it is that they have twisted it. There might be several accounts of a particular event and none of it might be true, or there might be true pieces in each. The historian recognizes the problem, and looks to solve them. They give explanations with developed reasons. Theories, arguments and accounts all examined and questioned.

And plus, there is a pressing moral need for us to acknowledge the reality of the past. ‘Those who cannot remember the past are condemned to repeat it’ Santayana.

In conclusion for history, I think it cannot be characterized as either invented or discovered. I think, it is BOTH, invention AND discovery.

The next area of knowledge I would discuss is mathematics. Maths- invented or discovered? This question has been debated on since a very long time but till now, a particular conclusion has not yet been reached. Some people believe that maths was invented, while some believe that it was discovered. The problem that arises here is that people who say that maths is invented and people who say that maths is discovered both have reasonable evidences to prove themselves, which is why not even one can be proved wrong.

The view that ‘maths is out there waiting to be discovered’ is called the platonic view of maths, named after Plato, who thought that mathematical truths are eternal and unchanging. For example, if we consider the Pythagoras theorem, of course it did not exist before as a theorem, but surely their truth values did exist. For instance, anyone who happened to build squares from the sides of a right angled triangle would find that the area of the square of the hypotenuse would equal the area of the other two squares combined. The name of Pythagoras theorem is definitely an invention, but the mathematical relationship obviously existed before it was discovered.

But then again, there are some difficult questions raised in response to Plato’s theory, such as where did maths exist? How do we discover maths? Many believe that the only reasonable answers suggest that maths is purely in the mind. And Plato could probably not have argued on this because he had argued that we are just remembering things that we already knew but had forgotten. But if maths really is in the mind, then isn’t it an invention?

In counter argument to the above two questions, I can give an example. For example you are in a maths class and given a problem to solve. Has it never happened that you solved the problem without being provided with a method to solve it? Yes! It has happened. At least with me it has. We were give a math question and not told a method of how to solve it. But surprisingly, a few students in the class got the correct answer. This means that the solution was found all the by those few students all by themselves. That solution existed which is why it occurred to the students and they solved it. This somehow proves Plato’s theory.

Phi (Golden Ratio) as a mysterious number has been discovered in many areas, such as art, architectures, humans, and plants. According to the history of maths, Phi was first understood and used by the ancient mathematician in Egypt, two to three thousand years ago, due to its frequent appearance in Geometry. Phidias (500BC-432 BC), a Greek sculptor and mathematician, studied Phi and used the Phi in many designs of his sculptures, such as the statue of the goddess Athena in Athena, and the state of god Zeus in Olympiad. This means that the theorem of phi did exist before, and it was discovered but the name phi (golden ratio) was obviously invented. Same is the case with natural constants (e and ln), their values, properties and functions did exist before which discovered but their names and symbols were invented.

In my opinion, like history, it is not accurate to characterize maths as either invented or discovered. It is both invention and discovery; they work hand in hand. People think that there is an enormous body of mathematical knowledge, partially discovered, and waiting patiently for people to come along and dig it out. Well, that’s definitely fairly the case; nobody is ever going to invent any maths that wasn’t already true. I mean, no matter how hard you try, you’re never going to be able to prove that 2+2=6. The concepts and theorems are discovered while the symbols are invented.

In conclusion, I will say that I don’t agree with the main claim that some areas of knowledge are discovered and others are invented. I think it is not accurate to say that some areas of knowledge are either invented or being discovered. In my opinion, they work hand in hand, together supporting a particular subject. Without either (discovery or invention), the subject remains incomplete, meaning that both are interdependent to complete a subject.