> 1. Young children seem to have the biggest capability in learning languages.

Is there any evidence that this is actually due to their capability? I would say it's far more likely it's their environment. IE, people are constantly talking to young kids. They simplify what they say to make themselves understood. And children have a huge incentive to learn to communicate - to get what they want from parents, or just understand the world around them. The same isn't true for a grown adult trying to learn a second language, in isolation, that they don't really need in their day to day lives.

Disclaimer: this is pure conjecture.

There's extensive research literature strongly suggesting an age link: https://scholar.google.com/scholar?q=language%20learning%20a...

I'm also aware of a few other age/skill type relations.

Musical ability frequently manifests early -- by age 4-5 in numerous historical cases.

Talents requiring physical coordination -- ballet and gymnastics -- around age 9-10 by Russian tradition.

Maths and scientific curiosity perhaps early adolescence.

Complex logic and activities requiring a fully developed inhibitory function (avoiding reflex and rash actions) possibly early 20s.

I'm suspecting other forms of more synthetic (as in: assembling from parts) logic might not develop fully until the 30s or 40s. Other skills might similarly not develop until later.

My guess is that math teaching can be a benefit to anyone at any age, but the usual curriculum on average mainly teaches people to hate math. (That's what's happening with my niece in grade school right now.) For some kids arithmetic may be boring, but at least it's easy, and they suffer less of this damage. If you start it later when they're readier, more of them will be open to learning a little actual math, not just gritting through baffling seemingly-arbitrary procedures.

Montessori schools are said to be better on this score, though I haven't looked into them.

I've been looking at John Cleese's presentations on creativity, and suspect he's very much on to something with the idea of play and humour as key to real learning. I also think that there are approaches which take this too far (video games and such), though I've learned a number of things from unexpected places.

Neal Stephenson's Cryptonomicon, The Baroque Cycle, and Anathem, for example, are all explorations of ideas. The first two of business, banking, and money, in contemporary and historical times, respectively. The latter covers a great deal of historical thought.

Better authors of topics often incorporate humour in their writing -- someting the past few generations of academic literature would do well to consider. OTOH, it's a cure for insomnia.