Earlier quoted context omitted.
Unfortunately this argument, while imho entirely valid and also frequently seen in discussion, is unable to stop the massive train that has been set in motion. There are various types of retorts: i) the brain is also doing gradient descent; ii) what the brain does does not matter (if you can fake intelligence you have intellegence) iii) the pace is now so fast that has not happened in decades will happen in the next…
If not convincing what argument for and against do you think is the strongest?
There is a case to be made that with sufficient ingenuity at some point people will expand the algorithmic toolkit into more flexible and powerful dimensions. It may integrate formal logic in some shape or form, or yet to be conceived mathematical constructs.
But the type of mental leap that I think would be required just to breakout of the statistical fitting straight-jacket cannot be invented to satisfy the timing of some market craze.
If you look at the broad outline of the development of mathematics there are many areas where we have hit a complexity wall and generations of talent have not advanced an iota.
Even if we condition on some future breakthrough, the next level of mathematical / algorithmic dexterity we might reach will follow its own intrinsic logic, which will probably be very interesting but may or may not have anything to do with human intelligence.