Imagining Numbers

peterwayner writes "One mathematician I know told me that the most important lesson he learned was how to read a math book. It did no good, he said, to just start plowing through the theorems because that brought confusion. The key was to skim the book five or six times to get an idea of what the writer was trying to do. Then, and only then, was it possible to figure out the equations. This is what Barry Mazur tries to do in his book Imagining Numbers . There are some equations, graphs and diagrams, but first and foremost he offers plenty of poetry, philosophy and history to lay a foundation for understanding imaginary numbers." Peter's review continues below -- despite its complicated, abstract subject matter, he says that it's "simple enough to be accessible to most who will be interested in it." Imagining Numbers author Barry Mazur pages 267 publisher Farrar, Straus and Giroux rating 8 reviewer Peter Wayner ISBN 0374174695 summary How to imagine imaginary numbers like the square root of minus fifteen.

Much of modern mathematical literature is structured with crisp, scripted precision. First there is theorem one, then theorem two, which leads to theorem three, which could only be followed by theorem four, and so on until we reach theorem n. If you want to learn the mathematics of complex numbers (a +bi), then classic texts (this or this) will get you there.

Some may like this logical progression, but it leaves others cold in the same way that crisp, modern architecture by Mies van de Rohe leaves some craving a more layered, fractured, ornate, organic and just plain fun place to live and work. Less isn't more, as Robert Venturi said, less is a bore.

If you happen to feel a chill when churning through an assembly line of theorems, you might enjoy the treatment of Mazur, a professor at Harvard who seems to spend as much time reading poets like Rilke or Stevens as he does examining old mathematical texts. Mazur is not the kind of machine that turns coffee into theorems-- he's too busy stopping to smell the rhetorical flourishes.

The book isn't aimed at mathematicians per se. The publisher, Farrar, Strauss and Giroux specializes in mainstream literature and that's probably the best pigeonhole for this book. Mazur wants the reader to understand how to think about imaginary numbers, not evaluate some integrals -- and that reader could really be anyone with the desire to think about mathematical things. The book is simple enough to be accessible to most who will be interested in it.

In many ways, Mazur attempted a much harder task than just teaching complex analysis. It's one thing to learn how to find the roots of polynomials, but it's another thing to try to help people get a feeling or an intuition for the square root of minus fifteen. Integers are easy to understand and even feel by counting out things, but imaginary numbers don't seem to exist. Mathematicians have spent many years trying to find the best metaphors and structures to understand how to find answers for all polynomials and it's never been an easy struggle.

The best part of the book is, without doubt, the historical treatment of how other mathematicians confronted the question of irrational and complex numbers. These ideas have always been hard to grasp and it took time to evolve the most compact and consistent nomenclature.

If you're interested in mathematics as more than just a mechanism that churns out answers, you'll probably enjoy the book. It's a light, friendly, philosophical expedition looking for a way to make imaginary numbers work in our minds.

Peter Wayner is the author of Translucent Databases , a book on how to imagine databases that hold no information yet still do useful work. You can purchase Imagining Numbers from bn.com. Slashdot welcomes readers' book reviews -- to see your own review here, read the book review guidelines, then visit the submission page.

Comments

Re:Let me get this straight...

[Hepkat]

uhm... how about this: you live your life and you let others live theirs.

Imagining numbers, eh?

[Junior J. Junior III]

So what's the connection to Beowulf clusters? What kind of computational power do these "numbers" things have?

Re:President Bush

[Night War]

ell, I still don't understand why you're posting this on a book's review, but anyways, I suppose you didn't read Michael Moore's "Stupid White Men", did you? It will teach you a lot of things about the (supposedly) #1 of states, the USA. And also check out this link: http://www.michaelmoore.com And since this is a math book: Try computing the number of civilian dead. This won't be a imaginary number. So get a feel for that number, read some war poems and then think again of God, Glory and Gore.

Re:President Bush

[borgdows]

>God bless our great leader President Bush!!

in 1939, people would have said "God bless our great Fuhrer G.W Bush!!"

it's sad to see people forget History! and don't that stupid Saddam=Hitler thing, Saddam didn't ever had the biggest army in the world, Hitler in 1939 did!

USAF is #1!

[Thud457]

Wouldn't the firebombing of Dresen be the largest single loss of life?

"The death toll was staggering. The full extent of the Dresden Holocaust can be more readily grasped if one considers that well over 250,000 -- possibly as many as a half a million -- persons died within a 14-hour period"

And technically, it isn't terrorism when the government does it. Right?

Re:USAF is #1!

[BobRooney]

um, there was no USAF until 1947...after WWII which ended in 1945. At the time it was the Army Air Core. I agree, its sad that people have to die in war, but isnt that your point? If you're going to be a tree hugging anti-war hippy at least be an educated one. Huah! First Amendment...

Re:President Bush

[jgerman]

I know responding to an OT post is wrong but still:

Yeah, having the biggest army in the world is what made Hitler bad. You've got a great understanding of history there. Perhaps you should write a book.