Maybe the problem isn't the algorithm but the hardware. Numerically simulating the thermal flow in a lightbulb or CFD of a Stone flying through air is pretty hard, but the physical thing isn't that complex to do. We're trying to simulate the function of a brain which is basically an analog thing using a digital computer. Of course that can be harder than running the brain itself.
If you think of human neurons they seem to basically take inputs from bunch of other neurons, possibly modified by chemical levels and send out a signal when they get enough. It seems like something that could be functionally simulated in software by some fairly basic adding up inputs type stuff rather than needing the details of all the chemistry.
Isn’t that exactly what we’re currently doing? The problem is that doing this few billion times for every token seems to be harder than just powering some actual neurons with sugar.
The algorithm (of a neural network) is simulating connections between nodes with specific weights and an activation function. This idea was derived from the way neurons are thought to work.