<i><a href="https://bookstore.ams.org/pcms-25/">The Mathematics of Data</a></i> may go some way towards answering your question.  As one example of a mathematically interesting topic that is motivated by data science, you might want to look at the concept of <a href="https://www.ams.org/journals/bull/2008-45-01/S0273-0979-07-01191-3/S0273-0979-07-01191-3.pdf">persistent homology</a>.