I've recently purchased Oliver Byrne's reproduction of Euclid's Elements. It's a beautiful tome, that's rather unique in its presentation of the material as it demonstrates many of Euclid's proofs as lurid and lusciously coloured geometric figures. See below:
So, my question is:
What are some other mathematics books that convey a topic in a manner that breaks from orthodoxy?
Now I doubt there are very many books that meet at the intersection of art and mathematics such as this, so this should not be the sole criteria by which the 'unconventionality' of a book should be judged. In all probability any departure from orthodoxy will likely manifest itself in the form of pedagogical organisation/exposition distinctions, and so this should be the predominant criteria by which you should judge a book's eligibility for recommendation. It would also be appreciated if you could provide a justification as to why you believe a given book is unconventional.
I'm sorry if this is off-topic, hopefully I can at the very least expose a few people to this lovely book.
Best Answer
Carl Linderholm's Mathematics Made Difficult is quite interesting. It was described by Halmos (Linderholm's PhD adviser) as a sort of "mathematical in-joke." But you'll find reviews that, while unanimously positive, are all over the map. I think that officially makes it a work of art, since the meaning of the content is truly in the eye of the beholder (whether that was intentional or not).
At any rate, it revisits elementary mathematics armed with words like "endomorphism" and is full of incredibly weird story-telling.
Despite all the incredibly weird things that happen and its confusing nature, I do think it's nice to be reminded that the germ of our sophisticated modern mathematics is absolutely contained in the "basic math" all children learn. There's also some fun-poking at how asinine things like, for example, "mixed fractions" may be, and what children are subjected to, pedagogically.