2) How is a solution by LLMs supposed to be verified without such a formalisation?

I am pretty sure that a finetuned smaller model would be better and faster for this task. It would be great to start finetuning and sharing such smaller models: they do not really have to be really better than commercial LLMs that run online, as long as they are not at least worse. They are already much faster and cheaper, which is a big advantage for this purpose. There is already need for these tasks to be offline when one cannot share the data with openai and the like. Higher speed and lower cost also allow for more experimentation with more specific finetuning and prompts, with less care about token lengths of prompts and cost. This is an application where smaller, locally run, finetunable models can shine.

- I interpreted the comment in the context of the answer to a specific article/interview. In the linked content, for example, there is a video of a 2.5yo doing a "flashcard class". While I do not think there is anything inherently harmful or anything, it is not a way that 2.5yos learn about the world, and even if it is not harmful it is not needed for 2.5yos to sit on a chair and doing a class to learn about the world. Their curiosity and own exploration drive is enough for pulling them into learning, and this is what I mean by parents should feed, ie see what their kids are most curious and interested in and feeding them inputs to that direction. The comment you answered to was referring to this article, and I interpreted your answer in that context. If I misinterpreted anything, I can only see the context that is shared here, not in your mind.

- To reiterate and clarify more on the context, "Speaking and reading to children is a natural activity" is _not_ what OP was about. What OP was about is applying a specific strategy for kids at 2+ years, ie to learn to read using a specific exploitation-based approach. If that is all you meant by your previous comment, then you may want to reread the comment you answered to from that perspective. Nobody here is saying "leave the kids do what they want and do not care about interacting with them much/talking around them" that you seem to suggest. When I say parents building upon kids' own curiosity and exploration drive I mean seeing what sort of inputs their kids become more curious and interested in at a certain time and feeding them inputs like that. When a kid starts being interested in sounds and music, feed them with sounds and music and sound/music-related books and toys. There is no handbook that is gonna say which month and day exactly this should happen for a specific kid.

- I may miss a lot of knowledge indeed, but I still find setting goals of "maximising language exposure" and "maximising IQ" weird and unclear. No, I have never read or heard this way of approaching development and learning. Parents doing their best and being mindful of the importance of language exposure is different than "maximising" anything. Maximising with respect to which parameters? Even defining this as an optimisation problem, any complex optimisation problem like this is a tradeoff between different parameters and outcomes. What happens to the other parameters and outcomes when you optimise on just one?

- If "you do not speak the jargon" is what you prefer to focus, just say that and any more discussion will not be needed.

Current research in early mathematical education now focuses on teaching certain spatial skills to very young kids rather than (just) numbers. Mathematics is about understanding of relationships, and that is not a detached kind of understanding that we can make into an algorithm, but deeply invested and relational between the "subject" and the "object" of understanding. Taking the subject and all the relations with the world out of the context of learning processes is absurd, because that is in the exact centre of them.

For example

> child language development milestones that are waymarked by age down to the month

is totally false. It is quite known that developmental milestones are acquired by children in different times and even in different orders and sequences. This "down to the month" is pure non-sense for most of the milestones.

Young children are better served to be guided by their own curiosity, interest and exploration drives and which parents feed with variable inputs and building upon, rather than by anxious parents feeding them with whatever terabytes of exploitation-intended information they think is gonna "serve to maximize IQ".

Yes, reading to kids in certain ways (using numbers/spatial relationships/theory of mind stuff/interactively) has been found in some studies to correlate with certain outcomes but there is nothing to suggest a totally linear relationship such that talking to a kid 24/7 since the womb is gonna produce the next Einstein.

Not just that: people learn mathematics mainly by _thinking over and solving problems_, not by memorising solutions to problems. During my mathematics education I had to practice solving a lot of problems dissimilar what I had seen before. Even in the theory part, a lot of it was actually about filling in details in proofs and arguments, and reformulating challenging steps (by words or drawings). My notes on top of a mathematical textbook are much more than the text itself.

People think that knowledge lies in the texts themselves; it does not, it lies in what these texts relate to and the processes that they are part of, a lot of which are out in the real world and in our interactions. The original article is spot on that there is no AGI pathway in the current research direction. But there are huge incentives for ignoring this.

Blind people can have spatial reasoning just fine. Visual =/= spatial [0]. Now, one would have to adapt the colour-based tasks to something that would be more meaningful for a blind person, I guess.

[0] https://hal.science/hal-03373840/document

Not all world is "big data".

Where do they belong? When we set forever chemical loose in the environment, it is expected that a quantity of them will reach the ones in the top of the food chain, which humans are. Where are forever chemicals supposed to end up when we decide it is less costly economic-wise to use them?