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.
Not taking a stance on whether "intelligence" can emerge out of gradient descent but it's certainly not biological.
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 five years etc.
None of them is remotely convincing. I would really start getting worried if indeed some of the AI fanboys had a convincing argument. But we are where we are.
Somehow this whole episode will be just another turn of the screw in adopting algorithms in societal information processing. This in itself is fascinating and dangerous enough.