[lll-o-lll]

I really appreciate your response.

There seems to be a fundamental difference in mindset between the “applications” based learning of mathematics, and this pure math based version. Are there benefits to be had for a person that only intends to use mathematics in an applied fashion?

[chongli]

This depends on who you ask. Personally, I found studying pure math incredibly rewarding. It gave me the confidence to be able to say that I can look at any piece of mathematics and figure it out if I take the time to do so.

I can't speak for those who have only studied math at an applied level directly. My impression of them (as an outsider but also a math tutor) is that they are fairly comfortable with the math they have been using for a while but always find new mathematics daunting.

I have heard famous mathematicians describe this phenomenon as "mathematical maturity" but I don't know if this has been studied as a real social/educational phenomenon.