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np-compete: a Science Hack Day 2010 elevator pitch

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The central idea of the np-compete platform is to semantically mark up, with essentially "hand wavy" types of proofs, proofs from the complexity theory literature written in documents that start out as TeX or LaTeX and subsequently get converted into XHTML+MathML. The aim is to find and generate new ideas that might eventually lead to a complete solution of the "P vs. NP" problem.

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np-compete: a Science Hack Day 2010 elevator pitch

  1. 1. np-compete
  2. 2. Some problems are easy...
  3. 3. 3×7=?
  4. 4. O(n²)
  5. 5. Some problems are a little harder...
  6. 6. × =?
  7. 7. O(n³)
  8. 8. Some problems are really hard...
  9. 9. http://xkcd.com/399/ CC-BY-NC
  10. 10. O(n²), O(n³), ... problems are in the complexity class P O(n!) problems or worse are in NP
  11. 11. But are P and NP the same?
  12. 12. http://commons.wikimedia.org/wiki/File:P_np_np-complete_np-hard.svg CC-SA
  13. 13. “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”
  14. 14. “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”
  15. 15. np-compete will be a framework to aggregate every new “N vs. NP” solution idea that’s out there
  16. 16. np-compete will filter for any known ideas to find all the genuinely new ideas
  17. 17. The filter will be a competition amongst every solution idea based on novelty and correctness
  18. 18. But how will it work?
  19. 19. Take the following example...
  20. 20. Can you find whole numbers p and q so that √2 = p/q?
  21. 21. http://en.wikipedia.org/wiki/Square_root_of_2
  22. 22. Yeah, I’m gonna need you to summarize that in a tweet
  23. 23. How about just three words?
  24. 24. PROOF BY CONTRADICTION
  25. 25. Mathematicians have a phrase for that kind of proof...
  26. 26. http://www.flickr.com/photos/craigporteous/3801016250/ CC-BY
  27. 27. ...hand waving
  28. 28. Although there are many proofs that √2 ≠ p/q, they generally follow one of just a handful of proof patterns
  29. 29. 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
  30. 30. Mathematicians talk in TeX or LaTeX so this will be our input Anyone will be able to submit solutions
  31. 31. 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
  32. 32. 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
  33. 33. Think of it as massively collaborative peer-review and idea generation
  34. 34. Get involved! The project needs people like you: UI Designers Semantic Web Experts Java Hackers Database Gurus ...
  35. 35. 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

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