(2-minute read)

It’s 2004, and two elderly Russian brothers have just finished explaining how they famously they generated the 1 billionth digit of pi (and then later the 2 billionth and later the 4 billionth). The critical path issue had been a pragmatic one: how to cool that many homemade 1990-vintage parallel computers in a cramped Brooklyn apartment?

“What’s your favorite equation?” someone asks in Q&A, baiting them into recitation of a credal answer the geeky audience expects:  e^i(pi)+1=0.    

“Why?” comes the follow-up question.

And the answer is that mathematicians adore the elegant and mysterious union of disparate concepts: exponential growth, imaginary numbers, and the defining ratio of the circle. It contains all the key operations: addition, equality, multiplication, exponent. And a beautiful zero. And a prime number.  

Leonhard Euler (pronounced “oiler”) is among the most prolific and important of mathematicians, and this 18th-century equation is his most popular legacy. Euler’s identity has long greeted visitors on my doormat:

But, beyond pleasing aesthetics, what does it mean? How are exponential growth and the ratio of diameter to circumference of a circle related? A satisfying explanation had to wait.

At Burning Man 2013, an early morning quest for serendipity crashes my decrepit cruiser bike in thick desert dust… right in front of a banner proclaming e^i(pi)+1=0. The math-themed camp plies me with hot, heavily-liquored espresso while musing about mathematical beauty. It’s only when an applied math professor dressed as a robot happens along, that someone is able to address my pressing question as to what it means: something to do with signal processing. Think of a coil. It’s a circle, that grows.

Then, in 2015, I get a job in telecom, working with radio frequency engineers, developing next-generation wireless routers. Suddenly this beautiful equation becomes applicable in real life (at least in the abstract—it’s not like I was the one doing the engineering calculations). So, my faded, old doormat acquires a new layer of meaning, of foreshadowing. “Poetic justice”, as some say.

My hyper-rational mind would simply call this a random, yet “fitting”, event. But, after years of priming from my surrounding new-age culture, I prefer to entertain it as a “fateful” sign: that there is satisfying structure in the not-so-random walk of life. Ironically, this is the same, ineffably satisfying feeling—of things mysteriously interlocking—that Euler’s equation provokes among those who don’t need to know what it means.

– May 2015