What do applied mathematicians deal with?

[mech-eng]

TL;DR Summary

I am looking for the basic differences of applied mathematicians from pure mathematicians and physicists.

Hello. I have this question in my mind many years. I need to clarify my confused mind. I wonder how applied mathematicians differ from pure mathematicians and physicists. Many years ago I read that applied mathematicians and pure mathematicians do not like each other. Is this true? To me, as the name suggests, applied mathematics is application of mathematics, and this mostly happens in physics, biology (maybe computational biology?), chemistry and economics.

1. Physics also deals a lot with mathematics. Physicists already apply mathematics. There are even fields as "mathematical physics" and the books written on that fields full of application of mathematics to physical phenomena.

2. I have checked the fields of pure mathematics. One of them was topology and geometry. But aren't topology and geometry also find application in physics, so they are applicable fields, not pure.

Would you please explain the facts?

Regards,

 

[PeroK]

Pure mathematics is like classical music; applied mathematics is more like jazz; and physics is like rock and roll.

 

[jedishrfu]

A physicist would throw some equations together on the blackboard and say see that seems to work.

The applied mathematician would look at the mess and say we need to clean that up a bit.

The pure mathematician would say what's with all those numbers and ugh you use that brand of chalk, I only use Hagoromo chalk to write my sublime proofs found in The Book.



Dyson's life story may give an idea of the differences too:

https://plus.maths.org/content/freeman-dyson-dies-96

 

[jedishrfu]

And here's Feynman's take on mathematicians:

 

[fresh_42]

1. Physics also deals a lot with mathematics. Physicists already apply mathematics. There are even fields as "mathematical physics" and the books written on that fields full of application of mathematics to physical phenomena.

My mentor used to say: 'There are two types of physicists: mathematicians and blacksmiths.'

This probably describes the mindsets more than the actual fields.

2. I have checked the fields of pure mathematics. One of them was topology and geometry. But aren't topology and geometry also find application in physics, so they are applicable fields, not pure.

You can find applications for almost all parts of mathematics. If you look at the real world and take applied literally, then you are left with statistics and stochastics, maybe also numerical analysis (but this is widely substituted by shear computer power) as applied mathematics, and the rest is pure mathematics, regardless of any flimsy applications notwithstanding.