Difference between revisions of "Timeline"

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Some highlights of the polymath1 project to date.
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A partial list of events occurring during the polymath1 project to date.
  
 
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Trevisan: [http://lucatrevisan.wordpress.com/2009/02/01/a-peoples-history-of-mathematics/ A people's history of mathematics]
 
Trevisan: [http://lucatrevisan.wordpress.com/2009/02/01/a-peoples-history-of-mathematics/ A people's history of mathematics]
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Blank: [http://hyperpapeterie.wordpress.com/2009/02/01/massively-collaborative-mathematics/ Massively collaborative mathematics]
 
| [http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/#comment-1648 Solymosi.2]: IP-corners problem proposed
 
| [http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/#comment-1648 Solymosi.2]: IP-corners problem proposed
  
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| Feb 2
 
| Feb 2
|  
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| Vipulnaik: [http://whatisresearch.wordpress.com/2009/02/02/on-new-modes-of-mathematical-collaboration/ On new modes of mathematical collaboration]
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| [http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/#comment-1661 Gowers.9]: Reweighting vertices needed for Varnavides?
 
| [http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/#comment-1661 Gowers.9]: Reweighting vertices needed for Varnavides?
  
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| Feb 5
 
| Feb 5
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| Tea time: [http://virtualteatime.blogspot.com/2009/02/introspection.html Introspection]
 
| [http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/#comment-1853 Tao.130]: DHJ(2.5)?
 
| [http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/#comment-1853 Tao.130]: DHJ(2.5)?
  
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|-
 
|-
 
| Feb 11
 
| Feb 11
| [http://docs.google.com/Doc?id=dhs78pth_15dfw8jhz4 Tao.470]: Proto-wiki created
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| le Bruyn: [http://www.neverendingbooks.org/index.php/yet-another-math20-proposal.html Yet another Math 2.0 proposal]
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[http://docs.google.com/Doc?id=dhs78pth_15dfw8jhz4 Tao.470]: Proto-wiki created
 
| [http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2086 Tao.451]: 01-insensitive case OK
 
| [http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2086 Tao.451]: 01-insensitive case OK
  
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|-
 
|-
 
| Feb 20
 
| Feb 20
| Vipulniak: [http://whatisresearch.wordpress.com/2009/02/20/a-quick-review-of-the-polymath-project/ A quick review of the polymath project]
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| Vipulnaik: [http://whatisresearch.wordpress.com/2009/02/20/a-quick-review-of-the-polymath-project/ A quick review of the polymath project]
 
| [http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2296 Solymosi.563]: Moser(6) implies DHJ(3)
 
| [http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2296 Solymosi.563]: Moser(6) implies DHJ(3)
 
| [http://terrytao.wordpress.com/2009/02/11/a-reading-seminar-on-density-hales-jewett/#comment-36041 Tao.630]: IP convergence lemma
 
| [http://terrytao.wordpress.com/2009/02/11/a-reading-seminar-on-density-hales-jewett/#comment-36041 Tao.630]: IP convergence lemma
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[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36059 Tao.753]: Sequences submitted to OEIS
 
[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36059 Tao.753]: Sequences submitted to OEIS
|-
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| Feb 22
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|-
 
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| Feb 23
 
| Feb 23
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|  
 
|  
 
| Gowers: [http://gowers.wordpress.com/2009/03/02/dhj3-851-899/ DHJ 851-899]
 
| Gowers: [http://gowers.wordpress.com/2009/03/02/dhj3-851-899/ DHJ 851-899]
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[http://gowers.wordpress.com/2009/03/02/dhj3-851-899/#comment-2525 Tao.853] Mass increment; connection with Hahn decomposition
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[http://gowers.wordpress.com/2009/03/02/dhj3-851-899/#comment-2530 Gowers.854] Higher-D Ajtai-Szemeredi?
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|  
 
|  
 
|  
 
|  
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|-
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| Mar 3
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|
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|
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| [http://gowers.wordpress.com/2009/03/02/dhj3-851-899/#comment-2555 McCutcheon.864] Caution: 12-sets not sigma-algebra!
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| [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36277 Dyer.786] <math> \overline{c}^\mu_6 < 18</math>
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[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36287 Cantwell.787] 125-sets have at most 41 points in middle slices
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|-
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| Mar 4
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|
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|
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|
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|[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36298 Markstrom.788]: <math> c^\mu_n = 4,6,9,12</math> for <math>n=2,3,4,5</math>
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[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36303 Marc.791]: <math>\overline{c}^\mu_{10} \geq 29</math>
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[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36310 Tao.793]: "score" introduced
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Tao: [http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers DHJ3 (900-999) Density Hales-Jewett type numbers]
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[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36331 Tao.901]: 125-sets have D=0
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[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36332 Dyer.902]: <math>\overline{c}^\mu_6 < 17</math>
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[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36333 Carr.903]: Genetic algorithm implemented
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|-
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| Mar 5
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|
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|
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|
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| [http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36343 Peake.904] Scores for 6D Moser?
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[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36349 Tao.908] Find Pareto-optimal and extremal statistics?
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[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36350 Dyer.909] Wildcard variants of Moser
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 +
[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36360 Cantwell.912] 125-sets have at most 40 points in middle slices
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 +
[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36362 Cantwell.913] 125-sets have D=0 (alternate proof)
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[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36379 Peake.914] Pareto-optimal 3D statistics
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|-
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| Mar 6
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|
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| [http://gowers.wordpress.com/2009/03/02/dhj3-851-899/#comment-2595 Gowers.873] 12-set density increment difficulty identified
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|
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| [http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36399 Dyer.917] <math>\overline{c}^\mu_7 \leq 22</math>
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[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36401 Cantwell.920] <math>c'_6 \leq 373</math>
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[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36404 Cantwell.921] 125-sets have C=78 or 79
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[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36406 Markstrom.923] <math>\overline{c}^\mu_n = 6,9,12,15,18,22,26,31,35,40</math> for <math>n=3,\ldots,12</math>
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 +
[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36417 Guest.930] GA without crossover?
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|-
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| Mar 7
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|
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| [http://gowers.wordpress.com/2009/03/02/dhj3-851-899/#comment-2609 Solymosi.880] Shelah-type flip-flop spaces?
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|
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| [http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36421 Peake.931] 3D extremals and inequalities
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[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36431 Cantwell.932] 125-sets have a middle slice of at most 39 points
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[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36432 Cantwell.933] 125-sets have A=6,7,8
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[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36433 Cantwell.934] If C=78 then A=7,8
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[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36436 Tao.935] 125-sets have stats (6,40,79,0,0,0), (7,40,78,0,0) or (8,39,78,0,0)
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|-
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| Mar 8
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|
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| [http://gowers.wordpress.com/2009/03/02/dhj3-851-899/#comment-2613 Gowers.881] Iterative partitioning of 12-sets?
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[http://gowers.wordpress.com/2009/03/02/dhj3-851-899/#comment-2622 Gowers.882] New proof of Ajtai-Szemeredi
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[http://gowers.wordpress.com/2009/03/02/dhj3-851-899/#comment-2626 O'Donnell.884] Multidimensional Sperner written up
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|
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| [http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36463 Peake.939] <math>c'_6 \leq 365</math>
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[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36465 Carr.940] <math>c'_6 \geq 353; c'_7 \geq 978</math>
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 +
[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36469 Tao.941] Seeding GA?
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[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36475 Cantwell.942] (6,40,79,0,0) eliminated
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 +
[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36481 Tao.943] Linear programming proof of <math>c'_4 =43</math>
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[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36487 Tao.944] <math>c'_6 \leq 364</math>
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|-
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| Mar 9
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|
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| [http://gowers.wordpress.com/2009/03/02/dhj3-851-899/#comment-2633 Gowers.885] Sketch of DHJ(3)
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[http://gowers.wordpress.com/2009/03/02/dhj3-851-899/#comment-2636 Gowers.886] DHJ(4)?
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[http://gowers.wordpress.com/2009/03/02/dhj3-851-899/#comment-2666 Gowers.897] Writing of DHJ(k) begins
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| [http://gowers.wordpress.com/2009/03/02/dhj3-851-899/#comment-2656 Austin.894] New ergodic proof of DHJ(k)
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| [http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36508 Cantwell.945] (7,40,78,0,0) eliminated
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[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36515 Cantwell.949] (8,39,87,0,0) eliminated: <math>c'_5 = 124</math>
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[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36519 Tao.950] <math>\overline{c}^\mu_n</math> submitted to OEIS
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[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36528 Carr.954] <math>c'_7 \geq 988</math>
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|-
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| Mar 10
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| Gowers: [http://gowers.wordpress.com/2009/03/10/polymath1-and-open-collaborative-mathematics/ Polymath1 and open collaborative mathematics]
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OU Math club: [http://oumathclub.wordpress.com/2009/03/10/problem-solved-probably/ Problem solved (probably)]
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| Gowers: [http://gowers.wordpress.com/2009/03/10/problem-solved-probably/ Problem solved (probably)] (1000-1049)
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[http://gowers.wordpress.com/2009/03/10/problem-solved-probably/#comment-2700 Gowers.1005.1] Tower-type bounds
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| [http://gowers.wordpress.com/2009/03/10/problem-solved-probably/#comment-2689 Tao.1003] 1-sets, 2-sets locally independent
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|
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|-
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| Mar 11
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| Kalai: [http://gilkalai.wordpress.com/2009/03/11/polymath1-probable-success/ Polymath1: probable success]
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| [http://gowers.wordpress.com/2009/03/10/problem-solved-probably/#comment-2713 Gowers.1007] Correlation component of DHJ(k) proof complete
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[http://gowers.wordpress.com/2009/03/10/problem-solved-probably/#comment-2733 Solymosi.1011] Shelah-type argument?
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|
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| [http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36575 Markstrom.961] Partial confirmation of HOC for n=6,7
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[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36577 Elsholtz.962] Analysis of GA solutions
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[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36599 Tao.969] Integer programming for Behrend sphere statistics
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[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36600 Tao.970] <math>c'_7 \leq 1086</math>
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|-
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| Mar 12
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|
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| [http://gowers.wordpress.com/2009/03/10/problem-solved-probably/#comment-2805 O'Donnell.1021] DHJ(k) => Varnavides completed
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[http://gowers.wordpress.com/2009/03/10/problem-solved-probably/#comment-2799 Gowers.1020] No apparent obstacles to proving DHJ(k)
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[http://gowers.wordpress.com/2009/03/10/problem-solved-probably/#comment-2826 O'Donnell.1025] Work exclusively with equal (non-degenerate) slices measure?
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| [http://gowers.wordpress.com/2009/03/10/problem-solved-probably/#comment-2825 Tao.1024] Informal combinatorial translation of Austin's proof
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| [http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36609 Markstrom.972], [http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36614 Dyer.973], [http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36617 Tao.974], [http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36625 Markstrom.977]: Integer programming problem discovered, isolated, fixed
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[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36617 Tao.974]: <math>c'_6 \leq 361</math>, <math>c'_7 \leq 1078</math>
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[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36624 Cantwell.976]: Partial recovery of 4D stats by hand
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|-
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| Mar 13
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| Nielsen: [http://michaelnielsen.org/blog/?p=579 Biweekly links for 03/13/2009]
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Galdino: [http://prafalardecoisas.wordpress.com/2009/03/13/links-semanais/ Links seminais]
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Flaxman: [http://healthyalgorithms.wordpress.com/2009/03/13/gowers-polymath-experiment-problem-probably-solved/ Gowers' polymath experiment: problem probably solved]
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|
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|
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| [http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36652 Elsholtz.980]: Use e=1, f=1, etc. refinements
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[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36655 Peake.982]: xxyyzz inequalities
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[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36657 O'Bryant.984], [http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36680 O'Bryant.993]: <math>c_n \gg 3^{n - 4\sqrt{\log 2}\sqrt{\log n}+\frac 12 \log \log n}</math>
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[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36659 Cantwell.985]: Human proof of <math>c^\mu_3=6</math> begins
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[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36666 Peake.989]: xxyyz inequalities
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[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36667 Tao.990]: <math>c'_7 \leq 1071</math>
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[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36672 Peake.991]: xxxyz, xxxxyz, xxxyyz inequalities
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[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36694 Seva.994]: Kakeya in [3]^n?
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|-
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| Mar 14
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| Hariss: [http://maxwelldemon.wordpress.com/2009/03/14/polymath/ Polymath]
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|
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| [http://gowers.wordpress.com/2009/03/10/problem-solved-probably/#comment-2871 Tao.1035] Ramsey-free translation of Austin's proof
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| Tao: [http://terrytao.wordpress.com/2009/03/14/dhj3-1100-1199-density-hales-jewett-type-numbers/ DHJ(3) 1100-1199]
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|-
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| Mar 15
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| Neylon: [http://blog.openwetware.org/scienceintheopen/2009/03/15/there-are-crowds-and-then-there-are-crowds/ There are crowds, and then there are crowds...]
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|
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|-
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| Mar 16
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|
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| Gowers: [http://gowers.wordpress.com/2009/03/16/dhj3-and-related-results-1050-1099/ DHJ(3) and related results: 1050-1099]
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|
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|-
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| Mar 18
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| Polymath hits front page of Slashdot with [http://science.slashdot.org/article.pl?sid=09/03/18/194228  this article]
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Nielsen: [http://michaelnielsen.org/blog/?p=581 How changing the technology of collaboration can change the nature of collaboration]
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|-
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| Mar 20
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| Nielsen: [http://michaelnielsen.org/blog/?p=584 The Polymath project: scope of participation]
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|-
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| Mar 21
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| Gans: [http://economics.com.au/?p=3000 Something interesting is going on in Maths]
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|-
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| Mar 24
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| Gowers: [http://gowers.wordpress.com/2009/03/24/can-polymath-be-scaled-up/#comments Can Polymath be scaled up?]
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Vipulnaik: [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]
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|-
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| Mar 25
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| Nielsen: [http://michaelnielsen.org/blog/?p=588 On scaling up the polymath project]
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Dyer: [http://numberwarrior.wordpress.com/2009/03/25/a-gentle-introduction-to-the-polymath-project/ A gentle introduction to the Polymath project]
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Latest revision as of 15:47, 5 April 2009

A partial list of events occurring during the polymath1 project to date.

Date General Uniformity Ergodic theory Small n
Jan 26 Nielsen: Doing science online
Jan 27 Gowers: Is massively collaborative mathematics possible?
Jan 28 Kalai: Mathematics, science, and blogs
Jan 30 Gowers: Background to a polymath project

Nielsen: Is massively collaborative mathematics possible?

Feb 1 Gowers: Questions of procedure

Gowers: A combinatorial approach to DHJ (1-199)

Gowers: Why this particular problem?

Tao: A massively collaborative mathematical project

Trevisan: A people's history of mathematics

Blank: Massively collaborative mathematics

Solymosi.2: IP-corners problem proposed

Tao.4: Analytic proof of Sperner? Regularisation needed?

Hoang.4: Naive Varnavides for DHJ fails

Gowers.1: Carlson-Simpson theorem useful?

Tao.4: Stationarity useful?

Feb 2 Vipulnaik: On new modes of mathematical collaboration Gowers.9: Reweighting vertices needed for Varnavides?

Tao.17: Should use [math]O(\sqrt{n})[/math] wildcards

Tao.18: Use rich slices?

Gowers.19: Collect obstructions to uniformity!

Kalai.29: Fourier-analytic proof of Sperner?

O'Donnell.32: Use uniform distribution on slices

Gowers.38: Can't fix # wildcards in advance

Tao.39: Can take # wildcards to be O(1)

Bukh.44: Obstructions to Kruskal-Katona?

Tao.8: [math]c_0=1[/math], [math]c_1=2[/math], [math]c_2=6[/math], [math]3^{n-O(\sqrt{n}} \leq c_n \leq o(3^n)[/math]

Kalai.15: [math]c_n \gg 3^n/\sqrt{n}[/math]

Tao.39: [math]c_n \geq 3^{n-O(\sqrt{\log n})}[/math]

Tao.40: [math]c_3=18[/math]

Elsholtz.43: Moser(3)?

Feb 3 Nielsen: The polymath project Gowers.64: Use local equal-slices measure?

Gowers.70: Collection of obstructions to uniformity begins

Tao.86: Use Szemeredi's proof of Roth?

Jakobsen.59: [math]c_4 \geq 49[/math]

Tao.78: [math]c_4 \leq 54[/math]

Neylon.83: [math]52 \leq c_4 \leq 54[/math], [math]140 \leq c_5 \leq 162[/math]

Feb 4 Gowers: Quick question Tao.100: Use density incrementation?

Tao.118: Szemeredi's proof of Roth looks inapplicable

Jakobsen.90: [math]c_4=52[/math]
Feb 5 Tea time: Introspection Tao.130: DHJ(2.5)?

Bukh.132, O'Donnell.133, Solymosi.135: Proof of DHJ(2.5)

Tao.148: Obstructions to uniformity summarised

Tao: Upper and lower bounds for DHJ (200-299)
Feb 6 Solymosi.155: Pair removal for Kneser graphs

Gowers: The triangle removal approach (300-399)

Neylon.201: Greedy algorithm

Tao.206: Use [math]D_n[/math]

Feb 7 Gowers.335: DHJ(j,k) introduced Jakobsen.207: [math]c_5 \geq 150[/math], [math]c_6 \geq 450[/math]

Peake.217: [math]c_7 \geq 1308[/math], [math]c_8 \geq 3780[/math]

Peake.218: Lower bounds up to [math]c_{15}[/math]

Feb 8 Gowers: Quasirandomness and obstructions to uniformity: (400-499)

Ajtai-Szemeredi approach proposed

Tao.402: Standard obstruction to uniformity?

Gowers.403: Complexity 1 sets are more fundamental obstructions

Gowers.411: Are global complexity 1 sets the only obstructions?

Peake.219: [math]c_{99} \geq 3^{98}[/math]

Tao.225: Spreadsheet set up

Feb 9 Nielsen: Update on the polymath project Bukh.412: Negative answer to Gowers' question

Gowers.365: Equal slices measure introduced

Tao.419: Use low-influence instead of complexity 1?

Gowers.420: Need DHJ(0,2)

Tao.431: Use local obstructions rather than global obstructions?

Kalai.233: Higher k?
Feb 10 Tao.439: Use hypergraph regularity? Peake.241: [math]c_5 \leq 155[/math]; xyz notation

Peake.243: [math]c_5 \leq 154[/math]

Feb 11 le Bruyn: Yet another Math 2.0 proposal

Tao.470: Proto-wiki created

Tao.451: 01-insensitive case OK

Kalai.455: Hyper-optimistic conjecture

Tao.460: Connections with ergodic approach

Tao: A reading seminar on DHJ (600-699)

Tao.249: [math]\overline{c}^\mu_0 = 1[/math], [math]\overline{c}^\mu_1 = 2[/math], [math]\overline{c}^\mu_2 = 4[/math]

Dyer.254: [math]\overline{c}^\mu_3 = 6[/math]

Feb 12 Wiki set up O'Donnell.476: Fourier-analytic Sperner computations

McCutcheon.480: Strong Roth theorem proposed

Jakobsen.257: [math]\overline{c}^\mu_4 = 9[/math]

Jakobsen.258: [math]\overline{c}^\mu_5 = 12[/math]

Peake.262: Extremisers for [math]c_4[/math]

Feb 13 Gowers: Possible proof strategies (500-599) McCutcheon.505: IP uniformity norms?

Tao.614: Carlson-Simpson not needed for stationarity

Tao: Bounds for first few DHJ numbers (700-799)
Feb 14 Gowers.496: Equal slices implies uniform McCutcheon.508: Ergodic proof strategy

Tao.618: More randomness needed to invert maps

O'Donnell.622: [math][3]^n[/math] should already provide enough randomness

Tao.510: Finitary analogue of stationarity

Sauvaget: A proof that [math]c_5=154[/math]?
Feb 15 Tao.498: Uniform implies equal slices

Tao.514: DHJ(2.6) proposed

McCutcheon.518: Ramsey proof of DHJ(2.6)

Sauvaget: A new strategy for computing [math]c_n[/math]

Markström.706: Integer program, [math]c_5=150[/math]

Cantwell.708: [math]c_6=450[/math]

Tao.715: Genetic algorithm?

Feb 16 Tao.524: Simplification of proof

O'Donnell 529: Ramsey-free proof of DHJ(2.6)?

McCutcheon.533: Ramsey theory incompatible with symmetry

Tao.626: Ramsey theorems summarised Peake.730: [math]c_5[/math] extremisers

Tao.731: Human proof that [math]c_5 \leq 152[/math]; [math]c_7 \leq 1348[/math]

Feb 17 Tao.536: Fourier-analytic proof of DHJ(2.6)

McCutcheon.541: "Cave-man" proof of DHJ(2.6)

Chua.736: [math]c'_5 \geq 124[/math]

Peake.738: Connection between Moser(3) and sphere packing

Feb 18 Gowers.544: Corners(1,3)?

Gowers.545: Fourier computations on equal-slices measure begin

Markström.739: [math]c_6[/math] extremiser unique
Feb 19 Markström.742: 43-point Moser sets in [math][3]^4[/math] listed

Peake.743: 43-point sets analysed

Cantwell.744: [math]c'_5 \leq 128[/math]

Tao.745: 50+ point line-free sets in [math][3]^4[/math] listed

Feb 20 Vipulnaik: A quick review of the polymath project Solymosi.563: Moser(6) implies DHJ(3) Tao.630: IP convergence lemma Markström.747: 42-point Moser sets listed

Peake.751: Human proof of [math]c_5 \leq 151[/math]

Feb 21 Gowers: To thread or not to thread Gowers.580: Extreme localisation + density increment = DHJ(3)?

Gowers.581: Multidimensional Sperner

Gowers.582: Use Ajtai-Szemeredi argument to get density increment?

Tao.631: Informal combinatorial translation of ergodic DHJ(2)

Tao.578: Finitary ergodic proof of DHJ(2) proposed

Tao.632: Special cases of DHJ(3) translated

Peake.752: Human proof of [math]c_5=150[/math], [math]c_6=450[/math]

Tao.753: Sequences submitted to OEIS

Feb 23 McCutcheon.593: DHJ(2.7)

O'Donnell.596: Fourier-analytic proof of DHJ(2)

Gowers: Brief review of polymath1 (800-849)

O'Donnell.800: Fourier-analytic + density increment proof of DHJ(2)

Markström.463: 42-point Moser sets analysed

Tao.464: [math]c'_5 \leq 127[/math]

Chua.766: 3D Moser sets with 222 have [math] \leq 13[/math] points

Tao.767: 4D Moser sets with 2222 have [math] \leq 39[/math] points

Feb 24 Tao.809.2: Low-influence implies Sperner-positivity

Gowers.812: Fourier vs physical positivity

O'Donnell.814: [math]\ell_1[/math], [math]\ell_2[/math] equivalence

Feb 25 Gowers.820: Density increment on complexity 1 set Tao.818: Finitary ergodic sketch of DHJ(3)

O'Donnell.821: Simplified Fourier proof of DHJ(2) structure theorem

Cantwell.769: 5D Moser sets with 2222* have [math] \leq 124[/math] points

Peake.771: Exotic 43-point Moser sets described

Feb 26 Gowers.824: Complexity 1 + Ajtai-Szemeredi DHJ(3) sketch
Feb 27 Tao.826: Non-Fourier proof of DHJ(2) structure theorem

Gowers.828: Does correlation with 1-set imply density increment?

Tao.828.4: Energy increment proof for Gowers Q?

McCutcheon.832.2: Use dense fibres to answer Gowers Q? Elsholtz.775: Human proof of 2222* result

Cantwell.776: [math]c'_5 \leq 126[/math]

Feb 28 Tao.834: Use pullbacks for Gowers Q?

Gowers.835: Pullbacks don't work

O'Donnell 839: Increment-free Fourier proof of DHJ(2)

Tao.837.2: Dense fibres argument for Gowers Q Markström.779: 41-point Moser sets listed
Mar 1 Cantwell.782, Peake.784: [math]c'_5 \leq 125[/math]
Mar 2 Gowers: DHJ 851-899

Tao.853 Mass increment; connection with Hahn decomposition

Gowers.854 Higher-D Ajtai-Szemeredi?

Mar 3 McCutcheon.864 Caution: 12-sets not sigma-algebra! Dyer.786 [math] \overline{c}^\mu_6 \lt 18[/math]

Cantwell.787 125-sets have at most 41 points in middle slices

Mar 4 Markstrom.788: [math] c^\mu_n = 4,6,9,12[/math] for [math]n=2,3,4,5[/math]

Marc.791: [math]\overline{c}^\mu_{10} \geq 29[/math]

Tao.793: "score" introduced

Tao: DHJ3 (900-999) Density Hales-Jewett type numbers

Tao.901: 125-sets have D=0

Dyer.902: [math]\overline{c}^\mu_6 \lt 17[/math]

Carr.903: Genetic algorithm implemented

Mar 5 Peake.904 Scores for 6D Moser?

Tao.908 Find Pareto-optimal and extremal statistics?

Dyer.909 Wildcard variants of Moser

Cantwell.912 125-sets have at most 40 points in middle slices

Cantwell.913 125-sets have D=0 (alternate proof)

Peake.914 Pareto-optimal 3D statistics

Mar 6 Gowers.873 12-set density increment difficulty identified Dyer.917 [math]\overline{c}^\mu_7 \leq 22[/math]

Cantwell.920 [math]c'_6 \leq 373[/math]

Cantwell.921 125-sets have C=78 or 79

Markstrom.923 [math]\overline{c}^\mu_n = 6,9,12,15,18,22,26,31,35,40[/math] for [math]n=3,\ldots,12[/math]

Guest.930 GA without crossover?

Mar 7 Solymosi.880 Shelah-type flip-flop spaces? Peake.931 3D extremals and inequalities

Cantwell.932 125-sets have a middle slice of at most 39 points

Cantwell.933 125-sets have A=6,7,8

Cantwell.934 If C=78 then A=7,8

Tao.935 125-sets have stats (6,40,79,0,0,0), (7,40,78,0,0) or (8,39,78,0,0)

Mar 8 Gowers.881 Iterative partitioning of 12-sets?

Gowers.882 New proof of Ajtai-Szemeredi

O'Donnell.884 Multidimensional Sperner written up

Peake.939 [math]c'_6 \leq 365[/math]

Carr.940 [math]c'_6 \geq 353; c'_7 \geq 978[/math]

Tao.941 Seeding GA?

Cantwell.942 (6,40,79,0,0) eliminated

Tao.943 Linear programming proof of [math]c'_4 =43[/math]

Tao.944 [math]c'_6 \leq 364[/math]

Mar 9 Gowers.885 Sketch of DHJ(3)

Gowers.886 DHJ(4)?

Gowers.897 Writing of DHJ(k) begins

Austin.894 New ergodic proof of DHJ(k) Cantwell.945 (7,40,78,0,0) eliminated

Cantwell.949 (8,39,87,0,0) eliminated: [math]c'_5 = 124[/math]

Tao.950 [math]\overline{c}^\mu_n[/math] submitted to OEIS

Carr.954 [math]c'_7 \geq 988[/math]

Mar 10 Gowers: Polymath1 and open collaborative mathematics

OU Math club: Problem solved (probably)

Gowers: Problem solved (probably) (1000-1049)

Gowers.1005.1 Tower-type bounds

Tao.1003 1-sets, 2-sets locally independent
Mar 11 Kalai: Polymath1: probable success Gowers.1007 Correlation component of DHJ(k) proof complete

Solymosi.1011 Shelah-type argument?

Markstrom.961 Partial confirmation of HOC for n=6,7

Elsholtz.962 Analysis of GA solutions

Tao.969 Integer programming for Behrend sphere statistics

Tao.970 [math]c'_7 \leq 1086[/math]

Mar 12 O'Donnell.1021 DHJ(k) => Varnavides completed

Gowers.1020 No apparent obstacles to proving DHJ(k)

O'Donnell.1025 Work exclusively with equal (non-degenerate) slices measure?

Tao.1024 Informal combinatorial translation of Austin's proof Markstrom.972, Dyer.973, Tao.974, Markstrom.977: Integer programming problem discovered, isolated, fixed

Tao.974: [math]c'_6 \leq 361[/math], [math]c'_7 \leq 1078[/math]

Cantwell.976: Partial recovery of 4D stats by hand

Mar 13 Nielsen: Biweekly links for 03/13/2009

Galdino: Links seminais

Flaxman: Gowers' polymath experiment: problem probably solved

Elsholtz.980: Use e=1, f=1, etc. refinements

Peake.982: xxyyzz inequalities

O'Bryant.984, O'Bryant.993: [math]c_n \gg 3^{n - 4\sqrt{\log 2}\sqrt{\log n}+\frac 12 \log \log n}[/math]

Cantwell.985: Human proof of [math]c^\mu_3=6[/math] begins

Peake.989: xxyyz inequalities

Tao.990: [math]c'_7 \leq 1071[/math]

Peake.991: xxxyz, xxxxyz, xxxyyz inequalities

Seva.994: Kakeya in [3]^n?

Mar 14 Hariss: Polymath Tao.1035 Ramsey-free translation of Austin's proof Tao: DHJ(3) 1100-1199
Mar 15 Neylon: There are crowds, and then there are crowds...
Mar 16 Gowers: DHJ(3) and related results: 1050-1099
Mar 18 Polymath hits front page of Slashdot with this article

Nielsen: How changing the technology of collaboration can change the nature of collaboration

Mar 20 Nielsen: The Polymath project: scope of participation
Mar 21 Gans: Something interesting is going on in Maths
Mar 24 Gowers: Can Polymath be scaled up?

Vipulnaik: Concluding notes on the polymath project - and a challenge


Mar 25 Nielsen: On scaling up the polymath project

Dyer: A gentle introduction to the Polymath project