Edo-period teens tackling math's toughest problems
nippon.com
nippon.com
This is the least startling part. I was repeatedly told "you can't study that, it's postgraduate-level mathematics" by my teachers, starting from primary school, when asking obvious follow-up questions about the material we were covering. An undergraduate mathematics course starts by covering basic arithmetic, and doesn't progress much beyond that. Anything beyond plugging numbers into memorised formulae, or reciting taught proofs (perhaps slightly-adapted), is post-graduate level stuff.
In our system, people are actively discouraged from pursuing problems outside of a curriculum that's fairly standardised across the Occident. Of course, if they had a lay tradition of mathematics that wasn't based on that curriculum, they wouldn't have such barriers!
"that's fairly standardised across the Occident. " I'm still thinking across Western countries that math lessons in a school are very different.
Discouragement looks like "wow, that's really hard maths!" "maybe you should try something else first," "very impressive, but you should focus on your schoolwork," "quit doodling and pay attention," the library having no books on maths outside the curriculum, getting marked down for using concepts from outside the curriculum in schoolwork…
This is completely understandable, for a system that works how ours does. I'm not saying I could run schools any better. I am saying that you wouldn't expect the cultural practices described in the article to have the same outcomes as our schools do.
" the library having no books on maths outside the curriculum, " Where I grow up there have been university books for math and physic at the local library which I read.
" getting marked down for using concepts from outside the curriculum in schoolwork… " Many universities in Germany offer courses for high schoolers and I was supported by my teacher to visit them. Also I could present "a proof" ih high school why the e - function's derivate is the e-function. Or an introduction into particle physics.
This is only one datapoint but much more than the zeros proof of this thread. My gut feeling of HN says its again American to extrapolate their home grown problems to other parts of the world.
I'm glad your teacher supported you towards actual learning. My teachers supported me, too, as well as they knew how: I got to work from a Year 7 textbook for a few weeks in Year 5, and I got handed a curriculum-restricted calculus textbook when I kept asking why we had to memorise the constant-acceleration equations of motion. Whenever I asked for more, I consistently got told to wait until the next stage of education.
We had one lesson where we were given an open-ended problem from outside the curriculum – about balls bouncing around snooker tables – and asked to solve it. This was something I'd worked on before, and while I didn't quite have enough time to write down everything I could, I did get far enough that I got in trouble for being incomprehensible. (They could follow the beginning bit, but then the reading order instructions got too hard to parse. Don't know why: I made sure none of the arrow-lines were parallel for more than half the page, so you could follow them fairly easily with your eyes.)
Now let's make our anecdotes fight to the death.
As for why I generalise across "all Western nations": it's because the problem I describe is present in all the countries I listed, and while I have no information about the others, my theoretical model (incentives due to curriculums and exams) says it's probably present everywhere in this education system that's near-universal amongst… sigh… "Western" countries.
By the way, the "solution" cited in the article is "divide the blue radius by 3", with no proof, so there's no superior mathematical prowess on display in this example.
The article says "Fukagawa Hidetoshi, a wasan researcher and former high school mathematics teacher who received his PhD from the Bulgarian Academy of Sciences, explains the problem and its solution as follows." but there is no explanation of the problem or it's solution.
Also, the article incorrectly transcribed the problem from the photograph into the computer diagram, and the original woodcut doesn't even show an eclipse (so maybe the Edo Japanese wasn't describing an ellipse at all), and the problem doesn't make a whole lot of sense (the red and white circles are completely irrelevant to the problem) so the whole thing is suspect overall.
It's cool that Edo people were drawing pictures and writing about geometry, though.
Finally, the article title is a clickbait lie.
And I don't know the Japanese education system. I know that the Chinese high-school-equivalent mathematics curriculum is slightly different to what I've seen from English and French and German (and American) schools, so the current Japanese system might be different as well. (Though, the Chinese system also has the issues I've described.)
> By the way, the "solution" cited in the article is "divide the blue radius by 3", with no proof,
Many results in mathematics are published without proof, and are still considered significant. Heck, Euclid's Elements, which is known for its generally rigorous attitude, omits full proofs of several results.
> Also, the article incorrectly transcribed the problem from the photograph into the computer diagram,
Arguable. I'd say they just chose different values for the free parameters.
> and the original woodcut doesn't even show an eclipse
You're right. But it does show a sketched ellipse – at least, that's similar to how I drew them before I became familiar with computer-rendered examples. The insistence on geometry diagrams being to-scale is a fairly recent phenomenon: generally, owing to the difficulty of producing to-scale diagrams, the attitude has been "don't trust the diagram", and the focus when creating a diagram is making sure that intersection points are obvious.
Look into the modern tradition of curve sketching.
> and the problem doesn't make a whole lot of sense (the red and white circles are completely irrelevant to the problem)
They're not irrelevant: they constrain the relative positions of everything as the size and position of the blue circle varies. They're not relevant when the blue circle is at its maximum, but that's part of solving the problem.
> Finally, the article title is a clickbait lie.
The subtitle, “A Historical Look at Japan’s “Wasan” Math”, is much better.