reading through this I eventually realized a situation similar to my experience of it is what my dog sees if I attempt to explain Python programming to him.
I really don’t think IQ has much to do with it. Understanding this stuff is like a skill you practice. Yes, granted, if you had a low IQ your chances of ever understanding it goes down, if you have a high IQ maybe you can gain the prerequisite understanding faster.
A lot of maths is about both being able to wrap your head around hard problems and gaining the prerequisite knowledge to make it easier to do so.
I recently saw a photo of an alligator lying on top of a pool floatie shaped like an alligator. That alligator could be trained in every way possible for ten years, and never ever recognize the mutual resemblance.
Like you, I wonder if we will soon cross the boundary where we are the alligator.
(I suspect that we have been the alligator all along, outside the context of AI.)
The difference is your dog will never understand the Python code but you could probably understand this post in a matter of days or weeks if you really wanted to. Can we all please stop acting like this Terry guy is so special?
I certainly do not think that the average HN reader "could probably understand this post in a matter of days or weeks". I think the level of background information you need is something like an undergraduate degree in mathematics and at many universities that's probably not enough either.
There's a difference between understanding something and being able to do something. For example you can get a broad understanding of what calculus does in a matter of minutes: a derivative is just the rate of change of a curve, and an integral is the total area under a curve - you're practically there! Of course it'd take months of work to understand how to apply it yourself, let alone all the tricks involved, but a basic understanding of what stuff is, is very easy to obtain.
And I think that generalizes to math. Its normal presentation is completely impenetrable due to a large use of symbols and terms with no outside meaning (or, even worse, a meaning that contradicts the colloquial usage). But I think if we somehow resolved that issue, the average person would be fully capable of following along even if they're going to have to take everything at face value as opposed to being able to meaningfully understand the exact methods and tricks being used to get from A to B.
I basically completely disagree with your analysis. I am already taking into account the "understanding vs doing" distinction in my assessment. I think it takes ~an undergraduate math education to have the background to work through this post, but there's no way that most people with that background would be able to produce it.
If, like the vast majority of people, you have never studied math past a college calculus sequence and perhaps a (practically-oriented) linear algebra class, then you are missing some pretty fundamental ways of viewing and thinking about math. The basic mechanisms of algebra, for one: spaces and operations, morphisms, products and quotients... You don't know what a group is, never mind the idea of a group action. You don't have any familiarity with some basics of geometry: the Riemann sphere, Mobius transformations... And you certainly don't know anything about algebraic geometry: what an affine variety is, what birational equivalence is, what a fiber is.
All of these are concepts required to understand this blog post. And it's not just a matter of understanding the definitions of the terms, but having at least some intuition of what they really mean and how they work. Most people cannot go from zero to understanding all of this in a few days or a couple weeks, at least not for any reasonable definition of "understanding". There's too much basic mathematical background that's missing.
And chances are that humanity at large will be soon trying to follow ai inventions and discoveries not unlike your dog follows your Python code.