Enough admonishment—it's time for the warning. A word of caution, children, before we discuss the arcane contents of this stygian course: some mathematics were not meant for man to understand. This is Cartesian devilry of a black and necromantic sort, dreamed up by the twisted designs of sinister scholastic gods, existing purely to tempt and destroy mankind with its elusive secrets. Topics to be covered include: non-Euclidean geometry, dividing by zero, Cthulu's Principle of Inverse Sanity, approaching and surpassing asymptotes, Fermat's Next-to-Last Theorem, gazing into the depths of a parabola, and the dreaded unit circle. There will be a midterm approximately halfway through the semester, a final exam, and a group project in which you will be made to calculate the precise time of your own death using an abacus made of haunted rosary beads. (source here, do not read it)
I think it might be better to improve one's state when dying by making a rosary of non-haunted abacus beads, but apart from that, is modern mathematics as bad as this?
Well, when his famous curve is put into such asocial purposes as making school grades relative (middle quality grades always being the most and high and low quality having equal minorities, one starts to wonder.
THEN there is the famous "3 i" times "3 i" equals "minus nine", in other words, the assumption that "minus nine" is one number and needs a square root.
And that comes from "if plus nine is a number nine more than zero, there must be a number minus nine which is nine below zero". Which is rubbish. It is rubbish, but it has some conventional uses, like reading thermometres, and such where "zero" means something other than "nothing". But going from "3i * 3i = -9" to an application would get you into trouble. Even for a "numbers' field" a X-axis and a Y-axis would maybe multiply by each other, but hardly each land on the "minus side" of the other while multiplying by itself.
I advocate a return to Greco-Roman, Classico-Mediæval concepts in mathematics. What Euclid and Boëthius hold in common would hardly deserve things like this persiflage, preparing for mathematical studies as if preparing to study black magic.