Indeed, nowadays no electrical engineer could get along without complex numbers, and neither could anyone working in aerodynamics or fluid dynamics.

The human brain finds it extremely hard to cope with a new level of abstraction. This is why it was well into the eighteenth century before mathematicians felt comfortable dealing with zero and with negative numbers, and why even today many people cannot accept the square root of minus-one as a genuine number.

Given the brief - and generally misleading - exposure most people have to mathematics at school, raising the public awareness of mathematics will always be an uphill battle.

I've never met Hans Rosling, but I just knew him through his many YouTube videos, and they were absolute dynamite.

There can be very little of present-day science and technology that is not dependent on complex numbers in one way or another.

Cardinal arithmetic will be quite important for us, so we spend some time on it. Since, however, it tends to be trivial, we shall not need to spend much of this time on proofs.

A PhD in Mathematics is three years of guessing it wrong, plus one week of getting it right and writing a dissertation.