Sorry, late reply, hope you get this!
I believe it's totally "system 1", and actually by design.
First of all it's not a new kind of NN, it's more about applying a given problem to another technique, name consider math syntax as just another kind of language:
> represent complex mathematical expressions as a kind of language and then treating solutions as a translation problem
(which might seem obvious but I guess it took that much refinement to yield actual results)
Now, take these quotes, emphasis mine:
> Humans who are particularly good at symbolic math often rely on a kind of intuition. They have a sense of what the solution to a given problem should look like
> By training a model to detect patterns in symbolic equations, we believed that a neural network could piece together the clues that led to their solutions, roughly similar to a human’s intuition-based approach to complex problems.
Intuition, intuition-based approach: this is exactly what system 1 represents.
Also note the results:
> Our model demonstrated 99.7 percent accuracy when solving integration problems, and 94 percent and 81.2 percent accuracy, respectively, for first- and second-order differential equations.
One major difference between systems 1 and 2 is that 1 is fuzzy, intuitive, it's not always exact, it's very analog; whereas system 2 is able to be correct, exact, precise — and like the researchers themselves validating the 5,000 answers, you'd expect a "well trained" math intelligence to solve 100% (or close enough) of these problems. It may take time but give yourself 20 years and you'll get there no doubt; whereas this narrow language-AI with one hundred million examples still makes mistakes.
Very system 1 indeed.