Simon is enchanted by Gödel’s incompleteness theorem (that he has learned about from Numberphile) and keeps talking about it:
“There’re problems that we just can’t solve. But if we prove that we can’t prove them, then we prove them! We can’t prove that we can’t prove that we can’t prove, and so on… Quirky! Standard math doesn’t really accept that because the statement goes on forever: you’ll just never get to what we can’t prove. What follows from Gödel’s incompleteness theorem is that that statement is actually true!”
The same evening, Simon is also bothered about the lies pupils are told in school. He repeatedly quotes James Grime that it’s a big lie that mathematics is about numbers. — “What is mathematics about? Mathematics is actually about proving! But there’s one more lie that even professional mathematicians don’t know. It’s that it’s about logic. Actually, mathematicians are a lot more creative!”
Simon saw this proof on the Numberphile channel.
Simon and Neva work on the math problem called ‘The Dollar Game’ late in the evening before the day school officially starts in Belgium and continue as soon as they wake up the following morning:
Simon explains why train wheels are actually shaped like truncated cones. Inspired by a Numberphile video about stable rollers. The wooden slopes for the experiment Simon designed himself and his grandma (an ingenious craftswoman and woodworker, although a physician by profession) manufactured them for him.
The lucky numbers are the ones that didn’t get eliminated. A lucky number is dependent on the previous one. Inspired by Numberphile.
Simon saw this pattern in a Numberphile video featuring Tadashi Tokieda and recreated it in Excel, adding colours. There are 30 columns and 45 rows of digits in this picture, which means it is made of 1350 digits – the year that Trinity Hall (in Cambridge) was founded. the bottom is all zeros, apart from a few glitches. The glitches were necessary because the whole thing (reading from right to left, top to bottom) is also one number and it is a prime number!
Simon is pretty obsessed with Knot Theory at the moment (a mathematical theory that is widely used in advanced biology and chemistry, for example in handling tangled DNA).
He also learned a few tricks from one of his favourite teachers on Numberphile – Tadashi Tokieda – that probably also have something to do with Knot Theory. By folding a strip of paper in a certain way and placing rubber bands and paper clips on it and then pulling the ends of the paper strip, Simon gets the paper clips and the rubber bands linked together:
Making mathematical knots using rubber bands. A trefoil knot (the main prime knot):
Simon says “it’s good for meditation”, too:
Inspired by a Numberphile video with Tadashi Tokieda.
Simon made a remix of the Numberphile video called “Round Peg in a Square Hole” (by Tadashi Tokieda) and worked out the albraic formula behind the trick.
Simon learned this from Tadashi Tokieda in a Numberphile video called “Reflected Cats” and recreated the experiment.