np-compete

Some problems are easy...

3 × 7 = ?

O(n²)

Some problems are a little harder...

× = ?

O(n³)

Some problems are really hard...

http://xkcd.com/399/ CC-BY-NC

O(n²), O(n³), ... problems are in the complexity class P

O(n!) problems or worse are in NP

But are P and NP the same?

http://commons.wikimedia.org/wiki/File:P_np_np-complete_np-hard.svg CC-SA

“Of all the Millennium Problems, the P versus NP problem is the one most likely to be solved by an “unknown amateur” – someone largely untrained in mathematics, possibly someone very young, who is unknown to the mathematical community.”

Keith Devlin, “The Millennium Problems”

“Not only is it relatively easy to understand what the problem says, it is possible that all it will take to solve it is one good new idea.”

Keith Devlin, “The Millennium Problems”

np-compete will be a framework to aggregate every new “N vs. NP”

solution idea that’s out there

np-compete will filter for any known ideas to find all the

genuinely new ideas

The filter will be a competition amongst every solution idea

based on novelty and correctness

But how will it work?

Take the following example...

Can you find whole numbers

p and q so that √2 = p/q?

http://en.wikipedia.org/wiki/Square_root_of_2

Yeah, I’m gonna need you to summarize that in a tweet

How about just three words?

PROOF BY CONTRADICTION

Mathematicians have a phrase for that kind of proof...

http://www.flickr.com/photos/craigporteous/3801016250/ CC-BY

...hand waving

Although there are many proofs that √2 ≠ p/q, they generally

follow one of just a handful of proof patterns

The central idea of the np-compete platform is to semantically mark up complete and rigorous proofs with essentially hand wavy types of proofs with the aim of finding

new ideas

Mathematicians talk in TeX or LaTeX so this will be our input

Anyone will be able to submit solutions

Proof by TeX

“The proof is typeset using TeX or LaTeX, preferably using one of the AMS or ACM stylesheets. When laid out so professionally, it can't possibly have any flaws.”

http://uncyclopedia.wikia.com/wiki/Proof CC-BY-NC-SA

np-compete will take a proposed “P vs. NP” solution written in TeX,

convert this source file into XHTML+MathML and allow users to annotate proof structures in

the document with RDFa

Think of it as massively collaborative peer-review and

idea generation

Get involved!

The project needs people like you:

UI Designers

Semantic Web Experts

Java Hackers

Database Gurus

...

np-compete

See you at Science Hack Day 2010

http://sciencehackday.pbworks.com/

Me:

Blog: http://www.danhagon.me.uk/blog/

Twitter: @axiomsofchoice

With thanks to @leipie for the initial collaboration at HackCamp 2010 and Cameron Neylon for discussions and slide template