- What is the difference between a conjecture and a theorem?
A conjecture is an idea formed without solid proof, while a theorem is a statement that has been proved based on other existing truths or formulas.
- Saenz de Cabezon claims that the truths in maths are eternal. Do you think this gives maths a privileged position in TOK?
In a way, having eternal truths does give maths a privileged position in TOK because this means that any knowledge produced in maths cannot be disproved and can always be used. This could be an advantage because there wouldn’t be any “false” knowledge in maths and therefore it can always be reliable. Even concepts from centuries ago, such as the Pythagorean theorem, still hold true to this day and are widely used. On the contrary, it can also be argued that just because truths in maths are eternal, maths does not have a privileged position in TOK. It can be just as valuable to have knowledge that is constantly changing depending on the area of knowledge. For example, in the natural sciences, theories are continuously being disproved by scientists through experimentation, meaning that a “truth” in science is not eternal. This doesn’t make the natural sciences any less valuable than maths because through the process of disproving theories and proposing new ones, we are still able to learn more and more about science each time.
- List any of the knowledge questions related to maths that came out of your discussion in class.
- In what ways does knowledge produced in maths differ from knowledge produced in the natural sciences?
- To what extent does assumption limit or enhance the production of knowledge in maths
- How is knowledge gained in maths helpful in producing knowledge in the arts?