>>25320807
If the average IQ of you and your spouse is over 115 then starting at 15 or 16: Geometry (with proofs, the whole point), derivative integral and multivariate calculus, and linear algebra, and fundamental probability/statistics. The last might be the most important. Math in general is most important imo.

Otherwise idk, history tailored to your heritage and locale. A general survey of "the great books of western civilization", no need to read entire works but they should get tastes of the important stuff. Plato and Aristotle especially. See what they like at that point and encourage any productive interests. I got a lot out of reading classical literature and philosophy as a teenager but not when I hated it and was forced into it.

I don't have any specific references to recommend except MIT OCW for math, if you choose to do relatively advanced math like I recommened.

I guess if I had to choose some specifics:
- Some selection of Plato's Socratic dialogues. The death of Socrates or whatever it's called at a bare minimum
- Aristotle's metaphysics
- The illiad and odyssey (selections, where appropriate)
- Shakespeare's greatest plays. Hamlet for sure.
- LOTR and the Hobbit especially as an entryway into learning about myth, linguistics, and northern European history and legend. Branch into Beowulf if relevant. Benefit of being kid friendly.
- Jane Austens books are relatively kid friendly iirc and very valuable
And if you're Christian obviously you should pretty intensively, but not feverishly or forcibly (that can cause resentment), study the Bible.
- I wouldn't bother with Nitchy or Choppyhour or Corncob or any of that shit even if you personally like depressing philosophy or literature. Let your kids be happy while they can.

I'm a 32 year old childless boomer so some of this might be too mature, use your own judgement. I was "homeschooled" pretty badly and still managed to end up ok so don't worry too much. I didn't get much direct instruction but having fairly high level books sitting on the shelf I could read when I wanted was a tremendous boon.

Do make sure they are prepared to do their absolutely best on the SAT and are prepared to blitz through college. If I had that I'd be a multimillionaire by now, but I had to take algebra in college and did not get into a great school which set me back significantly. Also dont beat your kids or psychologically torture them. Try to keep them away from the Internet as well.

>>25320854
Oh re: Linguistics probably not a bad idea to have them study an ancient language like Latin or Koine Greek or whatever if they seem interested in it.

As far as specific sciences the main thing that will benefit them imo (not that it's sufficient in itself) is to encourage self learning anywhere and everywhere.

>>25320854
>>25320861
Two last things:
- you'll have to research everything I mentioned on your own, extensively. I'm not giving you enough detail to just hand the books mentioned to your kid and have a guaranteed fruitful outcome.
- in general you should understand the material at the level you want your child to learn it. If not, outside tutoring might be necessary. Much as AI is distasteful it can help here.

Good luck op

Other anon is right, math is good.
Teaching the trivium is also a must.

Teach at least one other language, preferably one of the academic languages. You may need an outside teacher for this if you are a monolingual. Good choices would be French, German, Russian, Latin, or Classical Greek.

If you are smart, hopefully the young will be too. You will be able to teach at a much better pace than normal schooling. If you really need a framework to figure out what to teach look for a historical curriculum. Once they are in teenage years let them pick specific topics to focus on, you should be done with most of the prerequisite stuff by then. Don't let them pick everything, but at least a few "classes" that they will enjoy.

Homeschooling is not necessarily difficult as much as it is demanding. The ideal outcome of homeschooling is that you give your child the foundations of knowledge and instill within them the passion of learning, so that you don't have to keep teaching them when you become unable to keep up with the expanding breadth of information they wish to engage with.

If it is too much to gather the necessary resources from this information to create a homeschool curriculum, the task of complete homeschooling may be too much for you. This is fine. I was only partially homeschooled, and that can work too given the prior stated goal.

Whatever you do, keep your kid away from the schizophrenia machine that is the internet. You wouldn't want to raise an anon, would you?

>>25320807
>Metaphysics
The Talmud
>Epistemology
Why Trust Science? - Naomi Oreskes
>Ethics
How to Be an Antiracist - Ibram X. Kendi
>Politics
The Communist Manifesto - Karl Marx
>Aesthetics
Everyone Poops - Tarō Gomi