- What is the difference between a conjecture and a theorem?
A conjecture is one step shy of a theorem – it is the foundation of a theorem as an idea of a rule or concept is present, but not with the full supporting evidence. A theorem, on the other hand, appears to be fully supported with evidence and at least valid to a certain extent.
- 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?
A large component of mathematics is based on theorems, which are supported by seemingly empirical evidence that is deemed logical. The Ways of Knowing reason (logic) and intuition are closely intertwined, and consequently, it could be argued that one’s intuition is based on logic, meaning concepts that could be derived from (but are not limited to) ethics and morals etc. Creativity runs wild, and logic and intuition then offers a framework to the mind when thinking, for example about creative solutions when attempting to find supporting evidence for a theorem. I agree with what Saenz de Cabezon said – I agree that maths does dominate intuition and acts as an indicator of what might seem logical at a certain time, for example when answering a maths question. I also agree that maths tames creativity, as creativity appears to work collaboratively with logic to form reasonable but simultaneously, possibly outlandish ideas and evidence.
- Saenz de Cabezon claims that the truths in maths are eternal. Do you think this gives maths a privileged position in TOK?
I think that this statement would only give maths a privileged position in TOK if the framework of TOK revolved around believing that logic is the supreme way that humans can know and learn. This is because in TOK, we are encouraged to think about how all Ways of Knowing and Areas of Knowledge have their flaws and strengths. I think that the claim that the truths in maths are eternal is not entirely true. There are periods of time in between trying to find new evidence for a theorem if the previous evidence was discovered to be purely coincidental in its support to the statement.
- List any of the knowledge questions related to maths that came out of your discussion in class.
How objective can maths be?
Should maths be a compulsory subject at school? Who should be studying it?
What is maths?
What Ways of Knowing would be most applicable to maths?
How do we determine when maths is right or wrong?