## Math Scope

- What is the difference between a conjecture and a theorem?

In terms of mathematics, conjectures are mathematical statements that are unproven, but generally believed to be true. Theorems are mathematical statements that are proved using rigorous mathematical reasoning.

- In THE VIDEO 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?

He means that just the thought of the thickness of a normal piece of paper being folded 50 times, being the same height as the sun seems impossible. Your intuition tells you that it is impossible and blinds you to the possibility that the piece of paper’s thickness could be the same height as the sun. As a result mathematics ensures that our creativity does not go out of control, and giving us a set parameter for which our imagination to work within. For example, if we didn’t know that folding a normal piece of paper 50 times will reach a thickness as high as the sun, then there are many different possible alternatives that our minds can conjure up.

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

I believe that due to the eternal truths present in mathematics, it should be given a privileged position in TOK; or at least be recognised in some way. Out of the 6 different AOKs, maths is the only one whose ‘truths’ can be considered to be eternal. In the other 5 AOKs the information and ‘truths’ are not 100% eternal, and can always be upturned if new contradicting evidence arises.

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

As a result of math’s eternal truths, can math be considered the closest thing that we have to the words of ‘God’? Despite the cheesy line, I have always wondered whether this is true or not. If math is forever true, then can the conclusions that we make through math be considered to be eternally true? If so then are these eternal ‘truths’ universal laws? As a result, can maths always come up with the ultimate solution to everything; or at least provide a way to reach the ultimate solution?