What is the difference between a conjecture and a theorem?
A theorem is a mathematical statement that has been proved by rigorous mathematical reasoning, there is a firm belief that this is true without opportunity for it to be disproven. A conjecture is not backed up by evidence and remains unproved, but is believed by the mathematical community.
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?
I do agree with this. In terms of this example it seems illogical that folding a piece of paper 50 times could reach the moon, without math there wouldn’t be many people supporting this claim. But with calculations math is able to have solid proof to claims made from intuition. In terms of creativity people tend to create situations or false assumptions like “a rabbit could run a million meters an hour” could be an assumption but with the math and calculations this would create more boundaries for how people can think in terms of creativity.
Saenz de Cabezon claims that the truths in maths are eternal. Do you think this gives maths a privileged position in TOK?
I think in some ways it makes math less grey and unsure, it brings some certainty to the knowledge that one is gaining as opposed to all the other areas of knowledge where there is always opportunity for disproval. It may also be not privileged but a curse because if all truths in maths are eternal than what if two truths contradict. There is always grey area towards certain rules that can be challenged.