# The Use of Deep Learning for Symbolic Integration: A Review of (Lample and Charton, 2019)

arXiv: https://arxiv.org/abs/1912.05752 · HTML: https://mlsanity.com/paper/1912.05752/

## Key facts

- Cited by 11 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 12 Dec 2019.

## Built on by (most cited first, 11 of 11)

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- [The Liouville Generator for Producing Integrable Expressions](https://mlsanity.com/paper/2406.11631/) (2024)
- [Transformers to Predict the Applicability of Symbolic Integration Routines](https://mlsanity.com/paper/2410.23948/) (2024)
- [Tree-Based Deep Learning for Ranking Symbolic Integration Algorithms](https://mlsanity.com/paper/2508.06383/) (2025)
- [Feynman on Artificial Intelligence and Machine Learning, with Updates](https://mlsanity.com/paper/2209.00083/) (2022)
- [SC-Square: Future Progress with Machine Learning?](https://mlsanity.com/paper/2209.04361/) (2022)

## Abstract (arXiv)

Lample and Charton (2019) describe a system that uses deep learning technology to compute symbolic, indefinite integrals, and to find symbolic solutions to first- and second-order ordinary differential equations, when the solutions are elementary functions. They found that, over a particular test set, the system could find solutions more successfully than sophisticated packages for symbolic mathematics such as Mathematica run with a long time-out. This is an impressive accomplishment, as far as it goes. However, the system can handle only a quite limited subset of the problems that Mathematica deals with, and the test set has significant built-in biases. Therefore the claim that this outperforms Mathematica on symbolic integration needs to be very much qualified.