
Behind Wolfram Alpha’s Mathematical Induction-Based Proof Generator - eusebio
http://blog.wolfram.com/2016/07/14/behind-wolframalphas-mathematical-induction-based-proof-generator/
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aab0
It seems kind of strange that he never thought of using computer proof systems
for checking whether his proofs were right in class, and that he took a
pattern-matching approach rather than using any of the existing AI proof-
deriving systems like
[https://arxiv.org/abs/1606.04442](https://arxiv.org/abs/1606.04442) or
[https://intelligence.org/2013/12/21/josef-urban-on-
machine-l...](https://intelligence.org/2013/12/21/josef-urban-on-machine-
learning-and-automated-reasoning/)

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squobias
There is literally almost a century of research in this area, and even a
decade+ of much more impressive work on the natural language front.

If you care about anything beyond problem sets in freshman math courses, this
post is noise, not signal.

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auggierose
Well, that century of research can be summed up like this: There is no good
induction based proof generator.

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squobias2
That's simply not true. This isn't the first, and it's very, very likely not
the best.

Google the term invariant generator. There are many impressive inductive
invariant generators for interesting and challenging theories that contain the
sorts of formulas this tool appears to handle (ie that summation is for loop).

In fact, the field of inductive invariant generation is so well-established
that there are de facto benchmarks that the author could evaluate his work
against, if he cared to make the claim you've made here.

Going from an inductive invariant to an informal English prose proof is
slightly less well-trodden territory, but this isn't the first piece of work
to do that, either.

I don't mean to disparage the product innovation here, but that first sentence
needs to be edited out. Perhaps the right way of saying this is that the step-
by-step integral solver for WolframAlpha is a really nice product, but it
would have been dishonest to claim it was the first algorithm for computing
indefinite integrals.

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auggierose
It seems to me that all of these approaches are very limited in scope (mainly
linear arithmetic), and only capable of analysing pretty simple programs.
That's not the kind of induction proofs I deal with on a daily basis, which
prove arbitrary mathematical theorems. For those things you need to use just
hard manual sweat work.

