This blog is about Simon, a young gifted mathematician and programmer, who had to move from Amsterdam to Antwerp to be able to study at the level that fits his talent, i.e. homeschool. Visit https://simontiger.com
Simon prepared this project as a community contribution for The Coding Train (Simon came up with his own way to draw the Hilbert Curve and added interactive elements to enable the user to create other colourful space-filling curves (Hilbert Curve, Z-order Curve, Peano Curve and more!). You can see Daniel Shiffman’s Hilbert Curve tutorial and coding challenge on The Coding Train’s website (including a link to Simon’s contribution) via this link: https://thecodingtrain.com/CodingInTheCabana/003-hilbert-curve.html
Simon keeps thoroughly enjoying Brilliant’s approach to intelligence and learning (even though he sometimes dislikes the way the daily challenges are formulated). His latest stats:
From the courses he has done most I conclude he’s mostly into Computer Science and real world problem solving at the moment:
Below are some screen shots of the daily challenges he was especially curious about lately and also excerpts of his taking part in Brilliant’s discussions:
I noticed it’s a cyclic quadrilateral and I know that the opposite angles of a cyclic quadrilateral have to add up to 180 degrees. At first I thought: How am I even going to go about doing it, because it’s so cryptic and so full of information. But once I solved it, it actually became quite easy to draw!
For over a month, Simon has been fascinated by Presh Talwalkar’s channel Mind Your Decisions. The channel is full of short videos on famous math problems, logic riddles, proofs and mental math tricks. Simon has also ordered a compilation of Talwalkar’s five most interesting books, including “The Joy of Game Theory: An Introduction to Strategic Thinking”, that we are currently very much enjoying together, and four more, that Simon is reading on his own: “40 Paradoxes in Logic, Probability, and Game Theory”, “The Irrationality Illusion: How To Make Smart Decisions And Overcome Bias”, “The Best Mental Math Tricks”, and “Multiply Numbers By Drawing Lines”.
This one became Simon’s favourite brain teaser. It sounds like it’s filled with irrelevant information, but somewhat counterintuitively, every little bit of information in this puzzle helps! Here is the puzzle: A mathematician tells a census taker he has 3 children. The product of their ages is 72 and the sum of their ages is the house number. The census taker tries to figure it out but explains he still does not know. The mathematician says, “Of course not. I forgot to tell you my oldest child loves chocolate chip cookies.” Now the census taker figures it out. What are the ages of the children?
Simon has also picked up many nifty tricks and beautiful magic squares, both from the book and from the YouTube channel.
We devoted the beginning of January to a goofy stop-motion project: Simon and I baked 2048 cookies! No, we didn’t bake over two thousand cookies! We only baked and decorated a little over a hundred of them, Simon had calculated that that would be enough to play the 2048 game… with cookies. Simon came up with all the editing tricks to make this project work. In the video, he also explains his winning strategy and confesses he has made another attempt to program the game, without me knowing it. Apparently, that’s how he first came up with the idea to bake the cookies, by looking up pictures of 2048 while programming and stumbling upon this blog.
Here is a link to Simon’s previous attempt to program 2048, about a year ago (he got pretty far).
December was all about computer science and machine learning. Simon endlessly watched Welch Labs fantastic but freakishly challenging series Learning to See and even showed me all the 15 episodes, patiently explaining every concept as we went along (like underfitting and overfitting, recall, precision and accuracy, bias and variance). Below is the table of contents he made of the series:
While watching the series, he also calculated the solutions to some of the problems that Welch Labs presented, like the question about the number of possible rules (= grains of sand) for a simple ML problem if memorisation is applied. His answer was that the grains of sand would cover all land on earth:
Simon loved the historical/philosophical part of the course, too. Especially the juxtaposition of memorising vs. learning, the importance of learning to make assumptions, futility of bias-free learning, and the beautiful quotes from Richard Feynman!
I have since then found another Feynman quote that fits Simon’s learning style perfectly (and I believe is the recipe to anyone’s successful learning as opposed to teaching to the test): “Study hard what interests you the most in the most undisciplined, irreverent and original manner possible.” We have discussed the possibilities of continuing at the university again. I have also asked Simon how he sees himself applying his knowledge down the road, trying to understand what academic or career goals he may have set for himself, if any. Does he have a picture of himself in five years from now, where does he want to be by then? He got very upset, just like when asked to sum himself up in one sentence for an interview last spring. “Mom, I’m just having fun!”
Simon spent the morning of December 5 pondering about how to test whether a number is a triangle number. “To test if something is a triangle number: double it, ask if it’s a multiple of its own square root. If that square root has a decimal, round it down”. This was his initial hypothesis, later discarded.
Another formula he came up with was if n is even, m is a triangle number. After we got back home, he quickly wrote some code to check it: