Skimming just quickly gives a different impression.
> It was
clear to many people that this was just a mean-
ingless coincidence; after all, if you have enough
large integers from various areas of mathematics,
then a few are going to be close just by chance, and
John McKay was told that his observation was
about as useful as looking at tea leaves. John
Thompson took McKay’s observation further and ...
what follows is nothing to scoff at.
Finally, Borcherd's article concludes (2002, that was linked above):
> So the question “What is the monster?” now has
several reasonable answers:
> ...
> It is a group of diagram automorphisms of the
monster Lie algebra.
Unfortunately none of these definitions is
completely satisfactory. At the moment all con-
structions of the algebraic structures above seem
artificial; they are constructed as sums of two or
more apparently unrelated spaces, and it takes a
lot of effort to define the algebraic structure on the
sum of these spaces and to check that the monster
acts on the resulting structure. It is still an open
problem to find a really simple and natural
construction of the monster vertex algebra.
Which means, showing a natural relation should be outstanding?
Skimming just quickly gives a different impression.
> It was clear to many people that this was just a mean- ingless coincidence; after all, if you have enough large integers from various areas of mathematics, then a few are going to be close just by chance, and John McKay was told that his observation was about as useful as looking at tea leaves. John Thompson took McKay’s observation further and ...
what follows is nothing to scoff at.
Finally, Borcherd's article concludes (2002, that was linked above):
> So the question “What is the monster?” now has several reasonable answers:
> ...
> It is a group of diagram automorphisms of the monster Lie algebra. Unfortunately none of these definitions is completely satisfactory. At the moment all con- structions of the algebraic structures above seem artificial; they are constructed as sums of two or more apparently unrelated spaces, and it takes a lot of effort to define the algebraic structure on the sum of these spaces and to check that the monster acts on the resulting structure. It is still an open problem to find a really simple and natural construction of the monster vertex algebra.
Which means, showing a natural relation should be outstanding?