Mathematical Intuition, Deep Learning, and Robbins’ Problem

The present article is an essay about mathematical intuition and Artificial intelligence (A.I.), followed by a guided excursion to Robbins’ Problem of Optimal Stopping. The latter is still open. The first part of the essay (Sect. 1 to Sect. 4), is written in a narrative style with well-known examples and an easily accessible terminology. It is easy to read. Its goal is to motivate mathematicians to think about certain aspects of A.I., and to prepare people in A.I. for the special features of Robbins’ problem. The major objective is presented in the second part (Sect. 5 to Sect. 13). It is to guide readers through the probabilistic intuition behind Robbins’ problem and to show why A.I., and in particular Deep Learning, may contribute an essential part in its solution. This article is an essay, because it contains no new mathematical results, and no implementation of deep learning either. However it presents a clear mission statement which seems important to us. We substantiate it by proposing two concrete challenges to view and solve the main part of the problem.