The Case for the Brambles


In  a month, I’ll be returning to Heidelberg, Germany. I’ll interview young researchers, ask a few questions of Fields Medalists, and save my deepest inquiries for the German chocolate cake. It’s the kind of absurd opportunity I had no reason to believe my career would afford when I began teaching math in 2009.

This has me thinking about a brief conversation I had last year with John Hopcroft, one of the honored laureates in Heidelberg.

You could be forgiven for thinking that John Hopcroft’s impressive career has followed a preordained trajectory. Bachelor’s, PhD, professorship. Stanford, Princeton, Cornell. Textbook author; National Science Board appointee; Turing Award winner. A well-groomed C.V. born from strategic calculations, right?


“A sequence of strange events that happened,” summarizes Hopcroft.


Hopcroft describes his career in terms of chance encounters and curiosities pursued. “I’ve never really planned things,” he says. “I’ve just been lucky.”

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Three Rules for Tackling a World-Famous Math Problem

While I was listening to Sir Andrew Wiles speak, I saw the writer next to me had jotted three adjectives on his pad: “Calm. Elegant. Precise.”

Astute as those three words are, they miss the basic strangeness of Wiles’ life story. For all his calm, elegance, and precision, the guy is also a unicorn, a sasquatch, a one-of-a-kind creature from the pages of myth. He is, if you will, a walking oxymoron.

He is a celebrity mathematician.


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A Mathematician Looks at a Cat

I’m currently in the midst of an international move, from the UK back to the US. This means that my days unfold in confused montages of jet-lag, scone-longing, and trying to get in on the wrong side of the car. Haven’t had much time for the blog, but I did have these cartoons lying around.

ME: What do you think of these drawings?

MY WIFE: Hey, a cat with a mustache. What’s not to like?

ME: That’s not a mustache. It’s whiskers.

MY WIFE: Okay. I’m not going to tell you what to call your cat’s mustache.


Cats have a symmetry group of order two, because there are two ways to transform a cat while preserving its basic structure: reflect it in a vertical mirror, or leave it alone.

Most cats prefer the latter.




A cat’s activity can be modeled by a delta function. That’s a function whose value is zero everywhere, except at a single point, and yet whose integral is 1. Similarly, the cat is motionless except when it is destroying furniture in the space of a single Planck time.

Note: a delta function is not really a function, just a distribution with good branding. Continue reading