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That article is aimed at mathematicians. A high level summary is that there are two completely unrelated things, the Monster group and modular forms. (Groups

That article is aimed at mathematicians. A high level summary is that there are two completely unrelated things, the Monster group and modular forms. (Groups are sets of symmetries. Modular functions are special functions of complex numbers. The related topic of modular forms come up in the proof of Fermat's last theorem.) These two things are obviously unrelated, so when someone spotted a numerical coincidence in some numbers that show up in each, people scoffed. (Conway is the one that nicknamed it "moonshine".) It turns out it's completely true, and the proof uses a bunch of mathematical techniques that were developed when studying string theory for physics. The whole thing is an incredibly unlikely story.

posterboy 7y ago
> These two things are obviously unrelated 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?

posterboy 7y ago

> These two things are obviously unrelated 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?