[jp57]

The estrangement he observes aren't that surprising, in either direction. Many universities have both Math and Applied Math departments. Why have both unless the mathematicians in the Math department don't want to work on applications? I have spoken with people who say if you're working on an application, "it's not really math."

In biology, there is almost certainly a self-selection effect in which the field attracts people who want to study science but are not comfortable with math, or just people who have a particular interest in plants or animals, which is uncorrelated with math skills.

I suspect there is a self-selection effect in the other direction too. I was always good at math, but I never wanted to major in it or go to grad school in it. I got a PhD in AI and machine learning, which was quite mathematical enough, and yet I can't recall ever interacting with anyone from the math department. As far as I knew, they wanted to do "pure math" and weren't interested in applications. So the people who want to do practical things select them selves into other majors like physics, engineering, and computer science.

[nyssos]

> Many universities have both Math and Applied Math departments. Why have both unless the mathematicians in the Math department don't want to work on applications?

"Applied Mathematics" as a field is not literally "mathematics applied to something"; it's a fuzzy group of related topics (things like numerical analysis, PDEs, or computational linear algebra) that's grown large and culturally distinct enough to have its own department, much like theoretical CS or statistics. There are plenty of "applied" mathematicians who don't work on applications, and some "pure" mathematicians who do.

[Aromasin]

Applied Mathematics certainly has the intention of using Math to solve problems from other fields though. I studied Robotics, and shared several classes with people from the Applied Mathematics course; * Transportation Modelling (using math to model transport on roads, rail, and shipping, and solve optimisation problems) * Computer Vision (using math to recognise patterns in images) * Biomechanics (using math to model the movement and formation of all things biology; we did everything from a sperm cell locomotion to an Achilles tendon spring strength)

There were others, but all of them had a very practical purpose, and most of the people I spent time with on the Applied Mathematics course were actively pursuing a career in engineering of some sort, while the Mathematics course was made up of either Pure Math people looking to go into academia, or people destined for finance.

[jltsiren]

Each field has its own culture and its own way of thinking. People are often socialized to a particular culture in the university or even earlier, and it sticks. You can learn other fields on your own, but it's hard to adopt the culture without socialization.

I did theoretical computer science in the university, leaning towards more applied stuff by the end of my PhD. I'm still a computer scientist at heart. I can follow some topics in research mathematics, but I don't think like a mathematician and I'm not interested in the same things. I work in bioinformatics these days, but I often zone out when people start talking about the stuff that goes in the results section of a paper. I'm not a bioinformatician, and I'm not interested in the same things. I've seen a similar culture gap between bioinformatics and "proper" biology, but I don't have first-hand experience with that.

[kridsdale1]

“Pure Math” might as well be poetry, just in a given linguistic domain.