OP isn’t referencing “the imaginary numbers” as in the set of numbers that are multiples of the square root of -1. They’re referencing the fact that in grad school, you’re told “forget everything you’ve been taught about math up to now. We’re going to start with a couple of basic assumptions, and extrapolate all of Cartesian Algebra (the math taught in preschool through undergrad) from those assumptions. Now, let’s see what other algebras we can create by changing those assumptions.”
The only two “numbers” that need to exist to derive all of Cartesian Algebra are zero (additive identity) and one (multiplicative identity). All other numbers are just convenient identifiers that can be extrapolated rather than assumed, hence the overly simplified “all numbers are imaginary”.
This is similar to other STEM subjects, like how in Physics you’re taught Newtonian physics, then you’re taught why Newtonian physics is just a tiny subset of relativistic physics, and then in grad school you are taught everything you know is just a tiny subset of quantum mechanics. What’s taught in undergrad is “good enough” for your average person to do really complex things in typical day to day life, but for someone dedicating their academic career to the subject, they need to learn the dirty, overly complex details to have a true understanding of the subject.
OP isn’t referencing “the imaginary numbers” as in the set of numbers that are multiples of the square root of -1. They’re referencing the fact that in grad school, you’re told “forget everything you’ve been taught about math up to now. We’re going to start with a couple of basic assumptions, and extrapolate all of Cartesian Algebra (the math taught in preschool through undergrad) from those assumptions. Now, let’s see what other algebras we can create by changing those assumptions.”
The only two “numbers” that need to exist to derive all of Cartesian Algebra are zero (additive identity) and one (multiplicative identity). All other numbers are just convenient identifiers that can be extrapolated rather than assumed, hence the overly simplified “all numbers are imaginary”.
This is similar to other STEM subjects, like how in Physics you’re taught Newtonian physics, then you’re taught why Newtonian physics is just a tiny subset of relativistic physics, and then in grad school you are taught everything you know is just a tiny subset of quantum mechanics. What’s taught in undergrad is “good enough” for your average person to do really complex things in typical day to day life, but for someone dedicating their academic career to the subject, they need to learn the dirty, overly complex details to have a true understanding of the subject.