The maths ToK day started off in the computer room. There our teacher showed us the timetable for the day. We also looked at a few mathematical papers and their structure. Then the teacher showed us some examples of paradoxes. He also gave us a dossier. In there we could find texts and exercises which we were going to work on during the day. Then we started working. We had to discuss 4 pairs of opposite statements about maths in groups for a few minutes. The ones my group discussed were “Maths is the queen of science” and “Maths is the servant of science”, as well as “Maths is an invention” and “Maths is a discovery”. After what felt like 10 minutes we had our first little break in order to switch classrooms.
We then presented our opinions of these statements to the class. Often there wasn’t a statement which was clearly right or wrong. We followed the discussion up with a video of Roger Penrose and his opinion of the statements “Maths is an invention” and “Maths is a discovery”. He thinks of maths as something that is revealed using a few invented base rules. Another break followed.
After the break we looked at different fields of science and with which percentage of certainty a paper in these areas is allowed to be published. Surprising was that around 50% of published medical papers are “nonsense”. In geography 97% certainty is enough for the paper to be published, in maths on the other hand it should be 100% certainty. John P. Ionnidis wrote a paper on this issue claiming that most published papers are false and stating that to find any connection it simply has to be there and you have to discover it. This paper of his is the most referenced to paper to date. We took a quick break after which we had to read in the dossier. We read chapters 2.1 until 2.4. After the reading we also had to proof a mathematical equation and be ready to present this proof. This took us until lunch, 12:00.
At 13:20 we reconvened and had a quick discussion about some tricky job interview questions which are allegedly used by Elon Musk. Then two of us presented their proof to the maths equation which we had prepared before the lunch break. We talked a little about paradoxes like the barber paradox, the liar paradox and the potato paradox and then watched a 60 minute movie. It was called “The Proof” and was a documentary about a mathematician called Andrew Wiles who worked over 7 years in secrecy on proofing Fermats last theorem. We discussed the movie and read about important mathematicians in the dossier. We also learned about Gödels incompleteness theorem and how it destroyed David Hilberts dream of completeness in mathematics. With this the maths ToK day came to an end.
