1. What is the difference between a conjecture and a theorem?
A conjecture is an unproven accepted fact by society, an example of this would be the atomic theory. A theorem is a proven fact, usually by mathematics.
2. 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 takes creativity? Do you agree with this?
Most of the time, math can be seen in everything. However, sometimes math can be difficult to understand. Even though the math may already exist, we may not be able to understand it. I think he means that math must be understood every step of the way until it becomes intuition and that the interpretation of mathematical solutions takes creativity.
3. Saenz de Cabezon claims that the truths in maths are eternal. Do you think this gives maths a privileged position in TOK?
No. Of course, math is more reliable when it comes to theorems, however, most real life situations from social phenomenon to lab experiments use statistics. The analysis of numbers can be a very difficult and complicated process, where human error is likely to happen. Although math is more reliable, we must also consider that the analysis of new data may not be correct.
4. List any of the knowledge questions related to maths that came out of your discussion in class.