Wow, all I can think is how exceptionally lucky these kids are to be taught these concepts/exposed to these problems at such a young age by a willing and enthusiastic teacher. Most people professionally employed as K-12 math teachers wouldn’t even be able to teach this kind of curriculum well. I looked at the author’s blog history to find out if they were doing this for some huge amount of money and found a blog that suggests not only were they doing it for free (skimmed it, but didn’t see any reference to pay) but they had to try to convince other parents to let their kids participate! https://buttondown.email/j2kun/archive/a-foray-into-math-cir...
In my opinion, there is a relatively unknown (to those outside mathematics) huge “privilege” gap in mathematics education that makes it so those that only follow a cookie standard or accelerated curriculum are relatively unprepared for careers in mathematics compared to those tutored (or taught in special magnet programs, or by their mathematician parents) in these kinds of non-standard-curriculum concepts from a young age. Mostly, the problem is that the standard curriculum is almost purely rote-computational until you become a college ~Sophomore and it abruptly changes to being open ended and proof-based (which is the world most pro mathematicians live in) requiring skills in creatively applying logic. So students with this kind of exposure from a young age have a much easier transition to that while also scooping up all the math-career-builders like early papers and contest wins on the way.
Those other parents probably don’t know this but OP is providing an immensely valuable service that is hard to find in some areas and which some parents would pay a huge amount of money for.
+1, I didn't think of my upbringing as "underprivileged" in any way until I got to college and later did a math-adjacent PhD and was increasingly surrounded by people who had been doing math circle-type enrichment throughout their childhoods. I was OK at math but not especially precocious. I represented my middle school at a couple of local math competitions and didn't do very well, but looking back, it's kind of weird that I didn't have any help preparing at all.
Thinking about this more in the last year or two has led me to shift a lot of my charitable giving to math circle-type programs, even though I know they're less verifiable than a lot of the (pre-longtermist) effective altruism causes -- I think that kind of mathematical thinking is a very valuable tool that is not so easy to come by without these kinds of programs.
> those that only follow a cookie standard or accelerated curriculum are relatively unprepared for careers in mathematics
Culture-dependent? I recall the story from France of the second-grader who, asked what 2x3 equals, replied "3x2", knowing only that multiplication was commutative.
> the story from France of the second-grader who, asked what 2x3 equals, replied "3x2", knowing only that multiplication was commutative.
This is a classic joke making fun of the issues with French education based on the Bourbaki [1] school of mathematics, see [2] for more discussion. Different issues than the USA, but also bad in my opinion.
[2] is excellent satire because I honestly can’t tell if it is a parody of physicists with a contempt for mathematics (e.g. Feynman), or if the author truly believes it.
It's not satirical. It's a very well known opinion piece by one of the most famous former Soviet mathematicians.
FWIW, I understand where he's coming from but I fundamentally disagree (not in the least because for me, computer science applications of mathematics are much more interesting than physics ones, and these can be incredibly abstract).
> Detaching any science (or other knowledge-gathering-activity) from reality may well turn it into teology :/
The problem I have with that argument is how historically unsupported it is. Some of the most abstract branches of mathematics, completely devoid of any real world connection, have become insanely useful later on.
Nobody thought that number theory had any value before cryptography showed that it did.
And it was Hilbert's push to put mathematics on an abstract and axiomatic foundation that led the way to discovering what "computation" is (and what its limits are) and therefore to the birth of computer science.
Did you get that phrase backwards? It's hard for me to see how [2] could be interpreted as being about "physicists with a contempt for mathematics"; it's actually about mathematicians with a contempt for physics.
Vladimir Arnold was a well-known pure mathematician with a deep interest in physics. If you read his math books (many of them are good), he constantly uses examples from physics to explain math concepts.
In my opinion, there is a relatively unknown (to those outside mathematics) huge “privilege” gap in mathematics education that makes it so those that only follow a cookie standard or accelerated curriculum are relatively unprepared for careers in mathematics compared to those tutored (or taught in special magnet programs, or by their mathematician parents) in these kinds of non-standard-curriculum concepts from a young age. Mostly, the problem is that the standard curriculum is almost purely rote-computational until you become a college ~Sophomore and it abruptly changes to being open ended and proof-based (which is the world most pro mathematicians live in) requiring skills in creatively applying logic. So students with this kind of exposure from a young age have a much easier transition to that while also scooping up all the math-career-builders like early papers and contest wins on the way.
Those other parents probably don’t know this but OP is providing an immensely valuable service that is hard to find in some areas and which some parents would pay a huge amount of money for.