IB Maths Resources from Intermathematics
IB Maths Resources: 300 IB Maths Exploration ideas, video tutorials and Exploration Guides
https://www.youtube.com/watch?v=4dyytPboqvE This year's TOK question for Mathematics is the following: "How can we reconcile the opposing demands for specialization and generalization in the production of knowledge? Discuss with reference to mathematics and one other area of knowledge" This is a nice chance to discuss the Langlands program which was recently covered in a really excellent... Continue Reading →
Maths Invented or Discovered? The PBS Ideas Channel has just released a new video which discusses whether maths is invented by humans, or whether it is discovered (ie whether it can be said to really exist). It's an excellent 10 minute introduction to a pretty complicated topic - and certainly accessible for students: http://www.youtube.com/watch?v=TbNymweHW4E For... Continue Reading →
Plus Maths has a large number of great podcasts which look at maths ToK topics: 1) An interview with Max Tegmark (pictured above) about why he thinks that the universe is itself a mathematical structure. 2) An interview with physicists David Berman about how many dimensions exist. 3) A talk with cosmologist John Barrow about... Continue Reading →
This is a huge topic - closely related to some of the Theory of knowledge concepts. It also gets very complicated. Here are some of the basics (some of this information is simplified from the Stanford Encyclopedia which goes into far more detail). 1) Platonism The basic philosophical question in maths is ontological - ie concerned with... Continue Reading →