Reddit mentions of Unknown Quantity: A Real and Imaginary History of Algebra

Hey! This comment ended up being a lot longer than I anticipated, oops.

My all-time favs of these kinds of books definitely has to be Prime Obsession and Unknown Quantity by John Derbyshire - Prime Obsession covers the history behind one of the most famous unsolved problems in all of math - the Riemann hypothesis, and does it while actually diving into some of the actual theory behind it. Unknown Quantity is quite similar to Prime Obsession, except it's a more general overview of the history of algebra. They're also filled with lots of interesting footnotes. (Ignore his other, more questionable political books.)

In a similar vein, Fermat's Enigma by Simon Singh also does this really well with Fermat's last theorem, an infamously hard problem that remained unsolved until 1995. The rest of his books are also excellent.

All of Ian Stewart's books are great too - my favs from him are Cabinet, Hoard, and Casebook which are each filled with lots of fun mathematical vignettes, stories, and problems, which you can pick or choose at your leisure.

When it comes to fiction, Edwin Abbott's Flatland is a classic parody of Victorian England and a visualization of what a 4th dimension would look like. (This one's in the public domain, too.) Strictly speaking, this doesn't have any equations in it, but you should definitely still read it for a good mental workout!

Lastly, the Math Girls series is a Japanese YA series all about interesting topics like Taylor series, recursive relations, Fermat's last theorem, and Godel's incompleteness theorems. (Yes, really!) Although the 3rd book actually has a pretty decent plot, they're not really that story or character driven. As an interesting and unique mathematical resource though, they're unmatched!

I'm sure there are lots of other great books I've missed, but as a high school student myself, I can say that these were the books that really introduced me to how crazy and interesting upper-level math could be, without getting too over my head. They're all highly recommended.

Good luck in your mathematical adventures, and have fun!

Downmod any math-phobic comments.

Besides, the poster, John Derbyshire, knows his math.

Unknown Quantity - John Derbyshire

Fearless Symmetry - Avner Ash

Unknown Quantity by John Derbyshire.

EDIT: It deals specifically with algebraic notation. There's a great story on how we came to use "x", and it's mainly due to the French language.

Check out some pop math books.

John Derbyshire's Prime Obsession talks about today's most famous unsolved problem, both the history of and an un-rigorous not-in-depth discussion of the mathematical ideas.

There's also Keith Devlin's Mathematics: The New Golden Age, which, to quote redditor schnitzi, "provides an overview of most of the major discoveries in mathematics since 1960, across all subdisciplines, and isn't afraid to try to teach you the basics of them (unlike many similar books)."

Flatland by Edwin A. Abbott is an interesting novel about dimension and immersion. An absolute classic, first published in 1884.

You should also check out the books on math history.

Journey Through Genius covers some of the major mathematical breakthroughs from the time of the Greeks to modern day. I enjoyed this one.

Derbyshire wrote one too called Unknown Quantity: A Real and Imaginary History of Algebra which I've heard is good.

And finally, you should check out at least one book containing actual mathematics. For this I emphatically recommend Paul Halmos' Naive Set Theory. It is a small book, just 100 pages, absolutely bursting with mathematical insight and complexity. It is essentially a haiku on a subject that forms the theoretical foundation of all of today's mathematics (though it is slowly being usurped by category theory). After sufficient background material is introduced, the book covers the ever-important Axiom of Choice (remember the Banach-Tarski paradox?), along with its sisters, Zorn's Lemma and the Well Ordering Principle. After that it discusses cardinal numbers and the levels of infinity. The path he takes is absolutely beautiful and his experience and understanding virtually drips from the pages.

Oh yeah, there's an awesome reading list of books put out by the University of Cambridge that might be of interest too: PDF warning.

If anyone is interested in the history of algebra, the book Unknown Quantity is a great read.

Unknown Quantity: A Real and Imaginary History of Algebra

Just read unknown quantity. Mostly talks about the history of algebra. Really blew my mind how recent most of our ideas and notation are.

Unknown Quantity: A Real and Imaginary History of Algebra https://www.amazon.com/dp/0452288533/ref=cm_sw_r_cp_apap_ALHeY6WCDhbXV

For more concerning al-Khwarizmi and the development of modern algebra, check out Unknown Quantity by John Derbyshire.

two excellent books by John Derbyshire:

Prime Obsession regarding the Riemann Hypothesis

Unknown Quantity which is about the history of Algebra