While in Southern France, Simon really enjoyed solving this puzzle (he originally saw in a Brilliant.org vid). He was so happy with his solution he kept drawing it out on paper and in digital apps, and later shared the puzzle on Twitter. This sparked quite a few reactions from fellow math lovers, encouraged Brilliant to tweet new puzzles and now Brilliant follows Simon on Twitter, how cool is that!
What do I love most about Simon’s learning style and being around him are the precious moments he pulls me out of my regular existence, sits me down next to him and shares a piece of his sharp vision with me. I often take notes to make sure I haven’t missed out on the details. Reading back the notes I am often surprised at the hidden layers in his razor-sharp logic that hadn’t revealed themselves to me at first or had even seemed irrelevant to my journalist mind eager to cramp everything to the size of a cocktail bite. Sometimes, Simon takes over and types the rest of the blog entry himself. Like this time.
Dad says he saw someone by the swimming pool reading the book A Mathematician’s Apology. We google it and find out it’s a 1940 essay by British mathematician G. H. Hardy about the beauty of pure mathematics. Knowing how much Simon is drawn towards pure mathematics and that he, too, prefers pure mathematics to applied mathematics, I tell him about our discovery. Simon replies that it’s a silly question to ask him whether he knows Hardy: Yes, Hardy was actually the one who invited Ramanujan!
Simon pauses his breadboard tutorial, comes to the balcony with the view across the Cote D’Azur, sits down against the wall of bright purple flowers and patiently tells me an interesting fact about Hardy. It’s just a fleeting tiny conversation, but the beauty of Simon’s precise memory, the connection I feel to Simon and the setting is so striking I would rather grab my video camera but I don’t dare move as not to lose momentum. I later ask Simon to repeat the facts he told me so spontaneously.
“Hardy came up with the total number of chess games. Well, Shannon estimated it to be 10^120, however Hardy estimated it to be 10^…, 10^50.
Clarification: the former is:
1 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000
(1 with 120 zeros)
And the latter is:
1 with 100 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 000 zeros
(1 with, a 1 with 50 zeros, zeros)
Simon was showing Dad a graph of how technology is developing exponentially, y = a^x. Dad asked for a specific value of a, and Simon said: “All exponentials are stretched out or squished versions of the same thing.” He then quickly came up with the proof (“a few lines of relatively simple algebra”). “If all exponentials are pretty much the same, that means that all exponentials have proportionately the same derivative.”
This is Simon’s introductory video for the World Science Scholars program (initiative of The World Science Festival). In May this year, Simon has been chosen as one of the 30 young students worldwide, joining the 2019 cohort for exceptional talents in mathematics. Most of the other students are 14 to 17 years old, age was not a factor in the selection process. To help the students and their future mentors to get to know one another, every World Science Scholar was asked to record an introductory video, no longer than 3 minutes, answering a few questions such as what is the biggest misconception about math, what your favourite branches of math and science are and who among the living mathematicians you’d like to meet.
Throughout the program, the students are given access to over a dozen unique interdisciplinary online courses and have the option to complete an applied math project, alone or as a team, consulting real experts in the field of their project. Simon has already started the first course module, on Special Relativity by Professor Brian Greene. The course has been specifically recorded for the World Science Scholars and reflects the program’s ethos: it’s self-paced, no grades, it relies on beautiful animations and visualizations, it’s full of subtle humour, is dynamic, thought-provoking and quite advanced (exactly in The Goldilocks Zone for Simon, as far as I could judge), yet broken up into easy-to-digest pieces. It’s difficult to predict how Simon’s path as a World Science Scholar will unfold (I’m afraid of making any predictions as he is extremely autodidact), but so far we have been very pleased with the nature of this program and it seems to match our non-coercive, self-directed learning style. I have especially liked one of the course’s main postulates: “Simultaneity is in the eye of the beholder”.
Simon solving the Ackermann function (a function that cannot be de-recursed). It’s computable but the computer’s soon runs out of its computing power (see the last line of code below):