Timeline

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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