Behold, my new comrades, a monstrous yet straightforward puzzle, appearing on the order of that group of fellows occasionally visiting PSE but hitherto unable to join their simple friends. I assure you, there is no lie here (and I am undoubtedly male, if anyone is asking).


  • $\begingroup$ For my first foray into this site, a puzzle which will be solvable almost at a glance for some, but may take more time for others. The title and text are not essential to the solution but contain clues that may help the latter group. The key is recognition! $\endgroup$ – Anon Apr 14 '20 at 11:09

This is

a quotation from Nietzsche: "He who fights with monsters should be careful lest he thereby become a monster, and if thou gaze long into an abyss the abyss will also gaze into thee".


each letter is represented by (the decimal representation of) the order of one of the sporadic finite simple groups. For instance, our monstrous number begins with 50232960, the order of the third Janko group, which happens to represent the letter H. Next comes 604800, the order of the second Janko group, which happens to represent the letter E.

I haven't checked carefully but

I think the correspondence is that the smallest of the groups (M11, of order 7920) maps to A, the largest (the Monster, of order 808017424794512875886459904961710757005754368000000000) maps to Z, and the others are arranged in order of order in between.

A few remarks on the text:

"monstrous" alludes to the Monster and Baby Monster groups; "on the order of that group" alludes to the notion of order (number of elements) and of course group itself; "simple" to the fact that these are finite simple groups; perhaps "unable to join their simple friends" because these, the "sporadic" groups, are the ones that don't belong to infinite families of finite simple groups; there is "no lie" here because these are not the (continuous, very much not finite) objects called "Lie groups" after Sophus Lie. Perhaps the reason why "I am undoubtedly male" is that the usual abbreviation for one of the groups, the Held group, is "He". "Exceptional" in the title is probably either a rough equivalent for "sporadic" or a reference to the fact that some of the not-sporadic group families have "exceptional" in their names.

And on the context:

The great John Conway, who tragically died just recently in the Covid-19 pandemic, was among many other things one of the people involved in the classification of finite simple groups, and one of the authors of an important volume called the "Atlas of finite simple groups".

  • $\begingroup$ Well I expected this community to be fast, but not quite that fast! Congratulations! I can't upvote you just now but I will in the morning. $\endgroup$ – Anon Apr 14 '20 at 12:24
  • $\begingroup$ I assure you such speed is humbling. I think you picked up on almost everything in the text. Exceptional refers to the fact that these groups are exceptional in the classification of finite simple groups. "I am undoubtedly male" was envisaged with a slightly ruder meaning, similar to the Lie clue. But what about "neither good nor bad"? $\endgroup$ – Anon Apr 14 '20 at 12:28
  • $\begingroup$ Oh, you have no Tits. I see. I wondered about the good/bad thing but didn't come up with anything. Perhaps it's a hint towards the author of the quotation, who also wrote a book called "Beyond good and evil"? $\endgroup$ – Gareth McCaughan Apr 14 '20 at 12:36
  • $\begingroup$ As for speed: as you said, at a glance :-). For obvious reasons I was well prepared to see something with this sort of theme. The man himself would no doubt be gratified that the first puzzle here to memorialize him was concerned with one of his more "serious" bits of mathematical work. $\endgroup$ – Gareth McCaughan Apr 14 '20 at 12:37
  • 1
    $\begingroup$ Oh, the quotation's actually from that book? Duh. Indeed, not merely moonshine. (Though at a point when I'd figured out that the number was a concatenation of FSFG orders but hadn't yet worked out what to do with them I did wonder about posting a comment like "Looks like a load of moonshine to me".) $\endgroup$ – Gareth McCaughan Apr 14 '20 at 12:44

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