Euler's Partition Function Theory Finished

universegeek writes "Mathematician Ken Ono, from Emory, has solved a 250-year-old problem: how to exactly and explicitly generate partition numbers. Ono and colleagues were able to finally do this by realizing that the pattern of partition numbers is fractal (PDF). This pattern allowed them to find a finite, algebraic formula, which is like striking oil in mathematics."

Comments

Re:In English

[martin-boundary]

Suppose you have a large amount of data, and you've turned it into a whole lot of integers. You might not want to store the integers each in a full byte/word/double word, as you'd be wasting a lot of memory that way.

So you come up with a scheme where small integers are stored in a slot that only takes up the number of bits that they actually need. For example, the number 5 can be stored in 3 bits or more, and the number 3 can be stored in two bits or more, which is a far cry from the "standard" size of 64 bits per integer used on many computers these days.

The Euler partition function tells you in how many ways you can split 64 bits up into differently sized slots, which is great if you want to design flexible encoding schemes that make good use of those 64 bits.

Re:Ageism strikes again

[MarkRose]

He's too old? Is it time to start writing his eulergy?

Re:In English

[AchilleTalon]

Why should it gives us any practical applications right now or tomorrow? Do you know Boole was considered wasting his time when he put together the fundation of the boolean algebra which is a cornerstone of the logical circuitry? Do you know Maxwell was also considered wasting his time working on the unification of electrical and magnetic forces? Do you know Faraday was asked what the heck the electricity was for?

All pratical things begin with someone dreaming and working on useless things otherwise these discoveries wouldn't have been done if only practical purpose and necessity was the rule. I'm tired reading peoples always asking what it's for as if everything should have a pratical usage right away. We are talking about the foundations of reasoning here, we are talking about mathematics, not about engineering in case you didn't notice.