Here are the first few steps. What's the equation?
Morton and Vicary on the Categorified Heisenberg Algebra
- "In quantum mechanics, position times momentum does not equal momentum times position! This sounds weird, but it's connected to a very simple fact. Suppose you have a box with some balls in it, and you have the magical ability to create and annihilate balls. Then there's one more way to create a ball and then annihilate one, than to annihilate one and then create one. Huh? Yes: if there are, say, 3 balls in the box to start with, there are 4 balls you can choose to annihilate after you've created one but only 3 before you create one..." [more inside]
1,143,839,622,748,050,000,000,000,000 Sonnet Anagrams
and oodles of other oddities
from Mike Keith involving constrained writing, mathematics, music, and the number π.
Counting is one of the first and simplest concepts most people are taught. But when you get beyond simple 123s, counting can become an advanced subject
all its own. Essentially the science of counting, combinatorics
is a key component of everything from abstract algebra
(PDF). [more inside]
A generating function is a way to keep track of a lot of related numbers all at once... The study of generating functions is an art and a science known as 'generatingfunctionology,'
and its bible is free for all to download. [more inside]
Ever wondered what comes next, and why? The On-Line Encyclopedia of Integer Sequences
has the answers. (Previously.)
If you could use a great big free handbook of discrete math and algorithms, Jörg Arndt's fxtbook
wants to be your friend. Plain text table of contents
to whet your appetite.