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?

Nope.

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

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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.

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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.

 

 

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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