I have had the opportunity to work in data-driven analytics across a number of industries, the most advanced ones being the finance and investment folks. Now, I am in the oil and gas sector, where advanced data-driven analytics is starting to find a foot hold though there are skeptics a-plenty. This includes folks to whom a Microsoft Excel is the ultimate analytics tool, and scientists who believe that complex physics cannot be complemented (and in some cases as I believe replaced) by machine learning driven, continuously evolving models.
"… the distinguished differential geometer Eugenio Calabi volunteered to me his tongue-in-cheek distinction between pure and applied mathematicians. A pure mathematician, when stuck on the problem under study, often decides to narrow the problem further and so avoid the obstruction. An applied mathematician interprets being stuck as an indication that it is time to learn more mathematics and find better tools."
Dr. Ingrid Daubechies writes an delightful article in the Wired here, "Machine Learning Works Great — Mathematicians Just Don’t Know Why". She discusses supervised and unsupervised machine learning, with a nod to a bit of magic in machine learning that is still not understood.