Subject: categories: Re: [Fwd: du Sautoy]

From: Vaughan Pratt <[email-masked]>
Date: Sun, 16 Apr 2006 15:53:27 -0700

> The story of the primes is one of the sagas that I have found can pull
> young people on to the mathematical bandwagon. They are the building
> blocks of all numbers. And as you play with them, they very soon draw you
> into one of our biggest mathematical mystery stories.
>   Marcus du Sautoy is professor of mathematics at Oxford University and
> author of The Music of the Primes

Challenge would appear to be a key ingredient here.  To continue the
recent thread on bringing categories to the masses, is there a short
list of such sagas whose challenges big and small might pull young
people on to the category theory bandwagon?  Abelian categories?
Toposes?  Monads?  Synthetic differential geometry?  n-categories?

All would seem to be fairly easily accessed from very accessible parts
of respectively topology (coffee cups, Betti numbers), constructive
logic (Brouwer vs. Hilbert, proofs as programs), number systems (Galois
and unsolvability by radicals), analysis (infinitesimals according to
Cauchy, Weierstrass, Robinson, Kock), and cosmology (the organization of
strings).

What other challenges, big and small, met and unmet, might young people
find a compelling lead-in to categorical thinking?

In all these areas, bringing the novice to the mathematics is surely a
less promising strategy than bringing the mathematics to the novice.  If
home delivery can radicalize the pizza business, why can't it do the
same for category theory?

Vaughan Pratt