Who are the Foxes and Hedgehogs of Mathematics?

There’s an adorable proverb that goes like this: The fox knows many things; the hedgehog knows one big thing.

(Cute, right? I love a good hedgehog.)

In his essay “The Hedgehog and the Fox,” Isaiah Berlin expands this into a playful metaphor for two kinds of writers. It makes for a great game.

Who’s a fox, and who’s a hedgehog?

The hedgehogs are writers with a master theory. They “relate everything to a single central vision… a single, universal organizing principle.” One classic example is Plato, with his Theory of Forms (and, more generally, his faith in pure reason to resolve any question or controversy).

Meanwhile, the foxes are rummagers, explorers:

those who pursue many ends, often unrelated and even contradictory, connected, if at all, only in some de facto way, for some psychological or physiological cause, related to no moral or aesthetic principle. These last lead lives, perform acts and entertain ideas that are centrifugal rather than centripetal; their thought is scattered or diffused, moving on many levels…

The classification game makes for good long-car-ride fun. If Plato was a hedgehog, then Aristotle was a fox. Dante was a hedgehog; Shakespeare, a total fox.

It’s also applicable to politicians, filmmakers, tech moguls, and whoever else you like. Steve Jobs and Henry Ford, hedgehogs; Elon Musk and Jeff Bezos, foxes. Nate Silver self-identifies as a fox (hence the foxy logo for FiveThirtyEight).

I’m curious about mathematicians. But I don’t feel I know enough mathematics or history to judge myself, so this is a bleg as much as a blog. Knowledgeable mathematicians, help me out! My questions:

1. Who are the hedgehogs of mathematical history? Grothendieck? Lovelace? Euclid?
2. Who are the foxes? Gauss? Newton? Erdos?
3. What are the comparative merits of being a fox vs. a hedgehog in mathematics?

(Readers may notice a resemblance to Timothy Gowers’ “two cultures of mathematics,” theory-builders and problem-solvers. I suspect the two ways of carving up the world are not quite isomorphic – it seems to me that you could be a foxy theory-builder, or a hedgehog of a problem-solver – but feel free to argue otherwise!)

For more on the literary fox who dreamt of being a mathematical hedgehog, try my new book Change is the Only Constant: The Wisdom of Calculus in a Madcap World.

from Math with Bad Drawings https://ift.tt/2MWOwgp