TOK: Math Scope & Conjectures, Theories, Intuition and Creativity

by on December 16, 2017

1. What is the difference between a conjecture and a theorem?

A conjecture is a statement that is believed to be true, but has not been proven true yet. A theorem is a statement that has been proven true as there is strong imperial evidence backing up the statement.

1. In Eduardo Saenz de Cabezon uses the example of people being surprised that folding a normal piece of paper 50 times, will reach a thickness as high as the sun. He challenges us to ‘do the math’ and see that he is correct. What do you think meant when he said that Maths dominates intuition and tames creativity? Do you agree with this?

Eduardo Saenz de Cabezon claims that Math dominates intuition and tames creativity, and he uses the example of folding a piece of 0.01mm paper 50 times, it will reach the thickness from the sun to the earth. After first hearing it, our intuition says that it is impossible, however as he challenges us to ‘do the math’, to see that he is in fact correct. I agree with this statement because I think what he means by this is that in Math, when we get a situation as the one he gave, our intuition clouds are judgement, as we immediately think that it is impossible from a logical point of view. When you first hear him say that, you think that it is impossible and ridiculous. Because we used our intuition, we came up with the conclusion that it was impossible, whereas if we were to think about this creatively, we may have come up with another conclusion. Maths can tame creativity as there are limitations to Math (such as having to use certain formulas at certain times in order to achieve the correct answer). It’s not impossible to get creative in the field of mathematics, but it seems that we do primary use our intuition as we (sometimes incorrectly) feel/assume that using our intuition will lead us to getting an correct or more logical answer.

1. Saenz de Cabezon claims that the truths in maths are eternal. Do you think this gives maths a privileged position in TOK?

I agree with this statement and I think that it does give maths a prividliged position in TOK. Math is eternal as it cannot be erased from our society, regardless if it is a conjecture, theorem, right or wrong. Math is in a priviliged position in TOK due to its application in the different AOKs, such as in the Natural and Human Sciences. For example, almost all Physics fundamental laws have a mathematical formula associated with it, or involve calculating something. Math is used in chemistry as well to find things such as wavelength and is used in Biology to find the growth and decay of organisms. It is also used in the human sciences, such as in Economics and Business to calculate profits and many other things. All these equations that are used will be used forever, unless someone comes up with another more efficient, more ‘correct’ way to correct these things.

1. List any of the knowledge questions related to maths that came out of your discussion in class.

Who should study math?

Should everyone be required to study Math in school?