They give examples of problems their model could solve that Mathematica couldn't (within a 30 second timeout) - and that's awesome. Destroy Mathematica. But, I did anyone notice if there were problems that it couldn't solve that Mathematica could?
More importantly, I'm curious if there are problems that Mathematica knows it can't solve but for which this system silently gives wrong answers.
Another interesting extension to the experiments would be a longer timeout -- 30 seconds seems a bit arbitrary and quite low for a CAS. However, I suspect the reason for that time out is the fact that Mathematica licenses are insanely expensive. Otherwise the 5,000 (actually, only 500) test problems could be run for at least a few minutes at pretty trivial cost. Maybe there's a Mathematica employee here who can suggest Wolfram donate some compute (or at least limited licenses) for a small evaluation cluster. Especially if the authors decide to do follow-up work.
In any case, this is really interesting work. I think deep learning for symbolic mathematics is going to be a super interesting area to watch for a least the next few years. Good work, anonymous author(s).
To explain: the thing that's super interesting to me about this paper (i.e., "strong result" vs. "best paper contender") is not integration per se. It's the possible applications of the method to problems with much, much, much higher computational complexity than integration. On those problems, validating the correctness of a solution is also intractable. In those cases, a sound function approximation approach would be an absolute game changer for symbolic methods.
(Not that integration isn't interesting as well.)
Still, I fear, the numbers are currently too small to get past the information bottleneck (mere thousands). We'll see.
I had trouble finding the test cases they used. Where'd they list them?