Timeline

Some highlights of 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	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		Gowers.9: Reweighting vertices needed for Varnavides? Tao.17: Should use [math]\displaystyle{ 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]\displaystyle{ c_0=1 }[/math], [math]\displaystyle{ c_1=2 }[/math], [math]\displaystyle{ c_2=6 }[/math], [math]\displaystyle{ 3^{n-O(\sqrt{n}} \leq c_n \leq o(3^n) }[/math] Kalai.15: [math]\displaystyle{ c_n \gg 3^n/\sqrt{n} }[/math] Tao.39: [math]\displaystyle{ c_n \geq 3^{n-O(\sqrt{\log n})} }[/math] Tao.40: [math]\displaystyle{ 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]\displaystyle{ c_4 \geq 49 }[/math] Tao.78: [math]\displaystyle{ c_4 \leq 54 }[/math] Neylon.83: [math]\displaystyle{ 52 \leq c_4 \leq 54 }[/math], [math]\displaystyle{ 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]\displaystyle{ c_4=52 }[/math]
Feb 5		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]\displaystyle{ D_n }[/math]
Feb 7		Gowers.335: DHJ(j,k) introduced		Jakobsen.207: [math]\displaystyle{ c_5 \geq 150 }[/math], [math]\displaystyle{ c_6 \geq 450 }[/math] Peake.217: [math]\displaystyle{ c_7 \geq 1308 }[/math], [math]\displaystyle{ c_8 \geq 3780 }[/math] Peake.218: Lower bounds up to [math]\displaystyle{ 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]\displaystyle{ 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]\displaystyle{ c_5 \leq 155 }[/math]; xyz notation Peake.243: [math]\displaystyle{ c_5 \leq 154 }[/math]
Feb 11	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]\displaystyle{ \overline{c}^\mu_0 = 1 }[/math], [math]\displaystyle{ \overline{c}^\mu_1 = 2 }[/math], [math]\displaystyle{ \overline{c}^\mu_2 = 4 }[/math] Dyer.254: [math]\displaystyle{ \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]\displaystyle{ \overline{c}^\mu_4 = 9 }[/math] Jakobsen.258: [math]\displaystyle{ \overline{c}^\mu_5 = 12 }[/math] Peake.262: Extremisers for [math]\displaystyle{ 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]\displaystyle{ [3]^n }[/math] should already provide enough randomness Tao.510: Finitary analogue of stationarity	Sauvaget: A proof that [math]\displaystyle{ 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]\displaystyle{ c_n }[/math] Markström.706: Integer program, [math]\displaystyle{ c_5=150 }[/math] Cantwell.708: [math]\displaystyle{ 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]\displaystyle{ c_5 }[/math] extremisers Tao.731: Human proof that [math]\displaystyle{ c_5 \leq 152 }[/math]; [math]\displaystyle{ 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]\displaystyle{ 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]\displaystyle{ c_6 }[/math] extremiser unique
Feb 19				Markström.742: 43-point Moser sets in [math]\displaystyle{ [3]^4 }[/math] listed Peake.743: 43-point sets analysed Cantwell.744: [math]\displaystyle{ c'_5 \leq 128 }[/math] Tao.745: 50+ point line-free sets in [math]\displaystyle{ [3]^4 }[/math] listed
Feb 20	Vipulniak: 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]\displaystyle{ 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]\displaystyle{ c_5=150 }[/math], [math]\displaystyle{ c_6=450 }[/math] Tao.753: Sequences submitted to OEIS
Feb 22
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]\displaystyle{ c'_5 \leq 127 }[/math] Chua.766: 3D Moser sets with 222 have [math]\displaystyle{ \leq 13 }[/math] points Tao.767: 4D Moser sets with 2222 have [math]\displaystyle{ \leq 39 }[/math] points
Feb 24		Tao.809.2: Low-influence implies Sperner-positivity Gowers.812: Fourier vs physical positivity O'Donnell.814: [math]\displaystyle{ \ell_1 }[/math], [math]\displaystyle{ \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]\displaystyle{ \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]\displaystyle{ 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]\displaystyle{ 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]\displaystyle{ \overline{c}^\mu_6 \lt 18 }[/math] Cantwell.787 125-sets have at most 41 points in middle slices
Mar 4				Markstrom.788: [math]\displaystyle{ c^\mu_n = 4,6,9,12 }[/math] for [math]\displaystyle{ n=2,3,4,5 }[/math] Marc.791: [math]\displaystyle{ \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]\displaystyle{ \overline{c}^\mu_6 \lt 17 }[/math] Karr.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]\displaystyle{ \overline{c}^\mu_7 \leq 22 }[/math] Cantwell.920 [math]\displaystyle{ c'_6 \leq 373 }[/math] Cantwell.921 125-sets have C=78 or 79 Markstrom.923 [math]\displaystyle{ \overline{c}^\mu_n = 6,9,12,15,18,22,26,31,35,40 }[/math] for [math]\displaystyle{ 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'Donnel.884 Multidimensional Sperner written up			Peake.939 [math]\displaystyle{ c'_6 \leq 365 }[/math] Carr.940 [math]\displaystyle{ 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]\displaystyle{ c'_4 =43 }[/math] Tao.944 [math]\displaystyle{ 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]\displaystyle{ c'_5 = 124 }[/math] Tao.950 [math]\displaystyle{ \overline{c}^\mu_n }[/math] submitted to OEIS Carr.954 [math]\displaystyle{ 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