Machine-Learning Mathematical Structures

There has been a host of activity in the last 2-3 years to use techniques from modern data science, such as machine learning, data mining, and semantic/linguistic analyses, to understand the fundamental structures of mathematics. In mathematical physics, this began with deep learning explorations of the string landscape. In algebraic geometry, supervised learning has been applied to computing topological invariants as well as finding efficient Groebner bases. In algebra and representation theory, combinatorics, and graph theory, neural classifiers and regressors have been used, for instance, to distinguish finite simple groups, to detect Hamiltonian cycles, and to estimate Laplacian eigenvalues. In symbolic manipulation, neural networks such as the Ramanujan Machine, SciNet, and statistical learning networks have been used to generate the likes of new partial fractions and integral identities. It is clear that this emergent field will play a significant role in experimental mathematics, mathematical physics as well as conjecture formulation in pure mathematics across the disciplines. Such machine learning paradigms in mathematics should be in tandem with Voevodsky's dream of automated theorem proving. Indeed, in light of the interests of this journal, machine learning patterns in Clifford and Grassmann algebras and beyond beckon immediate attention. In this topical collection (in line with an attempted summary of some of the recent progress in the plenary lecture at the 12th International Conference on Clifford Algebras and Their Applications in Mathematical Physics in 2020), we invite experts working on the interface between machine learning and various branches of mathematics to contribute papers of high quality. We bear in mind the huge inter- and cross- disciplinary nature of this collection, and hope it will act as a new forum for dialogues between mathematicians, physicists, as well as computer and data scientists.