Mathematical reasoning would be one of the next frontiers for artificial intelligence to make significant progress. The ongoing surge to solve math word problems (MWPs) and hence achieve better mathematical reasoning ability would continue to be a key line of research in the coming time. We inspect non-neural and neural methods to solve math word problems narrated in a natural language. We also highlight the ability of these methods to be generalizable, mathematically reasonable, interpretable, and explainable. Neural approaches dominate the current state of the art, and we survey them highlighting three strategies to MWP solving: (1) direct answer generation, (2) expression tree generation for inferring answers, and (3) template retrieval for answer computation. Moreover, we discuss technological approaches, review the evolution of intuitive design choices to solve MWPs, and examine them for mathematical reasoning ability. We finally identify several gaps that warrant the need for external knowledge and knowledge-infused learning, among several other opportunities in solving MWPs.

We can think of the humongous field of deep learning as the Earth's crust, floating on a mantle of mathematical and algorithmic understanding. It is a vast sphere of knowledge that is divided into specializations, similar to how tectonic plates divvy up our world. Most important of all, the specializations of deep learning -- natural language processing and cognitive computational science, for instance -- can coincide to form beautiful mountain ranges that help to define landmark areas of deep learning. Curriculum learning is one such Himalayan-range of a deep learning technique between the two fields of AI-oriented cognitive science and NLP. While currently not known to many practitioners or enthusiasts (its Wikipedia page is currently pending approval), for those who choose to explore this hidden gem, the find is worth the time.

In this article, I will cover a new Neural Network approach to solving 1st and 2nd order Ordinary Differential Equations, introduced in Guillaume Lample and François Charton (Facebook AI Research)'s ICLR 2020 spotlight paper, "Deep Learning for Symbolic Mathematics"¹. This paper tackles symbolic computation tasks of integration and solving 1st & 2nd order ODEs with a seq2seq Transformer, we will focus on the latter today. To give context to this paper, although Neural Network methods have seen great success in clearly structured statistical pattern recognition tasks -- e.g. Not only does Symbolic Computation require AI to infer complex mathematical rules, they also require a flexible, contextual understanding of abstract mathematical symbols in relation to each other. At the time of authoring, Computer Algebra Systems (CAS) (such as Matlab, Mathematica) held state-of-the-art performance on symbolic mathematics tasks, driven by a backend of complex algorithms such as the 100-page long Risch algorithm for indefinite integration.

If today's college students could find a way to get their hands on a copy of Facebook's latest neural network, they could cheat all the way through Calc 3. They could even solve the differential equation pictured above in under 30 seconds. Okay, so maybe this isn't going to be a replacement for Wolfram Alpha anytime soon, but Facebook really did build a neural net that can complete complex mathematical problems for the first time, rather than the plain old arithmetic in which these AI models usually wheel and deal. The work represents a huge leap forward in computers' abilities to understand mathematical logic. The research is outlined in a new paper, "Deep Learning for Symbolic Mathematics," published in arXiv, a repository of scientific research in areas like math, computer science, and physics, run by Cornell University.