Difference between revisions of "Main Page"

From Polymath1Wiki
Jump to: navigation, search
(1004.5)
m (Existing polymath projects)
 
(251 intermediate revisions by 59 users not shown)
Line 1: Line 1:
comment4, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=399 Hello kitty massager,  :-]], http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=515 Cedar grove buyers agents, >:-P, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=335 Kgo radio,  >:DDD, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=428 Fart machine,  %O, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=489 Conference call vendors,  =(((, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=509 Stile project,  8-PPP, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=381 Tuberose,  37748, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=488 Ahima,  ldky, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=549 Wdiv,  519, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=336 Angus movie,  jdi, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=555 Staff scheduling software,  8[[, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=470 Cosmopolitan cocktail,  :-DDD, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=499 Neupogen,  :DD, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=529 Jeff stryker,  :DD, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=424 Butlins,  >:-(((, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=329 Texas lightning,  ikm, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=398 Lotto 649 numbers,  894, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=457 Free hallmark greeting cards,  zaaj, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=319 Housewives of orange county,  :-P, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=461 Outhouses,  ilhsgv, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=451 Dillards,  116785, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=400 2009 camero,  %-), http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=572 Canon digital camera sd400,  pigy, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=476 Revision cp,  961312, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=416 Rev jesse lee peterson,  sfxdrq, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=442 Softice,  615, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=519 Braided rug,  8)), http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=406 Craigs list eugene,  ism, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=508 Shotgun manufacturers,  698, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=423 Taco bell nutrition,  =O, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=350 Amanita muscaria,  :[, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=446 Tjmax,  20802, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=369 Lesbo 101,  540, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=354 Gutter guards,  %-))), http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=538 American greeting cards,  %DDD, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=382 Outlook express email,  qrrnzk, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=395 Hot moms nude,  sbjfdn, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=328 Proform treadmills,  bpq, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=371 M1a1,  =-[, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=363 Marture hand foot jobs,  >:[[[, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=550 Istj,  %DD, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=598 Marquis de lafayette,  313776, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=474 Northwest isd,  kxjjjv, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=448 Rammstein amerika,  %-[, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=507 Guilding,  zcs, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=497 Soutien scolaire lyon,  8))), http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=377 Polk county jail,  kclv, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=445 Roatan beaches,  lmcj, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=397 Lryics,  lcnqhy, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=425 Shaw carpet,  =-(, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=531 Wsmv,  =]], http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=609 Talambuhay ni lapu lapu,  %-))), http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=456 Dj cammy dancing in the dark,  188, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=561 Flouride,  =-(, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=429 Safc,  32560, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=595 Les humphries singers,  8935, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=443 Longs drug store,  :-)), http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=511 Ahvids,  oeq, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=527 Washington state child support,  nraxj, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=524 Unformat,  alk, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=358 Livejasmine,  461, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=486 Arne jacobsen handle,  8-[[, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=333 Gen e8ve,  dsbt, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=487 Penis photos,  278, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=594 Ayso,  8-((, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=532 Apartments in nerja,  %O, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=543 Zanessa,  ksrt, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=548 Nissan pavillion,  lanc, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=431 Fema prison camps,  8-PPP, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=571 Bcwipe,  jaso, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=430 Lincoln passenger vehicles e bay motors,  12245, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=388 Meguiars,  158007, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=514 Bill bixby,  6552, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=578 Orgys,  cfykq, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=331 Auctionzip,  47609, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=468 Michigan eft processing,  053202, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=560 Michelin motorcycle tires,  ddjiru, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=312 Romantic spanish phrases,  cyrrtf, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=345 Fanniemae,  63219, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=494 Chinua achebe,  5160, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=557 Bravoporn,  sgtwy, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=455 Wthr toilet paper,  09129, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=420 Mature cola,  wgb, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=485 Ripleys believe it or not,  znu, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=518 Sofft,  98988, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=313 Roundnbrown,  lyjcdh, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=574 Barksdale afb,  039, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=426 Devoir vacances cp,  3124, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=314 Wisconsin county map,  fspzoz, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=504 Peabody sisters,  %),
+
{{RightTOC}}
 +
This is the wiki for ''polymath'' projects - massively collaborative online mathematical projectsThe idea of such projects originated in Tim Gowers' blog post [http://gowers.wordpress.com/2009/01/27/is-massively-collaborative-mathematics-possible/ Is massively collaborative mathematics possible?]
  
comment1, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=642 French fry cutter, 8))), http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=631 Erotica vintage,  qgxxu, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=700 Mrdouble,  86841, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=772 Rude valentines poems,  %PP, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=865 Kirby vacuum cleaners,  :-[, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=684 Clopay garage doors,  fda, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=843 Airline job vacancies,  428695, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=771 Indienudes,  ahq, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=908 Santa claus history,  kcu, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=630 Erico,  =-[, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=853 Kielbasa,  8[, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=719 Arliss howard,  099111, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=699 Pussy spanking,  466194, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=620 Lesbians scissoring,  096, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=723 Wikkipedia,  pcl, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=873 Potato famine,  >:-(, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=717 Mature housewives,  =((, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=824 Mrsa pictures,  >:-PP, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=743 Ober gatlinburg,  1701, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=820 Junie b jones,  neqdae, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=809 Hot secretaries,  8]]], http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=724 Star tattoo design,  rvlft, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=747 Short ghost stories,  574, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=670 Sarah lancaster,  :OO, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=847 Fayetteville observer,  tias, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=814 Bioidentical hormones,  ppycv, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=798 Nicheflixx,  234277, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=796 Sixthseal,  690, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=720 Hallmark greeting cards,  ginpob, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=730 Teleblend,  8-O, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=846 Criminal mugshots,  75898, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=624 Shaved beaver,  xjnmkd, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=722 Emu oil shampoo,  239, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=801 Habor freight,  tavzj, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=788 Dollhouse miniatures,  yvxj, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=834 Alex trebek biography,  976850, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=797 Ryobi trimmer parts,  8[[[, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=760 Anime tickling forum,  1013, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=833 Riccar,  >:-], http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=652 Proxify,  8-]]], http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=815 Clearview cinemas,  999213, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=656 Women squirt when ejaculating,  ebqteg, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=706 Metanet forums,  8], http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=695 Whites metal detectors,  gnq, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=858 Illinois dmv,  000238, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=793 Sexhungrymoms,  519, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=756 Garmin 760,  241, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=618 Bunco rules,  9857, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=708 French fry cutter,  qngp, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=826 Photo de emma watson nue,  lpyxwz, http://www.bronsonmedia.se/thehiddentree/forum/topic.asp?topic_id=852 Kreg jig,  %-((,
+
Many polymath projects will be proposed, planned, and run at [http://polymathprojects.org/ This Blog].
  
==Basic definitions==
+
A Polymath [[logo]] is being trialled.  If you have more suggestions, please add them to the [[logo]] page, or add to the discussion at [[Talk:logo]].
  
*[[line|Algebraic line]]
+
The wiki is currently locked down due to a major influx of spam (July 29, 2013).  Please email mn@michaelnielsen.org if you'd like an account set up, and I'll do my best to reply quickly.
  
*[[line|Combinatorial line]]
+
== Existing polymath projects ==
  
*[[Combinatorial subspace]]
+
* [[Polymath1]]: New proofs and bounds for the density Hales-Jewett theorem.  Initiated Feb 1, 2009; research results have now been published.
 +
* [[Definable Banach Spaces|Polymath2]]: Must an “explicitly defined” Banach space contain <math>c_0</math> or <math>l_p</math>?  Initiated Feb 17, 2009; attempts to relaunch via wiki, June 9 2010.
 +
* [[imo 2009 q6|Mini-polymath1]]: Solving Problem 6 of the 2009 International Mathematical Olympiad.  Initiated July 20, 2009; five proofs obtained so far.
 +
* [[The polynomial Hirsch conjecture|Polymath3]].  The polynomial Hirsch conjecture.  Proposed July 17, 2009; launched, September 30, 2010. 
 +
* [[finding primes|Polymath4]]: A deterministic way to find primes.  Proposed July 27, 2009; launched Aug 9, 2009.  Research results have now been published.
 +
* [[The Erd&#337;s discrepancy problem|Polymath5]]: The Erd&#337;s discrepancy problem. Proposed Jan 10, 2010; launched Jan 19, 2010.  Activity ceased by the end of 2012, but results from the project were used to solve the problem in 2015.
 +
* [[imo 2010|Mini-polymath2]]: Solving Problem 5 the 2010 International Mathematical Olympiad.  Proposed Jun 12, 2010; launched and solved, Jul 8 2010.
 +
* [[Improving the bounds for Roth's theorem|Polymath6]]: Improving the bounds for Roth's theorem. Proposed Feb 5, 2011.
 +
* [[imo 2011|Mini-polymath3]]: Solving a problem from the 2011 International Mathematical Olympiad.  Proposed Jun 9, 2011; launched and solved, Jul 19, 2011.
 +
* [[imo 2012|Mini-polymath4]]: Solving a problem from the 2012 International Mathematical Olympiad.  Proposed, Jun 3, 2012; launched, July 12 2012.
 +
* [[The hot spots conjecture|Polymath7]]:  Establishing the Hot Spots conjecture for acute-angled triangles.  Proposed, May 31st, 2012; launched, Jun 8, 2012.
 +
* [[Bounded gaps between primes|Polymath8]]: Improving the bounds for small gaps between primes.  Proposed, June 4, 2013; launched, June 4, 2013.  Research results have now been published.
 +
* [[Discretized Borel Determinacy and P=NP|Polymath9]]: exploring Borel determinacy-based methods for giving complexity bounds.  Proposed, Oct 24, 2013; launched, Nov 3, 2013.
 +
* [[The Erdos-Rado sunflower lemma|Polymath10]]: improving the bounds for the Erdos-Rado sunflower lemma.  Launched, Nov 2, 2015.
 +
* [[Frankl's union-closed conjecture|Polymath11]]: proving Frankl's union-closed conjecture. Proposed Jan 21, 2016; launched Jan 29, 2016.  Concluded, Jan 17, 2017.
 +
* [[Rota's conjecture|Polymath12]]: proving Rota's conjecture.  Proposed Feb 28, 2017.
 +
* [[Intransitive dice|Polymath13]]: Intransitive dice.  Proposed Apr 28, 2017.
 +
* [[linear norm|Polymath14]]: Classifying homogeneous norms on groups.  Initiated Dec 16, 2017; solved Dec 21, 2017.  Research results have now been published.
 +
* [[De_Bruijn-Newman constant|Polymath15]]: Upper bounding the de Bruin-Newman constant.  Proposed, Jan 24 2018; launched Jan 27 2018.
 +
* [[Hadwiger-Nelson problem|Polymath16]]: Simplifying the lower bound proof for the Hadwiger-Nelson problem.  Proposed, Apr 10, 2018; launched, Apr 14, 2018.
  
*[[corners|Corner]]
+
== Polymath-like projects ==
  
*[[Density]]
+
* Scott Aaronson's "philomath project": "[http://scottaaronson.com/blog/?p=453 Sensitivity vs. Block sensitivity]" (see also [http://mathoverflow.net/questions/31482/the-sensitivity-of-2-colorings-of-the-d-dimensional-integer-lattice this Math Overflow question]).  Launched Jul 13, 2010.
 +
* A wiki page clearinghouse for the [[Deolalikar P vs NP paper]].  Launched Aug 10, 2010.
 +
* <del>[http://researchtrends.wikia.com/wiki/Main_Page Math Research Trends Wiki] "research in the middle"</del> This project is recommended to be discontinued in favor of <b>[https://conference.portonvictor.org/wiki/Research_in_the_middle Research in the middle project] at [https://conference.portonvictor.org Virtual scientific conference]</b>.
 +
* The page for the [[ABC conjecture]] contains links and information about Mochizuki's claimed proof of this conjecture.
  
*[[line|Geometric line]]
+
== Proposed polymath projects ==
  
*[[Slice]]
+
* [http://gilkalai.wordpress.com/2009/03/25/an-open-discussion-and-polls-around-roths-theorem/ The cap set problem].  Proposed March 25, 2009 (see also these [http://gilkalai.wordpress.com/2009/05/11/around-the-cap-set-problem-b/ two] [http://gilkalai.wordpress.com/2009/05/18/the-cap-set-problem-and-frankl-rodl-theorem-c/ followup] posts).
 +
* [[Boshernitzan’s problem]].  Proposed July 27, 2009.
 +
* [http://gowers.wordpress.com/2009/09/16/possible-future-polymath-projects/ Possible future polymath projects].  Discussion opened September 16, 2009.
 +
* [http://rjlipton.wordpress.com/2011/05/12/a-possible-polymath-project/ A possible polymath project:] Proposal by Richard Lipton to attack a conjecture due to Erdos, about a class of Diophantine equations.
  
== Useful background materials ==
 
  
Here is [http://gowers.wordpress.com/2009/01/30/background-to-a-polymath-project/ some background to the project.] There is also a [http://gowers.wordpress.com/2009/01/27/is-massively-collaborative-mathematics-possible/ general discussion on massively collaborative "polymath" projects.]  This is  [http://meta.wikimedia.org/wiki/File:MediaWikiRefCard.png  a cheatsheet for editing the wiki.]  Finally, here is the general [http://meta.wikimedia.org/wiki/Help:Contents Wiki user's guide].
+
A (partial) list of proposed projects can be found [http://polymathprojects.org/category/polymath-proposals/ here].
  
== Threads and further problems==
+
If you have a tentative proposal for a polymath project, you can either make a post on it on your own blog, or place it [[other proposed projects|here]].
  
* (1-199) [http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/ A combinatorial approach to density Hales-Jewett] (inactive)
+
== Discussions about polymath ==
* (200-299) [http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/ Upper and lower bounds for the density Hales-Jewett problem] (inactive)
+
* (300-399) [http://gowers.wordpress.com/2009/02/06/dhj-the-triangle-removal-approach/ The triangle-removal approach] (inactive)
+
* (400-499) [http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity Quasirandomness and obstructions to uniformity] (inactive)
+
* (500-599) [http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#more-441/ Possible proof strategies] (inactive)
+
* (600-699) [http://terrytao.wordpress.com/2009/02/11/a-reading-seminar-on-density-hales-jewett/ A reading seminar on density Hales-Jewett] (inactive)
+
* (700-799) [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/ Bounds for the first few density Hales-Jewett numbers, and related quantities] (inactive)
+
* (800-849) [http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/ Brief review of polymath1] (inactive)
+
* (850-899) [http://gowers.wordpress.com/2009/03/02/dhj3-851-899/ DHJ(3): 851-899] (active)
+
* (900-999) [http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/ DHJ(3): 900-999 (Density Hales-Jewett type numbers)] (active)
+
  
[http://blogsearch.google.com/blogsearch?hl=en&ie=UTF-8&q=polymath1&btnG=Search+Blogs Here is a further list of blog posts related to the Polymath1 project]. [http://en.wordpress.com/tag/polymath1/ Here is wordpress's list]. Here is a [[timeline]] of progress so far.
+
* [http://gowers.wordpress.com/2009/01/27/is-massively-collaborative-mathematics-possible/ Is massively collaborative mathematics possible?] Tim Gowers, January 27, 2009.
 +
* [http://lucatrevisan.wordpress.com/2009/02/01/a-peoples-history-of-mathematics/ A people's history of mathematics] Luca Trevisan, February 1, 2009.
 +
* [http://michaelnielsen.org/blog/?p=553 The polymath project] Michael Nielsen, February 3, 2009.
 +
* [http://www.neverendingbooks.org/index.php/yet-another-math20-proposal.html Yet another math 2.0 proposal] Lieven le Bruyn, February 11, 2009.
 +
* [http://gowers.wordpress.com/2009/03/10/polymath1-and-open-collaborative-mathematics/ Polymath1 and open collaborative mathematics] Tim Gowers, March 10, 2009.
 +
* [http://maxwelldemon.com/2009/03/14/polymath/ Polymath] Edmund Harriss, March 14, 2009.
 +
* [http://science.slashdot.org/article.pl?sid=09/03/18/194228 Massive open collaboration in mathematics declared a success] Slashdot, March 18, 2009.
 +
* [http://michaelnielsen.org/blog/?p=581 How changing the technology of collaboration can change the nature of collaboration] Michael Nielsen, March 18, 2009.
 +
* [http://michaelnielsen.org/blog/?p=584 The polymath project: scope of participation] Michael Nielsen, March 20, 2009.
 +
* [http://gowers.wordpress.com/2009/03/24/can-polymath-be-scaled-up/ Can polymath be scaled up?] Tim Gowers, March 24, 2009.
 +
* [http://whatisresearch.wordpress.com/2009/03/24/concluding-notes-on-the-polymath-project-and-a-challenge/ Concluding notes on the polymath project - and a challenge] Vilpulniak, March 24, 2009.
 +
* [http://michaelnielsen.org/blog/on-scaling-up-the-polymath-project/ On scaling up the polymath project] Michael Nielsen, March 25, 2009.
 +
* [http://numberwarrior.wordpress.com/2009/03/25/a-gentle-introduction-to-the-polymath-project/ A gentle introduction to the polymath project] Jason Dyer, March 25, 2009.
 +
* [http://blogs.telegraph.co.uk/technology/iandouglas/9656357/tim_gowers_and_the_polymaths/ Tim Gowers and the polymaths] Ian Douglas (the Telegraph), April 29, 2009
 +
* [http://terrytao.wordpress.com/2009/07/22/imo-2009-q6-mini-polymath-project-impressions-reflections-analysis/ IMO 2009 Q6 as mini-polymath project: impressions, reflections, analysis] Terence Tao, July 22, 2009.
 +
* [http://polymathprojects.org/2009/07/27/selecting-the-next-polymath-project/ Selecting the next polymath project] Terence Tao, July 27, 2009.
 +
* [http://blog.jonudell.net/2009/07/31/polymath-equals-user-innovatio/ Polymath equals user innovation] Jon Udell, July 31, 2009.
 +
* [http://scienceblogs.com/christinaslisrant/2009/08/an_overview_of_the_polymath_pr.php An overview of the polymath project] Christina Pikas, August 1, 2009
 +
* [http://whatisresearch.wordpress.com/2009/08/09/collaborative-mathematics-etc/ Collaborative mathematics etc.] Vipulniak, August 9, 2009
 +
* [http://www.nature.com/nature/journal/v461/n7266/full/461879a.html Massively collaborative mathematics] Tim Gowers, Michael Nielsen, Nature, October 15, 2009
 +
* [http://portonmath.wordpress.com/2009/10/25/collaborative-research-of-filters/ Collaborative math research – a real example] Victor Porton, October 24, 2009
 +
* [http://whatisresearch.wordpress.com/2009/10/26/polymath-again/ Polymath again] Vipulniak, October 26, 2009
 +
* [http://www.kennislink.nl/publicaties/wiskunde-met-zijn-allen Wiskunde met zijn allen] (Dutch), Alex van den Brandhof, Kennislink, November 12, 2009
 +
* [http://www.sciencenews.org/view/generic/id/50532/title/Mathematics_by_collaboration Mathematics by collaboration], Julie Rehmeyer, ScienceNews, December 8, 2009
 +
* [http://www.nytimes.com/projects/magazine/ideas/2009/#m Massively Collaborative Mathematics], Jordan Ellenberg, The Ninth Annual Year in Ideas, New York Times, 2009.
 +
* [http://www.hypios.com/thinking/2010/01/13/massively-collaborative-mathematics-lessons-from-polymath1/ Massively Collaborative Mathematics: lessons from polymath1], Hypios, Jan 13 2010
 +
* [http://ths1104.wordpress.com/2010/02/13/open-reflexions-sur-fond-de-polymaths/ Open réflexions sur fond de Polymaths] (French), ths1104, Feb 13 2010
 +
* [http://www.javiertordable.com/blog/2010/02/25/collaborative-mathematics-future-of-science Collaborative Mathematics and The Future of Science] Javier Tordable, February 26 2010
 +
* [http://www.scientificamerican.com/article.cfm?id=problem-solved-tic-tac-toe-blog Problem Solved, LOL: A Complex Tic-Tac-Toe Puzzle Falls Thanks to Blog Comments] Davide Castelvecchi, Scientific American, March 17 2010
 +
* [http://www.thebigquestions.com/2010/04/08/blogging-tic-tac-toe-and-the-future-of-math/ Blogging, Tic Tac Toe, and the Future of Math] Steve Landsburg, The Big Questions, April 4 2010
 +
* [http://www.siam.org/news/news.php?issue=0043.03 Massively Collaborative Mathematics] Julie Rehmeyer, SIAM News, Volume 43(3), April 2010 (to appear)
 +
* [http://mbarany.com/publications.html#WikiSymPolymath  `But this is blog maths and we're free to make up conventions as we go along': Polymath1 and the Modalities of `Massively Collaborative Mathematics.'] Michael Barany,  Proceedings of the 6th International Symposium on Wikis and Open Collaboration, Gdansk, Poland, 2010.
 +
* [http://www.cs.cmu.edu/~jcransh/papers/cranshaw_kittur.pdf J. Cranshaw and A. Kittur. The Polymath Project: Lessons from a successful online collaboration in mathematics]. In Proceedings of the Conference on Human Factors in Computing Systems, Vancouver, BC, Canada, May 2011.
 +
* [http://www.newscientist.com/article/mg21028113.900-how-to-build-the-global-mathematics-brain.html How to build the global mathematics brain], Jacob Aron, New Scientist, 4 May 2011.
 +
* [http://www.newscientist.com/article/mg21028112.900-mathematics-becomes-more-sociable.html Mathematics becomes more sociable], New Scientist, 5 May 2011.
 +
* [http://polymathprojects.files.wordpress.com/2011/03/polymathias.jpg Mathematical Advances: Lone or Massively Collaborative Endeavors?] from IAS Institute Letter for fall 2010 based on a discussion organized by IAS fall 2010.
 +
* [http://today.uconn.edu/blog/2010/10/will-crowdsourcing-revolutionize-scholarship Will ‘Crowdsourcing’ Revolutionize Scholarship?] An article in UConn Today by Jeremy Teitelbaum, Fall 2010.
 +
* [http://online.wsj.com/article/SB10001424052970204644504576653573191370088.html The New Einsteins Will Be Scientists Who Share] The Wall street journal, October 2011.
 +
* [http://www.nature.com/news/parallel-lines-1.14759?WT.ec_id=NATURE-20140227 Parallel lines], editorial, Nature 506, 407–408 (27 February 2014).
 +
Additional links are very welcome.
  
A spreadsheet containing the latest upper and lower bounds for <math>c_n</math> can be found [http://spreadsheets.google.com/ccc?key=p5T0SktZY9DsU-uZ1tK7VEg here].  Here are the proofs of our [[upper and lower bounds]] for these constants.
+
== Other links ==
  
We are also collecting bounds for [[Fujimura's problem]], motivated by a [[hyper-optimistic conjecture]].
+
* [http://polymathprojects.org/ The polymath blog]
 +
* [http://polymathprojects.org/general-polymath-rules/ General polymath rules]
  
There is also a chance that we will be able to improve the known bounds on [[Moser's cube problem]].
+
== Note on anonymous editing ==
  
Here are some [[unsolved problems]] arising from the above threads.
+
To help combat spam, anonymous editing has been disabled, and a captcha system added to hinder automated account creation. If this is causing problems, please email mn@michaelnielsen.org.
  
Here is a [[tidy problem page]].
+
== Note on image uploads ==
  
== Proof strategies ==
+
Image uploads have been disabled, as they were causing problems with spam. If you'd like to upload an image, please email mn@michaelnielsen.org
 
+
It is natural to look for strategies based on one of the following:
+
 
+
* [[Szemerédi's original proof of Szemerédi's theorem]].
+
* [[Szemerédi's combinatorial proof of Roth's theorem]].
+
* [[Ajtai-Szemerédi's proof of the corners theorem]].
+
* The [[density increment method]].
+
* The [[triangle removal lemma]].
+
* [[Ergodic-inspired methods]].
+
* The [[Furstenberg-Katznelson argument]].
+
* Use of [[equal-slices measure]].
+
 
+
== Related theorems ==
+
 
+
* [[Carlson's theorem]].
+
* The [[Carlson-Simpson theorem]].
+
* [[Folkman's theorem]].
+
* The [[Graham-Rothschild theorem]].
+
* The colouring [[Hales-Jewett theorem]].
+
* The [[Kruskal-Katona theorem]].
+
* [[Roth's theorem]].
+
* The [[IP-Szemer&eacute;di theorem]].
+
* [[Sperner's theorem]].
+
* [[Szemer&eacute;di's regularity lemma]].
+
* [[Szemer&eacute;di's theorem]].
+
* The [[triangle removal lemma]].
+
 
+
All these theorems are worth knowing. The most immediately relevant are Roth's theorem, Sperner's theorem, Szemer&eacute;di's regularity lemma and the triangle removal lemma, but some of the others could well come into play as well.
+
 
+
==Important concepts related to possible proofs==
+
 
+
* [[Complexity of a set]]
+
* [[Concentration of measure]]
+
* [[Influence of variables]]
+
* [[Obstructions to uniformity]]
+
* [[Quasirandomness]]
+
 
+
==Complete proofs or detailed sketches of potentially useful results==
+
 
+
*[[Sperner's theorem|The multidimensional Sperner theorem]]
+
*[[Line-free sets correlate locally with complexity-1 sets]]
+
*[[Correlation with a 1-set implies correlation with a subspace]] (Not finished)
+
*[[Fourier-analytic_proof_of_Sperner|A Fourier-analytic proof of Sperner's theorem]]
+
*[[A second Fourier decomposition related to Sperner's theorem]]
+
*[[A Hilbert space lemma]]
+
*A [[Modification of the Ajtai-Szemer&eacute;di argument]]
+
*[[DHJ(k) implies multidimensional DHJ(k)]]
+
 
+
==Attempts at proofs of DHJ(3)==
+
 
+
*[[An outline of a density-increment argument]] (ultimately didn't work)
+
*[[A second outline of a density-increment argument]] (seems to be OK but more checking needed)
+
 
+
== Bibliography ==
+
 
+
[[Density Hales-Jewett]]
+
 
+
# H. Furstenberg, Y. Katznelson, “[http://math.stanford.edu/~katznel/hj43.pdf A density version of the Hales-Jewett theorem for k=3]“, Graph Theory and Combinatorics (Cambridge, 1988). Discrete Math. 75 (1989), no. 1-3, 227–241.
+
# H. Furstenberg, Y. Katznelson, “[http://math.stanford.edu/~katznel/dhj12.pdf A density version of the Hales-Jewett theorem]“, J. Anal. Math. 57 (1991), 64–119.
+
# R. McCutcheon, “[http://www.msci.memphis.edu/~randall/preprints/HJk3.pdf The conclusion of the proof of the density Hales-Jewett theorem for k=3]“, unpublished.
+
 
+
[[Coloring Hales-Jewett theorem]]
+
 
+
# A. Hales, R. Jewett, [http://www.jstor.org/stable/1993764 Regularity and positional games], Trans. Amer. Math. Soc. 106 1963 222--229. [http://www.ams.org/mathscinet-getitem?mr=143712 MR143712]
+
# N. Hindman, E. Tressler, "[http://www.math.ucsd.edu/~etressle/hj32.pdf The first non-trivial Hales-Jewett number is four]", preprint.
+
# P. Matet, "[http://dx.doi.org/10.1016/j.ejc.2006.06.021 Shelah's proof of the Hales-Jewett theorem revisited]", European J. Combin. 28 (2007), no. 6, 1742--1745. [http://www.ams.org/mathscinet-getitem?mr=2339499 MR2339499]
+
# S. Shelah, "[http://www.jstor.org/stable/1990952 Primitive recursive bounds for van der Waerden numbers]", J. Amer. Math. Soc. 1 (1988), no. 3, 683--697. [http://www.ams.org/mathscinet-getitem?mr=929498 MR 929498]
+
 
+
[[Roth's theorem]]
+
 
+
# E. Croot, "[http://www.math.gatech.edu/~ecroot/szemeredi.pdf Szemeredi's theorem on three-term progressions, at a glance], preprint.
+
 
+
Behrend-type constructions
+
 
+
# M. Elkin, "[http://arxiv.org/abs/0801.4310 An Improved Construction of Progression-Free Sets ]", preprint.
+
# B. Green, J. Wolf, "[http://arxiv.org/abs/0810.0732 A note on Elkin's improvement of Behrend's construction]", preprint.
+
# K. O'Bryant, "[http://arxiv.org/abs/0811.3057 Sets of integers that do not contain long arithmetic progressions]", preprint.
+
 
+
Triangles and corners
+
 
+
# M. Ajtai, E. Szemerédi, Sets of lattice points that form no squares, Stud. Sci. Math. Hungar. 9 (1974), 9--11 (1975). [http://www.ams.org/mathscinet-getitem?mr=369299 MR369299]
+
# I. Ruzsa, E. Szemerédi, Triple systems with no six points carrying three triangles. Combinatorics (Proc. Fifth Hungarian Colloq., Keszthely, 1976), Vol. II, pp. 939--945, Colloq. Math. Soc. János Bolyai, 18, North-Holland, Amsterdam-New York, 1978. [http://www.ams.org/mathscinet-getitem?mr=519318 MR519318]
+
# J. Solymosi, [http://journals.cambridge.org/action/displayAbstract?fromPage=online&aid=206943 A note on a question of Erdős and Graham], Combin. Probab. Comput. 13 (2004), no. 2, 263--267. [http://www.ams.org/mathscinet-getitem?mr=2047239 MR 2047239]
+
 
+
[[Kruskal-Katona theorem]]
+
 
+
# P. Keevash, "[http://arxiv.org/abs/0806.2023 Shadows and intersections: stability and new proofs]", preprint.
+

Latest revision as of 10:10, 27 November 2018

This is the wiki for polymath projects - massively collaborative online mathematical projects. The idea of such projects originated in Tim Gowers' blog post Is massively collaborative mathematics possible?

Many polymath projects will be proposed, planned, and run at This Blog.

A Polymath logo is being trialled. If you have more suggestions, please add them to the logo page, or add to the discussion at Talk:logo.

The wiki is currently locked down due to a major influx of spam (July 29, 2013). Please email mn@michaelnielsen.org if you'd like an account set up, and I'll do my best to reply quickly.

Existing polymath projects

  • Polymath1: New proofs and bounds for the density Hales-Jewett theorem. Initiated Feb 1, 2009; research results have now been published.
  • Polymath2: Must an “explicitly defined” Banach space contain [math]c_0[/math] or [math]l_p[/math]? Initiated Feb 17, 2009; attempts to relaunch via wiki, June 9 2010.
  • Mini-polymath1: Solving Problem 6 of the 2009 International Mathematical Olympiad. Initiated July 20, 2009; five proofs obtained so far.
  • Polymath3. The polynomial Hirsch conjecture. Proposed July 17, 2009; launched, September 30, 2010.
  • Polymath4: A deterministic way to find primes. Proposed July 27, 2009; launched Aug 9, 2009. Research results have now been published.
  • Polymath5: The Erdős discrepancy problem. Proposed Jan 10, 2010; launched Jan 19, 2010. Activity ceased by the end of 2012, but results from the project were used to solve the problem in 2015.
  • Mini-polymath2: Solving Problem 5 the 2010 International Mathematical Olympiad. Proposed Jun 12, 2010; launched and solved, Jul 8 2010.
  • Polymath6: Improving the bounds for Roth's theorem. Proposed Feb 5, 2011.
  • Mini-polymath3: Solving a problem from the 2011 International Mathematical Olympiad. Proposed Jun 9, 2011; launched and solved, Jul 19, 2011.
  • Mini-polymath4: Solving a problem from the 2012 International Mathematical Olympiad. Proposed, Jun 3, 2012; launched, July 12 2012.
  • Polymath7: Establishing the Hot Spots conjecture for acute-angled triangles. Proposed, May 31st, 2012; launched, Jun 8, 2012.
  • Polymath8: Improving the bounds for small gaps between primes. Proposed, June 4, 2013; launched, June 4, 2013. Research results have now been published.
  • Polymath9: exploring Borel determinacy-based methods for giving complexity bounds. Proposed, Oct 24, 2013; launched, Nov 3, 2013.
  • Polymath10: improving the bounds for the Erdos-Rado sunflower lemma. Launched, Nov 2, 2015.
  • Polymath11: proving Frankl's union-closed conjecture. Proposed Jan 21, 2016; launched Jan 29, 2016. Concluded, Jan 17, 2017.
  • Polymath12: proving Rota's conjecture. Proposed Feb 28, 2017.
  • Polymath13: Intransitive dice. Proposed Apr 28, 2017.
  • Polymath14: Classifying homogeneous norms on groups. Initiated Dec 16, 2017; solved Dec 21, 2017. Research results have now been published.
  • Polymath15: Upper bounding the de Bruin-Newman constant. Proposed, Jan 24 2018; launched Jan 27 2018.
  • Polymath16: Simplifying the lower bound proof for the Hadwiger-Nelson problem. Proposed, Apr 10, 2018; launched, Apr 14, 2018.

Polymath-like projects

Proposed polymath projects


A (partial) list of proposed projects can be found here.

If you have a tentative proposal for a polymath project, you can either make a post on it on your own blog, or place it here.

Discussions about polymath

Additional links are very welcome.

Other links

Note on anonymous editing

To help combat spam, anonymous editing has been disabled, and a captcha system added to hinder automated account creation. If this is causing problems, please email mn@michaelnielsen.org.

Note on image uploads

Image uploads have been disabled, as they were causing problems with spam. If you'd like to upload an image, please email mn@michaelnielsen.org