Oh, I’ve thought a great about these things. None of your questions are new to me or are ones I’ve not considered. I did not come to my conclusion quickly.

Here are some more thoughts to ponder:

Children are easier to brain wash than adults and teaching basic math involves a great deal of brain washing. To what extent is it the case that a person with no exposure to algebraic concepts growing up is at a disadvantage to learning algebra as an adult? There is a theory that if one doesn’t learn a language in childhood then it is impossible for them to learn one as an adult. Is something similar applicable to Mathematics?

I do think something similar is applicable - for any subject. I was/am a math teacher and what I've found is those who couldn't learn algebra often didn't understand the 'language' or have a good grasp of what math means (like what is a fraction, what does it represent in real life, etc). Taking time to go over these basic concepts with them vastly improved their mathematical abilities, and eventually most got to the point where they could easily do algebra.

I don't think the issue is necessarily that they're incapable, it's more that they don't have the necessary background intuition or knowledge. At least in the state i taught in, this is not surprising as elementary school teachers often dread math and fail their standardized teaching test math portion several times sometimes. It's the blind leading the blind.

I've also noticed it in reading, when they have teachers who aren't readers themselves trying to teach it to them.

Would you mind sharing your conclusions?

Though I don't know of any studies about algebra in particular, kids show greater neuroplasticity in general than adults. So learning anything as an adult tends to be more difficult.

But I live with an American who reasonably fluent in Norwegian after 2 years of study in their 30s. It's certainly not impossible.

I have no doubt that math, like virtually everything, is more difficult for adults to pick up from scratch.

What is theorized to be impossible is learning a language as an adult if you did not learn a language as a child. That is, if at age 20 you know 0 languages then you’ll never be able really learn a language. For obvious reasons experiments in this regard are few.

My conclusion is that some people simply can’t learn algebra. Be it genetic, environmental, lack of intellectual fortitude, lack of “intelligence”, or any combination thereof it is simply the case that some people can’t learn algebra.

I wonder if you are equating "can't" and "lack of intellectual fortitude" with "aren't truly motivated to do so."

Considering that a small percentage of careers require more than basic algebra/geometry/statistics, it's not hard to see that math has a "why should I learn this?" problem more than a "am I able to learn this?" problem.

Environmental covers a lot. A mal-nourished homeless person probably cannot learn algebra - they would have much more immediate concerns to deal with.

However that feels really different from saying a not insignificant portion of the population, inherently cannot.

Yes everybody can learn to code and get rich if they just put their will into it.