Gorenstein, Lyons, and Solomon (and friends) have been writing a consolidated proof for the classification theorem for finite simple groups...since 1994. In fact, it's still a work in progress. How big will it be?
Thus far, nine volumes have been published:
Volume Number | First page number | Bibliography Page number | Number of Pages |
---|---|---|---|
1 | 22 | 159 | 137 |
2 | 14 | 216 | 202 |
3 | 18 | 420 | 402 |
4 | 18 | 350 | 332 |
5 | 14 | 476 | 462 |
6 | 14 | 532 | 518 |
7 | 12 | 352 | 340 |
8 | 14 | 498 | 484 |
9 | 12 | 530 | 518 |
At present, there is an expected additional 4 volumes coming (according to David Roberts's answer on Mathoverflow). Performing a linear regression on the number of pages in terms of the volume number, we can make a prediction. Here's the R code doing this:
df <- data.frame(vol = 1:9, start=c(22,14,18,18,14,14,12,14,12), bib=c(159,216,420,350,476,532,352,498,530)); df$pgs <- df$bib - df$start; lm0 <- lm(pgs ~ vol, data=df); summary(lm0); # Call: # lm(formula = pgs ~ vol, data = df) # # Residuals: # Min 1Q Median 3Q Max # -118.29 -53.62 -14.82 84.78 105.84 # # Coefficients: # Estimate Std. Error t value Pr(>|t|) # (Intercept) 174.56 62.68 2.785 0.0271 * # vol 40.53 11.14 3.639 0.0083 ** # --- # Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 # # Residual standard error: 86.27 on 7 degrees of freedom # Multiple R-squared: 0.6542, Adjusted R-squared: 0.6048 # F-statistic: 13.24 on 1 and 7 DF, p-value: 0.008296 predict(lm0, data.frame(vol=c(10,11,12,13))) # 1 2 3 4 # 579.8889 620.4222 660.9556 701.4889 sum(df$pgs) # [1] 3395 sum(predict(lm0, data.frame(vol=c(10,11,12,13)))) + sum(df$pgs) # [1] 5957.756
Tl;dr: the classification of finite simple groups is expected to be around 5957 pages, but could ostensibly reach up to 8243 pages.
Addendum
We can improve the estimate by dropping the constant term, and estimating the "additional pages" compared to the first volume:
df <- data.frame(vol = 1:9, start=c(22,14,18,18,14,14,12,14,12), bib=c(159,216,420,350,476,532,352,498,530)); df$pgs <- df$bib - df$start; df2 <- data.frame(vol = 1:9, pgs=df$pgs - df$pgs[1]); lm0 <- lm(pgs ~ 0 + vol, data=df2); summary(lm0) # Call: # lm(formula = pgs ~ 0 + vol, data = df2) # # Residuals: # Min 1Q Median 3Q Max # -122.24 -37.17 -24.70 92.68 125.61 # # Coefficients: # Estimate Std. Error t value Pr(>|t|) # vol 46.463 4.901 9.48 1.26e-05 *** # --- # Signif. codes: 0 ‘***’ 0.001 ‘**’ 0.01 ‘*’ 0.05 ‘.’ 0.1 ‘ ’ 1 # # Residual standard error: 82.75 on 8 degrees of freedom # Multiple R-squared: 0.9183, Adjusted R-squared: 0.908 # F-statistic: 89.86 on 1 and 8 DF, p-value: 1.263e-05 predict(lm0, data.frame(vol=c(10,11,12,13))) + df$pgs[1] # 1 2 3 4 # 601.6316 648.0947 694.5579 741.0211 sum(predict(lm0, data.frame(vol=c(10,11,12,13))) + 137) + sum(df$pgs) # [1] 6080.305
This gives us a better fit (adjusted R-squared of 0.908) with a better error estimate (with 95% probability, it will be 6080 pages give or take 40 pages).
Tl;dr2: the classification of finite simple groups can be expected to be around 6080±40 pages long.
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