AREAS of KNOWLEDGE: MATHEMATICS
Within the Theory of Knowledge course, you will explore knowledge questions related to one or more 'areas of knowledge'. These 'areas of knowledge' are fields of study in which we try to gain knowledge through the ways of knowing. The areas of knowledge roughly correspond with the groups of study within the IB programme, even though there are some additional realms of knowledge such as ethics, religion and indigenous knowledge which are relevant to TOK. Within your TOK classes, you will also explore boundaries and overlaps between different areas of knowledge. The knowledge frameworks are useful tools to analyse the historical development, language, methodology and scope of each area of knowledge. Given that we need to make links between different areas of knowledge, it is not advisable to discuss areas of knowledge in complete isolation. The articles and links immediately below are indeed examples of real life situations which touch upon TOK questions in a range of areas of knowledge. For practical purposes, however, I have organised the resources per area of knowledge. It is up to you to explore them and make further links between areas of knowledge and ways of knowing. Doing so, will hopefully inspire you to develop interesting knowledge questions, which form the basis of TOK assessment. This page discusses mathematics as an area of knowledge.
Knowledge framework, knowledge questions and topics of study (TOK Guide 2015):
Links between MATHEMATICS and other areas of knowledge:
Possible essay questions:
- “In some areas of knowledge we try to reduce a complex whole to simple components, but in others we try to integrate simple components into a complex whole.” Discuss this distinction with reference to two areas of knowledge. (November 2015)
- Assess the advantages and disadvantages of using models to produce knowledge of the world. (November 2015)
- “The main reason knowledge is produced is to solve problems.” To what extent do you agree with this statement? (November 2015)
- “There is no reason why we cannot link facts and theories across disciplines and create a common groundwork of explanation.” To what extent do you agree with this statement? (May 2015)
- “There are only two ways in which humankind can produce knowledge: through passive observation or through active experiment.” To what extent do you agree with this statement? (May 2015)
- There is no such thing as a neutral question. Evaluate this statement with reference to two areas of knowledge. (May 2015)
- “All knowledge depends on the recognition of patterns and anomalies.” Consider the extent to which you agree with this claim with reference to two areas of knowledge. (May 2015)
- "Without application in the world, the value of knowledge is greatly diminished." Consider this claim with respect to two areas of knowledge. (May 2016)
- “Error is as valuable as accuracy in the production of knowledge.” To what extent is this the case in two areas of knowledge? (November 2016)
Some students may feel that mathematics and Theory of Knowledge do not have much in common. In fact, the opposite is true. The mere fact that mathematicians use their own 'language of symbols' raises interesting TOK questions about language as a way of knowing. Mathematical 'truth' is considered irrefutable to some, but why is this the case? Reason plays a vital role in mathematics, but is there room for emotion as a way of knowing in maths? Mathematics has been used to prove what some people feel intuitively. For example, beauty can be (partly) explained through the 'golden ratio' calculation. This calculation illustrates how facial symmetry and harmony is linked to the concept of beauty. Some scientists have even discovered that a female uterus most closely approaches the golden ratio during a woman's most fertile years! Links between mathematics and other areas of knowledge can lead to interesting knowledge questions. Philosophers have also wondered about the nature of mathematics. Is mathematics discovered, given that mathematics is so 'perfect'? If so, could we come up with an ultimate mathematical formula which explains everything and even leads to God? Or, do you agree with formalists rather than Platonists because you think that mathematics is a human invention? Finally, it is worth remembering that many ancient mathematicians were also philosophers. The documentary 'The Story of Maths' and Mr Vickery's lesson on mathematics support this point (see below).