Exam. This was the 4th item on the 1st PowerPoint slide - written white on black- with which Mr. Benz commenced our 3rd TOK day. All those who were still slightly asleep were suddenly wide awake. Was it really necessary to write an exam today?
As soon as we were able to recover from this shock, we asked for more detailed information. Fortunately, he had only allowed himself a bad joke and replaced the program item "exam" right away with much friendlier words that included "watching a movie". Now that Mr. Benz had our full attention, we were ready to go.
What is mathematics?
This was the first question he threw at our heads. The resulting discussion was then moved on to the next, equally difficult questions. Is mathematics an invention or a discovery? Is mathematics creative or dull? Is mathematics the queen or the servant of all sciences? Is mathematics a universal language?
What exactly the objective right answers are, I still do not know. However, I know that in this aspect, one does not need to know with absolute certainty. When it comes to publishing a mathematical proposition, then one needs to be a 100% convinced that what one is stating is true. Or not? What about publishing something in the field of physics? Or psychology? What about medicine? How sure do I have to be of my new discovery before publishing it? These and many (MANY) more questions we discussed, from axioms to proofs and paradoxes, nothing was left out. With a head overheated by all the philosophizing, we were fortunately soon released into the lunch break.
With a full stomach and ventilated heads, the promised film then was started. It dealt with a mathematician who saw his purpose in life in finding a proof for a very specific formula. Touchingly his setbacks and his successes were described. Of course, there was no lack of mathematical explanations and mentions of many kinds of arithmetic procedures (with very complicated names that dared slipping out of my mind) were not missing either. After a short discussion, we read attentively a text about the incompleteness of mathematics. With knowledge-filled heads, we were then finally allowed to escape into the rainy afternoon.
Tiziana, 5i
