At a dinner I attended some years ago, 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. For more see the following link...
https://www.quantamagazine.org/20151203-big-datas-mathematical-mysteries/
Duke Mathematics Professor Ingrid Daubechies is featured in the December 2015 issue of Quanta Magazine.