Mathematics is a beautiful subject. Its symbols, notation and abstract structures
permit us to define, manipulate and resolve extremely complex problems.
The symbols by themselves, however, are meaningless – they are nothing more
than a calligraphic representation of a mental idea. If one does not understand
such symbols, then the encoded idea remains a secret.
Having spent most of my life using mathematics, I am still conscious of the
fact that I do not understand much of the notation used by mathematicians.
And even when I feel that I understand a type of notation, I still ask myself
“Do I really understand its meaning?”. For instance, I originally studied to
be an electrical engineer and was very familiar with i = √−1, especially when
used to represent out of phase voltages and currents. I can manipulate complex
numbers with some confidence, but I must admit that I do not understand the
meaning of i
i
. This hole in my knowledge makes me feel uncomfortable, but
I suppose it is reassuring to learn that some of our greatest mathematicians
have had problems understanding some of their own inventions