For hundreds of years, mathematicians even as great as Leonhard Euler(1) have tried to make sense of partition numbers, the basis for adding and counting.  Progress has been made but there has never been a full theory to explain partitions.   Answers have always led to more questions.

Basically, partitions are not considered by some to be part of number theory at all but to keep it simple for now, in number theory, a partition of a positive integer (n) is a way of writing n as a sum of positive integers.    

Here is an example from the Classic Encyclopedia:

Was the fall of the Roman Empire or, as often predicted, the coming fall of the American Empire, numerically predictable?

It is, according to research led by Sergey Gavrilets, associate director for scientific activities at the National Institute for Mathematical and Biological Synthesis and a professor at the University of Tennessee-Knoxville published in Cliodynamics: The Journal of Theoretical and Mathematical History.

Icon for Cosmic Embryo: Erupting star V838 Monocerotis 

”On 2010-09-26, at 5:01 AM, Frithjof A.S. Sterrenburg wrote:

Dear Richard!

Sorry to hear you have been in the claws of the barber-surgeons.  Hope everything is well now!… As for your itinerant existence, you begin to resemble the mathematician Erdös! Cheers, boy, get well soon!"

It's worth dusting this off: a simple, accurate equation that decides to the penny how much you should spend on anyone's gift this holiday season. Get cracking you slacker.

First, I'm afraid I fell victim to one of the classic blunders—the most famous of which is never get in involved in a land war in Asia, but only slightly less well known is this: probability is not additive (as a couple astute Times readers have now pointed out--before going further, you might want to read my Frankie the Fixer puzzle in the left sidebar of THIS PAGE).

Equations relating speed and mass go back to Newton and beyond.

But what about relating speed and MESS?

Simply, how fast should you expect a clean kids' room to get messy?

1,400,000 70-dimension histogram vectors about gamer behavior.  What can you do with that?

Me?  Nothing, the math is too much but, if you can make sense of it, a lot of data is there in the ongoing online gaming phenomenon known as World of Warcraft(WoW).   Keeping track of all that data would seem to be solely the purview of computer programmers but sociologists are starting to take notice.   Some people are just goofing off and writing a book about their experiences but others see gold in 'game mining' - the insights of anthropology we can get by seeing what 10 million people do in a virtual, controlled setting over a period of years.

Here we have two words, one in Arabic and one in Hebrew, which scholars of those languages will have no difficulty in recognizing as descending from the same ancient Semitic source. In Arabic the word means “error” in the sense of “error message” from a computer. The Arabic version is pronounced “khata” (with an emphatic “t”), and the Hebrew is quite similar.

I’m sticking with the Arabic for now, because this is the jumping-off point for an interesting bit of medieval mathematical history.

Want a real Halloween nightmare? Imagine filling your child's  too-small bucket in the first three houses and going home with only a  small slice of your kid's potential rake. But if you allow your little monster (or in my case, blue whale with pink and purple barnacles), to carry a big bag, you should be prepared to spend the hours and hours (and hours) needed to fill it.