1940, with James R. Newman*Mathematics and the Imagination*.

I have always had a soft spot for this book: it was what made me
*excited* about mathematics. Back in the dimly-remembered mists
of the early 70s -- I was about 14 -- my maths teacher lent me his
copy, and it just blew my mind. For the first time I realised there
was more to maths than the, admittedly interesting, but rather
uninspiring, topics in our school text books. I certainly didn't *understand*
all of what I was reading at the time, but it let me glimpse exotic
and fascinating lands, and I wanted to find out more. (I don't suppose
I could honestly claim to understand *all* of it even now -- the
Banach-Tarski paradox, for example, still gives me a headache!) I
believe it is important occasionally to read things one doesn't
understand -- it broadens horizons, and stimulates the mental taste
buds with something a bit spicier than the usual predigested pap. (But
it is also important to realise that that one *doesn't*
understand it, rather than to integrate it as a load of gobbeldygook
into one's world model -- that way lies crank science.)

Sort of like
enjoying the music without quite catching the lyrics.

-- Kevin Leary

[On enjoying a (fiction)
book he didn't quite understand all of]

In retrospect, this is just one of the early popular maths book. Topics include large numbers (introducing the googol), infinities, probability, non-Euclidean geometry, calculus, topology, mathematical games -- all with an emphasis on the weird and paradoxical. There is even a section on fractal curves (not yet called that, of course). The 1940s academic prose style may seem a little precious now, but there is some very deep stuff indeed in here, and it's still well worth a read, whether you are 14, or rather older!