4 ms·

Edo-period teens tackling math's toughest problems

95 points by benbreen 2y ago

deleted 2y ago
[deleted]
wizzwizz4 2y ago
> “This problem is at or above the level expected of an undergraduate math major, and it’s startling to learn that a sixteen-year-old girl was studying such difficult problems.” 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!
- xeonmc 2y ago
  relevant: https://worrydream.com/refs/Lockhart_2002_-_A_Mathematician's_Lament.pdf https://worrydream.com/refs/Lockhart_2002_-_A_Mathematician'...
  - deleted 2y ago
    [deleted]
- snowpid 2y ago
  "In our system, people are actively discouraged..." Who is we? "that's fairly standardised across the Occident. " I'm still thinking across Western countries that math lessons in a school are very different.
  - mnky9800n 2y ago
    This will likely turn into a treatise on why the op hasn't fulfilled his mathematical destiny.
    - wizzwizz4 2y ago
      Please. Someone with a "mathematical destiny" is unlikely to be held back by these obstacles, especially if they have internet access. Probably there are a few such cases, but I very much doubt I'm one of them.
  - wizzwizz4 2y ago
    British, French, German, USian, Canadian, Chinese, probably other places too. The curriculum varies a little (the Canadian and Chinese curricula are quite different), and I'm aware that schools vary, even within a jurisdiction, but there are prevailing attitudes. 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.
    - snowpid 2y ago
      " British, French, German, USian, Canadian, Chinese, probably other places too. " Can you give any proof for these very very different systems? " 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.
- lupire 2y ago
  Japan is not in the Occident. 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.
  - wizzwizz4 2y ago
    > Japan is not in the Occident. 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.
alexlur 2y ago
Is it just me or the “Read in other languages” links in the article are just plaintexts that don’t link to anywhere?
- layer8 2y ago
  Probably your browser. Japanese, Spanish and Russian works, the others are grayed out.

95 points by benbreen 2y ago

deleted 2y ago

[deleted]

> “This problem is at or above the level expected of an undergraduate math major, and it’s startling to learn that a sixteen-year-old girl was studying such difficult problems.” 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!

xeonmc 2y ago
relevant: https://worrydream.com/refs/Lockhart_2002_-_A_Mathematician's_Lament.pdf https://worrydream.com/refs/Lockhart_2002_-_A_Mathematician'...
- deleted 2y ago
  [deleted]
snowpid 2y ago
"In our system, people are actively discouraged..." Who is we? "that's fairly standardised across the Occident. " I'm still thinking across Western countries that math lessons in a school are very different.
- mnky9800n 2y ago
  This will likely turn into a treatise on why the op hasn't fulfilled his mathematical destiny.
  - wizzwizz4 2y ago
    Please. Someone with a "mathematical destiny" is unlikely to be held back by these obstacles, especially if they have internet access. Probably there are a few such cases, but I very much doubt I'm one of them.
- wizzwizz4 2y ago
  British, French, German, USian, Canadian, Chinese, probably other places too. The curriculum varies a little (the Canadian and Chinese curricula are quite different), and I'm aware that schools vary, even within a jurisdiction, but there are prevailing attitudes. 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.
  - snowpid 2y ago
    " British, French, German, USian, Canadian, Chinese, probably other places too. " Can you give any proof for these very very different systems? " 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.
lupire 2y ago
Japan is not in the Occident. 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.
- wizzwizz4 2y ago
  > Japan is not in the Occident. 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.

alexlur 2y ago

Is it just me or the “Read in other languages” links in the article are just plaintexts that don’t link to anywhere?

layer8 2y ago
Probably your browser. Japanese, Spanish and Russian works, the others are grayed out.