Math Scope

Reflection Questions

 

As you respond to these questions, try to focus on exercising your TOK thinking skills.

 

  1. What is the difference between a conjecture and a theorem?

The definition of a conjecture is: “an opinion or conclusion formed on the basis of incomplete information.” While the definition of a theorem is “a general proposition not self-evident but proved by a chain of reasoning; a truth established by means of accepted truths.”  Comparing the two definitions, a conclusion from a conjecture is more likely to be falsified due to its concluding statement formed from incomplete evidence while a theorem has been deduced from facts and true/sufficient statement.

 

 

  1. 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?

It is the social norm that majority of people who are required to learn maths as a subject will not particularly enjoy it as the conception of having to calculate using numbers is “boring”.  Although, Cabezon’s statement does hold partially true.  When he mentions that maths dominates intuition, he is completely correct because “maths” is made up from theorums, axioms and proof.  This shows a sign that it is reliable and hard to falsify as it has been deduced from hard evidence and it shows a sign of logic.  On the other hand, when he mentions “math tames creativity”, he is not entirely true.  The large majority of people who must learn maths through their highschool life may completely agree with this statement, however those who have a genuine interest in this subject may perceive maths as an extremely creative topic due to its abilities of creating formulas and theorems to prove or come to a conclusion.

 

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

This statement definitely gives maths a privileged position in TOK.  In the past, our class has talked about how reliable science can be.  It was a controversial topic as there was a polarisation of ideologies.  In the natural science, something can never be definitively true as science is only a model of the reality and cannot exactly replicate what happens in the real life world.  In maths, theorems have been made through logic rather than experiments that may not have reliable methods and procedures.  This allows maths to be eternal as it has been created through proof and axioms.

 

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

To what extent is sufficient reasoning needed in mathematics to create knowledge, used to definitive conclusion.