The Boy Loved by Mathematics (13)

“............................”

“Teacher, what’s wrong?”
“No, Keita, what you just said is something truly, truly amazing. Actually, parallel lines can sometimes intersect. I’m sorry for lying to you (cold sweat).”
“Huh... so they do intersect sometimes after all (laughs). That’s a relief (laughs).”
“The idea that parallel lines don’t intersect is based on the assumption of a perfectly flat board. The arithmetic and mathematics you learn at a regular school are all thought of on this perfectly flat board.”
“But the Earth is round, right? (laughs)”
“That’s right. There is no such thing as a perfectly flat ground in this world; it’s actually round, but it’s just so large that it feels flat.”
“Then, does that mean there are two types of arithmetic: one for a round Earth and one for a flat board?”
(This child is logical to the very end... Is this what Descartes meant by 'clear and distinct perception'...?)

Mr. Hironaka is troubled. It is clear that Keita has an extraordinary—truly, one can only call it extraordinary—talent for mathematics. Keita is not just one, but two or three steps ahead of the brilliant students Mr. Hironaka has taught in the past. Can he really nurture Keita’s talent using the same educational methods he has used for his students until now...? Various thoughts swirl in the teacher’s mind.

“Should I just let Keita do as he pleases?”
“If I do that, won’t he fall into his own way of doing things and end up taking a detour?”
“If I teach him poorly, won’t I just force him into a mold and prevent him from fully demonstrating his abilities?”
“.................! That’s it! Isn’t what Keita lacks just 'tools'?”
“If I teach him that there are various tools in mathematics, such as equations, trigonometric functions, vectors, and matrices, wouldn’t Keita be able to use those tools to develop his mathematical skills more freely without taking detours?”

“Teacher? Are you thinking again?”
“Oh, sorry, sorry. Keita, you like to try various things on your own and discover new things, don’t you?”
“But it seems like things I thought I discovered have already been discovered by someone else, so I feel like it’s better to be taught them beforehand (laughs). I’m glad I had you teach me various things today, Mr. Hironaka.”
“I see, I see... (laughs)... Oh my, is it already this time? (laughs). Keita, let’s call it a day for now. Can you come back again at 3 o’clock next Saturday?”
“Huh... tomorrow is Sunday, can’t I come tomorrow too?”
“It’s not that you can’t, but it’s important for you, Keita, not just to do math, but to play with friends and help out at home...”
“Understood. See you next week then. I’ll have discovered something else by then (laughs).”
Thus, the first study session with Mr. Hironaka came to an end. The teacher reflects on Keita’s ability to have discovered 'arithmetic progressions,' prime numbers, and 'non-Euclidean geometry' on his own.
“I’m impressed. Gauss was 7 when he calculated the sum from 1 to 100. Keita was born in August, so isn’t he only 6 now? That means he understood arithmetic progressions at a younger age than Gauss...”
“Now then, even if I decide to teach him mathematical tools, where should I start?........ That’s it! The scientific calculator Keita’s father has would be perfect. A scientific calculator has square roots, sin, cos, and tan. Just teaching him the meaning of these symbols in order would be valuable. I’ll contact Keita’s father right away (laughs).”