From an online discussion this month titled "US Army applying new areas of math", insightful comments by Danny Wells:

I love that new areas of math are being applied, but (as a PhD applied mathematician) I disagree with the quote "Applied mathematics is not a subject classification. It's an attitude".

It has taken me years — an entire career, really — to learn to effectively communicate my mathematical findings to other non-mathematical researchers and effectively bridge these gaps. I know a lot of mathematicians who say "well, sure, I could communicate my work to other fields, but ... <some excuse here>", when the truth is, they just don't have the training or expertise for how to do it. It's not just that they don't want to/are too good to bother/etc./etc. (as much as they would like it to seem that way).

The fact is, translating research findings is hard. Much harder than actually making them. And asking good questions, relevant to the scientific field you are working in, even harder. The quote above reflects a common, damaging hubris in mathematics research and is why most of the "best" math research never gets used in other fields of science.

(cf Good Mistakes (1999-09-06), Good Mathematician vs Great Mathematician (2016-01-03), ...) - ^z - 2019-03-28