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Is there a machine learning system that is able to "understand" mathematical problems given in a textual description, such as

A big cat needs 4 days to catch all the mice and a small cat needs 12 days. How many days need both, if they catch mice together?

?

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There was a lot of work on this topic at UT Austin, which has now migrated to the Alan Institute.

There is no off-the-shelf software that will answer your question (if there was, DARPA would stop funding its development!), but you can read about the latest development in a number of recent papers.

This paper (Seo et al. EMNLP 2015) discusses the techniques that are used to interpret diagrams that accompany geometry problems, while this one (Hosseini et al. EMNLP 2014) talks about how to automatically parse verbs to interpret the meaning of a question. The 2015 TACL paper (Koncel-Kedziorski et al. 2015) completes this by discussing how to extract the relevant equations from a word problem. Once you have the equations, know what question is being asked, and can interpret any diagrams, you can do most high school math problems.

However, I don't think this is yet a fully reliable system. It is one part of a larger, long running effort to create a program that can achieve higher education certifications in many subjects. You can see many projects related to this at the Alan Institute's website.

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Well this is a relatively new problem very tied to Question Answering. One of the recent systems is EUCLID that can answer those type of question the public Dolphin algebra question set by using a tree transducer cascade approach.

This paper details the proposed model Hopkins, M., Petrescu-Prahova, C., Levin, R., Le Bras, R., Herrasti, A., & Joshi, V. (2017). Beyond sentential semantic parsing: Tackling the math sat with a cascade of tree transducers. In Proceedings of the 2017 Conference on Empirical Methods in Natural Language Processing (pp. 795-804).

In the same sense, SEMEVAL has released a task related to Math QA, you can see the related bibliography and referenced works semeval 2019 task 10 internal.

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  • $\begingroup$ Welcome to AI.SE andres! I like the paper you've cited, but I think your answer could be improved. Question answering is a very old problem. Check out this paper from 1969 for example: dtic.mil/docs/citations/AD0696394. The rest of your answer looks pretty good though. $\endgroup$ – John Doucette Aug 22 '18 at 21:30
  • $\begingroup$ QA pretty Old!!! yes sure. But it is a an open problem and it is very interesting. You can see how it is important for Automatic Assistants, Conversational AI platforms, Knowledge Bases QA, QA over linked data, Qa over hybrid sources. You can also find old systems as LUNAR QA (1977), BASEBALL QA (1961) and new systems as WATSON (2011), MSRA QA, etc. $\endgroup$ – andres Aug 22 '18 at 22:04
  • $\begingroup$ Those look like great sources! You should consider editing your answer to incorporate them. $\endgroup$ – John Doucette Aug 23 '18 at 10:12

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