# Artificial Intelligence and Mathematics

## Introduction

An Essay on the Psychology of Invention in the Mathematical Field by Jacques Hadamard, The Psychology of Advanced Mathematical Thinking by David Tall, What is Mathematical Thinking by Robert J. Sternberg, Mathematical Thinking and Learning by Herbert P. Ginsburg, Joanna Cannon, Janet Eisenband and Sandra Pappas, Neuroscience of Mathematical Cognitive Development: From Infancy Through Emerging Adulthood by Rhonda D. Brown, Mathematical Problem Solving by Alan H. Schoenfeld, How to Solve It: A New Aspect of Mathematical Method by George Polya, The Computer Modelling of Mathematical Reasoning by Alan Bundy, Modelling the Way Mathematics is Actually Done by Joseph Corneli, Ursula Martin, Dave Murray-Rust, Alison Pease, Raymond Puzio and Gabriela R. Nesin, Advancing Mathematics by Guiding Human Intuition with AI by Alex Davies, Petar Veličković, Lars Buesing, Sam Blackwell, Daniel Zheng, Nenad Tomašev, Richard Tanburn, Peter Battaglia, Charles Blundell, András Juhász, Marc Lackenby, Geordie Williamson, Demis Hassabis and Pushmeet Kohli and Proof Assistants: History, Ideas and Future by Herman Geuvers.

## Knowledge Representation and Reasoning

Deep Learning for Symbolic Mathematics by Guillaume Lample and François Charton, Analysing Mathematical Reasoning Abilities of Neural Models by David Saxton, Edward Grefenstette, Felix Hill and Pushmeet Kohli and Deep Neural Solver for Math Word Problems by Yan Wang, Xiaojiang Liu and Shuming Shi.

## Function Approximation

Multilayer Feedforward Networks are Universal Approximators by Kurt Hornik, Maxwell Stinchcombe and Halbert White, Neural Network Approximation by Ronald DeVore, Boris Hanin and Guergana Petrova and Expressivity of Deep Neural Networks by Ingo Gühring, Mones Raslan and Gitta Kutyniok.

## Differential Equation Solving

DGM: A Deep Learning Algorithm for Solving Partial Differential Equations by Justin Sirignano and Konstantinos Spiliopoulos and DeepXDE: A Deep Learning Library for Solving Differential Equations by Lu Lu, Xuhui Meng, Zhiping Mao and George E. Karniadakis.

## Physics-informed Neural Networks

Physics-informed Neural Networks: A Deep Learning Framework for Solving Forward and Inverse Problems Involving Nonlinear Partial Differential Equations by Maziar Raissi, Paris Perdikaris and George E. Karniadakis.

## Program Synthesis

A Neural Network Solves and Generates Mathematics Problems by Program Synthesis: Calculus, Differential Equations, Linear Algebra, and More by Iddo Drori, Sunny Tran, Roman Wang, Newman Cheng, Kevin Liu, Leonard Tang, Elizabeth Ke, Nikhil Singh, Taylor L. Patti, Jayson Lynch, Avi Shporer, Nakul Verma, Eugene Wu and Gilbert Strang.

## Symbolic Regression

Integration of Neural Network-based Symbolic Regression in Deep Learning for Scientific Discovery by Samuel Kim, Peter Y. Lu, Srijon Mukherjee, Michael Gilbert, Li Jing, Vladimir Čeperić and Marin Soljačić, A Demonstration Platform for Deep Symbolic Regression by Sookyung Kim, Joanne T. Kim and Brenden K. Petersen and An Interactive Visualization Platform for Deep Symbolic Regression by Joanne T. Kim, Sookyung Kim and Brenden K. Petersen.

## Theorem Proving

Learning from Previous Proof Experience: A Survey by Jörg Denzinger, Matthias Fuchs, Christoph Goller and Stephan Schulz, Automatic Acquisition of Search Control Knowledge from Multiple Proof Attempts by Jörg Denzinger and Stephan Schulz, Reinforcement Learning of Theorem Proving by Cezary Kaliszyk, Josef Urban, Henryk Michalewski and Miroslav Olšák, Learning Heuristics for Automated Reasoning through Deep Reinforcement Learning by Gil Lederman, Markus N. Rabe and Sanjit A. Seshia, DeepMath - Deep Sequence Models for Premise Selection by Geoffrey Irving, Christian Szegedy, Alexander A. Alemi, Niklas Een, François Chollet and Josef Urban, Deep Network Guided Proof Search by Sarah M. Loos, Geoffrey Irving, Christian Szegedy and Cezary Kaliszyk, Generative Language Modeling for Automated Theorem Proving by Stanislas Polu and Ilya Sutskever, Learning to Prove with Tactics by Thibault Gauthier, Cezary Kaliszyk, Josef Urban, Ramana Kumar and Michael Norrish and Hierarchical Invention of Theorem Proving Strategies by Jan Jakubův and Josef Urban.