my entire math life
This is basically the problem with the entire modern educational system.
Time to do unpopular opinion? Time to do unpopular opinion.
Balancing a checkbook is applied addition and subtraction, stuff of the third grade. Okay, yeah, it is a failure of the modern educational system if he hasn’t learned it by now.
Imaginary numbers interact with real numbers (1, 2, π, 1.5, etc) for complex numbers, and are useful if you want to get into engineering or science — you know, high paying jobs.
Remember Tomb Raider? How they make her turn? Quaternions, which use THREE sets of imaginary numbers.
Like how your cell phone gets reception? That requires resonance, the understanding of which can be aided by complex numbers.
And don’t even get me started in the more exotic physics like fluid dynamics or quantum mechanics. That is, the forefront of how planes fly and how computer chips work.
There’s this term, innumeracy, that is to math what illiteracy is to english. One thing that bugs me is when ignorance is paraded about, when one acts as if math is an optional knowledge. Doubly so when it’s the very thing holding them back.
The failure is not in teaching these things, but the lack of teaching about why we should care about these things.