Timeline

2009-04-05T23:47:32Z

128.135.194.51: Correcting spelling of my name

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

{| border=1
|-
!Date!!General!! Uniformity !! Ergodic theory !! Small n
|-
| Jan 26
| Nielsen: [http://michaelnielsen.org/blog/?p=545 Doing science online]
|-
| Jan 27
| Gowers: [http://gowers.wordpress.com/2009/01/27/is-massively-collaborative-mathematics-possible/ Is massively collaborative mathematics possible?]
|-
| Jan 28
| Kalai: [http://gilkalai.wordpress.com/2009/01/28/mathematics-science-and-blogs/ Mathematics, science, and blogs]
|-
| Jan 30
| Gowers: [http://gowers.wordpress.com/2009/01/30/background-to-a-polymath-project/ Background to a polymath project]
Nielsen: [http://michaelnielsen.org/blog/?p=550 Is massively collaborative mathematics possible?]
|-
| Feb 1
| Gowers: [http://gowers.wordpress.com/2009/02/01/questions-of-procedure/ Questions of procedure]
Gowers: [http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/ A combinatorial approach to DHJ] (1-199)

Gowers: [http://gowers.wordpress.com/2009/02/01/why-this-particular-problem/ Why this particular problem?]

Tao: [http://terrytao.wordpress.com/2009/02/01/a-massively-collaborative-mathematical-project/ A massively collaborative mathematical project]

Trevisan: [http://lucatrevisan.wordpress.com/2009/02/01/a-peoples-history-of-mathematics/ A people's history of mathematics]

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

[http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/#comment-1648 Hoang.4]: Naive Varnavides for DHJ fails

| [http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/#comment-1646 Gowers.1]: Carlson-Simpson theorem useful?

[http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/#comment-1648 Tao.4]: Stationarity useful?

|-
| Feb 2
| Vipulnaik: [http://whatisresearch.wordpress.com/2009/02/02/on-new-modes-of-mathematical-collaboration/ On new modes of mathematical collaboration]

| [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-1673 Tao.17]: Should use <math>O(\sqrt{n})</math> wildcards

[http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/#comment-1674 Tao.18]: Use rich slices?

[http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/#comment-1675 Gowers.19]: Collect obstructions to uniformity!

[http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/#comment-1688 Kalai.29]: Fourier-analytic proof of Sperner?

[http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/#comment-1691 O'Donnell.32]: Use uniform distribution on slices

[http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/#comment-1698 Gowers.38]: Can't fix # wildcards in advance

[http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/#comment-1702 Tao.39]: Can take # wildcards to be O(1)

[http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/#comment-1710 Bukh.44]: Obstructions to Kruskal-Katona?
|
| [http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/#comment-1659 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>

[http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/#comment-1671 Kalai.15]: <math>c_n \gg 3^n/\sqrt{n}</math>

[http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/#comment-1702 Tao.39]: <math>c_n \geq 3^{n-O(\sqrt{\log n})}</math>

[http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/#comment-1703 Tao.40]: <math>c_3=18</math>

[http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/#comment-1707 Elsholtz.43]: Moser(3)?
|-
| Feb 3
| Nielsen: [http://michaelnielsen.org/blog/?p=553 The polymath project]
| [http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/#comment-1747 Gowers.64]: Use local equal-slices measure?

[http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/#comment-1757 Gowers.70]: Collection of obstructions to uniformity begins

[http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/#comment-1781 Tao.86]: Use Szemeredi's proof of Roth?
|
| [http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/#comment-1710 Jakobsen.59]: <math>c_4 \geq 49</math>

[http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/#comment-1771 Tao.78]: <math>c_4 \leq 54</math>

[http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/#comment-1776 Neylon.83]: <math>52 \leq c_4 \leq 54</math>, <math>140 \leq c_5 \leq 162</math>
|-
| Feb 4
| Gowers: [http://gowers.wordpress.com/2009/02/04/quick-question/ Quick question]
| [http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/#comment-1803 Tao.100]: Use density incrementation?

[http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/#comment-1831 Tao.118]: Szemeredi's proof of Roth looks inapplicable
|
| [http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/#comment-1790 Jakobsen.90]: <math>c_4=52</math>
|-
| Feb 5
| 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-1856 Bukh.132], [http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/#comment-1857 O'Donnell.133], [http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/#comment-1859 Solymosi.135]: Proof of DHJ(2.5)

[http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/#comment-1882 Tao.148]: Obstructions to uniformity summarised
|
| Tao: [http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/ Upper and lower bounds for DHJ] (200-299)
|-
| Feb 6
|
| [http://gowers.wordpress.com/2009/02/01/a-combinatorial-approach-to-density-hales-jewett/#comment-1895 Solymosi.155]: Pair removal for Kneser graphs

Gowers: [http://gowers.wordpress.com/2009/02/06/dhj-the-triangle-removal-approach/ The triangle removal approach] (300-399)
|
| [http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35495 Neylon.201]: Greedy algorithm

[http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35528 Tao.206]: Use <math>D_n</math>
|-
| Feb 7
|
| [http://gowers.wordpress.com/2009/02/06/dhj-the-triangle-removal-approach/#comment-1945 Gowers.335]: DHJ(j,k) introduced
|
| [http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35537 Jakobsen.207]: <math>c_5 \geq 150</math>, <math>c_6 \geq 450</math>

[http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35585 Peake.217]: <math>c_7 \geq 1308</math>, <math>c_8 \geq 3780</math>

[http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35593 Peake.218]: Lower bounds up to <math>c_{15}</math>
|-
| Feb 8
|
| Gowers: [http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/ Quasirandomness and obstructions to uniformity]: (400-499)

Ajtai-Szemeredi approach proposed

[http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2001 Tao.402]: Standard obstruction to uniformity?

[http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2002 Gowers.403]: Complexity 1 sets are more fundamental obstructions

[http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2019 Gowers.411]: Are global complexity 1 sets the only obstructions?

|
| [http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35597 Peake.219]: <math>c_{99} \geq 3^{98}</math>

[http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35608 Tao.225]: Spreadsheet set up
|-
| Feb 9
| Nielsen: [http://michaelnielsen.org/blog/?p=555 Update on the polymath project]
| [http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2029 Bukh.412]: Negative answer to Gowers' question

[http://gowers.wordpress.com/2009/02/06/dhj-the-triangle-removal-approach/#comment-2047 Gowers.365]: Equal slices measure introduced

[http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2056 Tao.419]: Use low-influence instead of complexity 1?

[http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2057 Gowers.420]: Need DHJ(0,2)

[http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2072 Tao.431]: Use local obstructions rather than global obstructions?

|
| [http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35631 Kalai.233]: Higher k?
|-
| Feb 10
|
| [http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2086 Tao.439]: Use hypergraph regularity?
|
| [http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35662 Peake.241]: <math>c_5 \leq 155</math>; xyz notation

[http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35672 Peake.243]: <math>c_5 \leq 154</math>
|-
| Feb 11
| le Bruyn: [http://www.neverendingbooks.org/index.php/yet-another-math20-proposal.html Yet another Math 2.0 proposal]

[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-2114 Kalai.455]: Hyper-optimistic conjecture

| [http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2120 Tao.460]: Connections with ergodic approach

Tao: [http://terrytao.wordpress.com/2009/02/11/a-reading-seminar-on-density-hales-jewett/ A reading seminar on DHJ] (600-699)
| [http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35691 Tao.249]: <math>\overline{c}^\mu_0 = 1</math>, <math>\overline{c}^\mu_1 = 2</math>, <math>\overline{c}^\mu_2 = 4</math>

[http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35709 Dyer.254]: <math>\overline{c}^\mu_3 = 6</math>
|-
| Feb 12
| [http://michaelnielsen.org/polymath1/index.php?title=Main_Page Wiki set up]
| [http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2143 O'Donnell.476]: Fourier-analytic Sperner computations

[http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2149 McCutcheon.480]: Strong Roth theorem proposed

|
| [http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35728 Jakobsen.257]: <math>\overline{c}^\mu_4 = 9</math>

[http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35733 Jakobsen.258]: <math>\overline{c}^\mu_5 = 12</math>

[http://terrytao.wordpress.com/2009/02/05/upper-and-lower-bounds-for-the-density-hales-jewett-problem/#comment-35749 Peake.262]: Extremisers for <math>c_4</math>
|-
| Feb 13
|
| Gowers: [http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#more-441/ Possible proof strategies] (500-599)
| [http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2179 McCutcheon.505]: IP uniformity norms?

[http://terrytao.wordpress.com/2009/02/11/a-reading-seminar-on-density-hales-jewett/#comment-35801 Tao.614]: Carlson-Simpson not needed for stationarity
| Tao: [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/ Bounds for first few DHJ numbers] (700-799)
|-
| Feb 14
|
| [http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2183 Gowers.496]: Equal slices implies uniform
| [http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2185 McCutcheon.508]: Ergodic proof strategy

[http://terrytao.wordpress.com/2009/02/11/a-reading-seminar-on-density-hales-jewett/#comment-35821 Tao.618]: More randomness needed to invert maps

[http://terrytao.wordpress.com/2009/02/11/a-reading-seminar-on-density-hales-jewett/#comment-35837 O'Donnell.622]: <math>[3]^n</math> should already provide enough randomness

[http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2188 Tao.510]: Finitary analogue of stationarity

| Sauvaget: [http://thomas1111.wordpress.com/2009/02/14/a-proof-that-c_5154/ A proof that <math>c_5=154</math>?]
|-
| Feb 15
|
| [http://gowers.wordpress.com/2009/02/08/dhj-quasirandomness-and-obstructions-to-uniformity/#comment-2195 Tao.498]: Uniform implies equal slices

[http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2196 Tao.514]: DHJ(2.6) proposed

[http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2206 McCutcheon.518]: Ramsey proof of DHJ(2.6)
|
| Sauvaget: [http://thomas1111.wordpress.com/2009/02/15/a-new-strategy-for-computing-c_n/ A new strategy for computing <math>c_n</math>]

[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-35853 Markström.706]: Integer program, <math>c_5=150</math>

[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-35865 Cantwell.708]: <math>c_6=450</math>

[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-35877 Tao.715]: Genetic algorithm?

|-
| Feb 16
|
| [http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2214 Tao.524]: Simplification of proof

[http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2222 O'Donnell 529]: Ramsey-free proof of DHJ(2.6)?

[http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2228 McCutcheon.533]: Ramsey theory incompatible with symmetry
| [http://terrytao.wordpress.com/2009/02/11/a-reading-seminar-on-density-hales-jewett/#comment-35921 Tao.626]: Ramsey theorems summarised
| [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-35926 Peake.730]: <math>c_5</math> extremisers

[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-35927 Tao.731]: Human proof that <math>c_5 \leq 152</math>; <math>c_7 \leq 1348</math>
|-
| Feb 17
|
| [http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2234 Tao.536]: Fourier-analytic proof of DHJ(2.6)

[http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2242 McCutcheon.541]: "Cave-man" proof of DHJ(2.6)
|
| [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-35945 Chua.736]: <math>c'_5 \geq 124</math>

[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-35951 Peake.738]: Connection between Moser(3) and sphere packing

|-
| Feb 18
|
| [http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2255 Gowers.544]: Corners(1,3)?

[http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2260 Gowers.545]: Fourier computations on equal-slices measure begin

|
| [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-35963 Markström.739]: <math>c_6</math> extremiser unique
|-
| Feb 19
|
|
|
| [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36011 Markström.742]: 43-point Moser sets in <math>[3]^4</math> listed

[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36017 Peake.743]: 43-point sets analysed

[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36018 Cantwell.744]: <math>c'_5 \leq 128</math>

[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36024 Tao.745]: 50+ point line-free sets in <math>[3]^4</math> listed

|-
| Feb 20
| 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://terrytao.wordpress.com/2009/02/11/a-reading-seminar-on-density-hales-jewett/#comment-36041 Tao.630]: IP convergence lemma
| [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36031 Markström.747]: 42-point Moser sets listed

[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36045 Peake.751]: Human proof of <math>c_5 \leq 151</math>

|-
| Feb 21
| Gowers: [http://gowers.wordpress.com/2009/02/21/to-thread-or-not-to-thread/ To thread or not to thread]
| [http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2327 Gowers.580]: Extreme localisation + density increment = DHJ(3)?

[http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2329 Gowers.581]: Multidimensional Sperner

[http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2331 Gowers.582]: Use Ajtai-Szemeredi argument to get density increment?

| [http://terrytao.wordpress.com/2009/02/11/a-reading-seminar-on-density-hales-jewett/#comment-36084 Tao.631]: Informal combinatorial translation of ergodic DHJ(2)

[http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2321 Tao.578]: Finitary ergodic proof of DHJ(2) proposed

[http://terrytao.wordpress.com/2009/02/11/a-reading-seminar-on-density-hales-jewett/#comment-36085 Tao.632]: Special cases of DHJ(3) translated
| [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36051 Peake.752]: Human proof of <math>c_5=150</math>, <math>c_6=450</math>

[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

|-
| Feb 23
|
| [http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2356 McCutcheon.593]: DHJ(2.7)

[http://gowers.wordpress.com/2009/02/13/dhj-possible-proof-strategies/#comment-2370 O'Donnell.596]: Fourier-analytic proof of DHJ(2)

Gowers: [http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/ Brief review of polymath1] (800-849)

[http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/#comment-2372 O'Donnell.800]: Fourier-analytic + density increment proof of DHJ(2)

|
| [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36112 Markström.463]: 42-point Moser sets analysed

[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36115 Tao.464]: <math>c'_5 \leq 127</math>

[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36126 Chua.766]: 3D Moser sets with 222 have <math> \leq 13</math> points

[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36127 Tao.767]: 4D Moser sets with 2222 have <math> \leq 39</math> points
|-
| Feb 24
|
| [http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/#comment-2400 Tao.809.2]: Low-influence implies Sperner-positivity

[http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/#comment-2404 Gowers.812]: Fourier vs physical positivity

[http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/#comment-2408 O'Donnell.814]: <math>\ell_1</math>, <math>\ell_2</math> equivalence
|
|
|-
| Feb 25
|
| [http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/#comment-2431 Gowers.820]: Density increment on complexity 1 set
| [http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/#comment-2427 Tao.818]: Finitary ergodic sketch of DHJ(3)

[http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/#comment-2435 O'Donnell.821]: Simplified Fourier proof of DHJ(2) structure theorem

| [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36157 Cantwell.769]: 5D Moser sets with 2222* have <math> \leq 124</math> points

[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36165 Peake.771]: Exotic 43-point Moser sets described
|-
| Feb 26
|
| [http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/#comment-2443 Gowers.824]: Complexity 1 + Ajtai-Szemeredi DHJ(3) sketch
|
|
|-
| Feb 27
|
| [http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/#comment-2447 Tao.826]: Non-Fourier proof of DHJ(2) structure theorem

[http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/#comment-2453 Gowers.828]: Does correlation with 1-set imply density increment?

[http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/#comment-2458 Tao.828.4]: Energy increment proof for Gowers Q?

| [http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/#comment-2469 McCutcheon.832.2]: Use dense fibres to answer Gowers Q?

| [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36188 Elsholtz.775]: Human proof of 2222* result

[http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36195 Cantwell.776]: <math>c'_5 \leq 126</math>
|-
| Feb 28
|
| [http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/#comment-2476 Tao.834]: Use pullbacks for Gowers Q?

[http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/#comment-2478 Gowers.835]: Pullbacks don't work

[http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/#comment-2496 O'Donnell 839]: Increment-free Fourier proof of DHJ(2)

| [http://gowers.wordpress.com/2009/02/23/brief-review-of-polymath1/#comment-2490 Tao.837.2]: Dense fibres argument for Gowers Q

| [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36216 Markström.779]: 41-point Moser sets listed
|-
| Mar 1
|
|
|
| [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36246 Cantwell.782], [http://terrytao.wordpress.com/2009/02/13/bounds-for-the-first-few-density-hales-jewett-numbers-and-related-quantities/#comment-36250 Peake.784]: <math>c'_5 \leq 125</math>
|-
| Mar 2
|
| Gowers: [http://gowers.wordpress.com/2009/03/02/dhj3-851-899/ DHJ 851-899]

[http://gowers.wordpress.com/2009/03/02/dhj3-851-899/#comment-2525 Tao.853] Mass increment; connection with Hahn decomposition

[http://gowers.wordpress.com/2009/03/02/dhj3-851-899/#comment-2530 Gowers.854] Higher-D Ajtai-Szemeredi?

|
|
|-
| Mar 3
|
|
| [http://gowers.wordpress.com/2009/03/02/dhj3-851-899/#comment-2555 McCutcheon.864] Caution: 12-sets not sigma-algebra!
| [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>

[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
|-
| Mar 4
|
|
|
|[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>

[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>

[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

Tao: [http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers DHJ3 (900-999) Density Hales-Jewett type numbers]

[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36331 Tao.901]: 125-sets have D=0

[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>

[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36333 Carr.903]: Genetic algorithm implemented
|-
| Mar 5
|
|
|
| [http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36343 Peake.904] Scores for 6D Moser?

[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?

[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36350 Dyer.909] Wildcard variants of Moser

[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

[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)

[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36379 Peake.914] Pareto-optimal 3D statistics
|-
| Mar 6
|
| [http://gowers.wordpress.com/2009/03/02/dhj3-851-899/#comment-2595 Gowers.873] 12-set density increment difficulty identified
|
| [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>

[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>

[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

[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>

[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36417 Guest.930] GA without crossover?
|-
| Mar 7
|
| [http://gowers.wordpress.com/2009/03/02/dhj3-851-899/#comment-2609 Solymosi.880] Shelah-type flip-flop spaces?
|
| [http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36421 Peake.931] 3D extremals and inequalities

[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

[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

[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

[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)

|-
| Mar 8
|
| [http://gowers.wordpress.com/2009/03/02/dhj3-851-899/#comment-2613 Gowers.881] Iterative partitioning of 12-sets?

[http://gowers.wordpress.com/2009/03/02/dhj3-851-899/#comment-2622 Gowers.882] New proof of Ajtai-Szemeredi

[http://gowers.wordpress.com/2009/03/02/dhj3-851-899/#comment-2626 O'Donnell.884] Multidimensional Sperner written up
|
| [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>

[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>

[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36469 Tao.941] Seeding GA?

[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

[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>

[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>
|-
| Mar 9
|
| [http://gowers.wordpress.com/2009/03/02/dhj3-851-899/#comment-2633 Gowers.885] Sketch of DHJ(3)

[http://gowers.wordpress.com/2009/03/02/dhj3-851-899/#comment-2636 Gowers.886] DHJ(4)?

[http://gowers.wordpress.com/2009/03/02/dhj3-851-899/#comment-2666 Gowers.897] Writing of DHJ(k) begins
| [http://gowers.wordpress.com/2009/03/02/dhj3-851-899/#comment-2656 Austin.894] New ergodic proof of DHJ(k)
| [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

[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>

[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

[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>
|-
| Mar 10
| Gowers: [http://gowers.wordpress.com/2009/03/10/polymath1-and-open-collaborative-mathematics/ Polymath1 and open collaborative mathematics]

OU Math club: [http://oumathclub.wordpress.com/2009/03/10/problem-solved-probably/ Problem solved (probably)]
| Gowers: [http://gowers.wordpress.com/2009/03/10/problem-solved-probably/ Problem solved (probably)] (1000-1049)

[http://gowers.wordpress.com/2009/03/10/problem-solved-probably/#comment-2700 Gowers.1005.1] Tower-type bounds
| [http://gowers.wordpress.com/2009/03/10/problem-solved-probably/#comment-2689 Tao.1003] 1-sets, 2-sets locally independent
|
|-
| Mar 11
| Kalai: [http://gilkalai.wordpress.com/2009/03/11/polymath1-probable-success/ Polymath1: probable success]
| [http://gowers.wordpress.com/2009/03/10/problem-solved-probably/#comment-2713 Gowers.1007] Correlation component of DHJ(k) proof complete

[http://gowers.wordpress.com/2009/03/10/problem-solved-probably/#comment-2733 Solymosi.1011] Shelah-type argument?

|
| [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

[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36577 Elsholtz.962] Analysis of GA solutions

[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

[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>
|-
| Mar 12
|
| [http://gowers.wordpress.com/2009/03/10/problem-solved-probably/#comment-2805 O'Donnell.1021] DHJ(k) => Varnavides completed

[http://gowers.wordpress.com/2009/03/10/problem-solved-probably/#comment-2799 Gowers.1020] No apparent obstacles to proving DHJ(k)

[http://gowers.wordpress.com/2009/03/10/problem-solved-probably/#comment-2826 O'Donnell.1025] Work exclusively with equal (non-degenerate) slices measure?

| [http://gowers.wordpress.com/2009/03/10/problem-solved-probably/#comment-2825 Tao.1024] Informal combinatorial translation of Austin's proof
| [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

[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>

[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
|-
| Mar 13
| Nielsen: [http://michaelnielsen.org/blog/?p=579 Biweekly links for 03/13/2009]

Galdino: [http://prafalardecoisas.wordpress.com/2009/03/13/links-semanais/ Links seminais]

Flaxman: [http://healthyalgorithms.wordpress.com/2009/03/13/gowers-polymath-experiment-problem-probably-solved/ Gowers' polymath experiment: problem probably solved]
|
|
| [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

[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36655 Peake.982]: xxyyzz inequalities

[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>

[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

[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36666 Peake.989]: xxyyz inequalities

[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>

[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36672 Peake.991]: xxxyz, xxxxyz, xxxyyz inequalities

[http://terrytao.wordpress.com/2009/03/04/dhj3-900-999-density-hales-jewett-type-numbers/#comment-36694 Seva.994]: Kakeya in [3]^n?

|-
| Mar 14
| Hariss: [http://maxwelldemon.wordpress.com/2009/03/14/polymath/ Polymath]
|
| [http://gowers.wordpress.com/2009/03/10/problem-solved-probably/#comment-2871 Tao.1035] Ramsey-free translation of Austin's proof
| Tao: [http://terrytao.wordpress.com/2009/03/14/dhj3-1100-1199-density-hales-jewett-type-numbers/ DHJ(3) 1100-1199]

|-
| Mar 15
| 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...]
|
|
|

|-
| Mar 16
|
| Gowers: [http://gowers.wordpress.com/2009/03/16/dhj3-and-related-results-1050-1099/ DHJ(3) and related results: 1050-1099]
|
|

|-
| Mar 18
| Polymath hits front page of Slashdot with [http://science.slashdot.org/article.pl?sid=09/03/18/194228 this article]

Nielsen: [http://michaelnielsen.org/blog/?p=581 How changing the technology of collaboration can change the nature of collaboration]
|
|
|

|-
| Mar 20
| Nielsen: [http://michaelnielsen.org/blog/?p=584 The Polymath project: scope of participation]
|
|
|

|-
| Mar 21
| Gans: [http://economics.com.au/?p=3000 Something interesting is going on in Maths]
|
|
|

|-
| Mar 24
| Gowers: [http://gowers.wordpress.com/2009/03/24/can-polymath-be-scaled-up/#comments Can Polymath be scaled up?]

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]
|
|
|

|-
| Mar 25
| Nielsen: [http://michaelnielsen.org/blog/?p=588 On scaling up the polymath project]

Dyer: [http://numberwarrior.wordpress.com/2009/03/25/a-gentle-introduction-to-the-polymath-project/ A gentle introduction to the Polymath project]
|
|
|

|}

Polymath Wiki - User contributions [en]

Timeline