[lotharbot]

I (as noted in another comment: Dove's husband and the father of the child in question) homeschool him. My wife and I both have graduate math-related degrees. We let him pretty much run wild with independent math research, while also making a point to probe for weaknesses -- last year I gave him the tests from some MIT Opencourseware calculus courses and about twice per year-of-calculus we ran into something he hadn't learned and spent a couple days working it up. On the future agenda is Gilbert Strang's linear algebra course, since there are full lectures online and everything.

What we did in past years was, largely, giving him unfettered access to math and math-related channels on youtube. Vi Hart, Numberphile, 3blue1brown, stuff like that. When he showed interest in something specific, we'd get him appropriate materials. Since his elementary school was a public montessori school, his teachers encouraged us to send him with appropriate math workbooks for his capability level.

[agileAlligator]

I envy today's generation and their free access to high quality maths resources haha

[kevindamm]

yes but they're missing the take-the-radio-apart or take-the-computer-apart or fit-whole-instruction-set-in-one's-head advantage that earlier eras were granted.

[ddingus]

Maybe. Those things can still be taught.

"What if there is no Internet?" No computer? Etc...

Papa (grandfather now, raising my granddaughter because... not important, lol) tends to impress the young ones with what can be done with what is in one's head.

I am hopeful. But maybe also naive.

The other idea I like to link to these skills is "thought is action" type mastery. And, just to be clear, that is a state of clarity coupled with having grokked[0] something valuable.

Having realized that state many times in my past makes it easier today. I can go there and perform, doing or dealing with whatever it is efficiently and effectively.

It also can mean agency where ones peers may well lack it.

[0] - ...having achieved a state of understanding so complete it is a part of us, who we are, automatic, almost instinct.

[doctorwho42]

The take things apart has become obfuscated by modern technology design. Most devices these days just drop one of a dozen chips into a circuit board as it's brains. Program it, and then ship it. More or less black boxing the device. It's one of the reasons the supply chain hit a lot of tech hard, those few chips were low cost and plentiful ... Until the knock on effects of the supply chain issues happened and they weren't as profitable to make compared to the high prices chips companies like auto manufacturers were bulk ordering for a premium.

Fascinating few years, a whole generation of designs rendered unusable - complete designs trying to be reworked for the chips they could get a hold of.

[JackFr]

In my day all we had was Martin Gardiner, and that was only once a month!!

[lotharbot]

13 year old also has "Mathematical Carnival" on his shelf.