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Comment by brianberns | Hacker News Reader

It seems that the neural net just spits out an answer, rather than deriving it step-by-step like humans do. That's interesting, but would still get you an F on a real calculus test.

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I think the idea with this kind of thing is that ML can make pretty-good guesses really quickly, and then a formalized process can verify them (usually much more quickly than it could derive them). This hybrid model fits lots of different kinds of problems.

Yes, and this is particularly problematic IMHO in sequence-to-sequence translators, as were used here. When fed enough training data, they do an amazing job at aping their training, but they are prone to spout utter nonsense in edge cases, and they don't really (to my knowledge) have any indication that they should have less confidence in one result than in the other.

So best case this system gives black box answers that may or may not hold up in verification. That does not seem to be a very useful way to do mathematical research.

One could view each layer of the neural net as doing "steps". They are rather opaque steps, though.

I think you'll notice that great human mathematicians and integrators also take pretty big jumps in their derivations, if they don't jump directly to the solution.

Going algorithmicly step by step is the clutches you use till you have built a strong enough intuition.

Mathematica doesn't give you a step-by-step derivation for its integration either (although Wolfram Alpha sometimes does). That doesn't bother most people using the software.

I think it's able to verify that the solution is correct, which is more than a lot of students manage.

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