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There were several videos that Numberphile did with Conway, including one where he talked about what problems he'd like to see before he died and his own mortal

by sndean 7y ago

There were several videos that Numberphile did with Conway, including one where he talked about what problems he'd like to see before he died and his own mortality [0]. In particular he wanted to know why the Monster group [1] exists, what it's about, why it's there [2]. I don't know enough about it to know if progress was made toward that in the past few years since the video was made. [0] https://www.youtube.com/watch?v=xOCe5HUObD4 https://www.youtube.com/watch?v=xOCe5HUObD4 [1] https://en.wikipedia.org/wiki/Monster_group https://en.wikipedia.org/wiki/Monster_group [2] https://youtu.be/xOCe5HUObD4?t=409 https://youtu.be/xOCe5HUObD4?t=409

QuesnayJr 7y ago
The Monster group is fascinating because we know it exists without quite knowing why it exists. There's a pattern that we can sense but it still escapes our understanding. There's just enough structure that you can imagine future generations someday saying, "Of course, of course."
DonHopkins 7y ago
TIL John Conway's son was once known as "the baby monster", and that Jupiter has a whole lot of elementary particles, but I can't quite grasp the rest of what I just read. http://www.ams.org/notices/200209/what-is.pdf http://www.ams.org/notices/200209/what-is.pdf >What is... The Monster? By Richard E. Borcherds. >When I was a graduate student, my supervisor John Conway would bring into the department his one year-old son, who was soon known as the baby monster. A more serious answer to the title question is that the monster is the largest of the (known) sporadic simple groups. Its name comes from its size: The number of elements is 8080, 17424, 79451, 28758, 86459, 90496, 17107, 57005, 75436, 80000, 00000 = 2^46 . 3^20 . 5^9 . 7^6 . 11^2 . 13^3 . 17 . 19 . 23 . 29 . 31 . 41 . 47 . 59 . 71, about equal to the number of elementary particles in the planet Jupiter.
- QuesnayJr 7y ago
  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?
- segfaultbuserr 7y ago
  It's an introduction to Monstrous Moonshine, an unexpected connection between the monster group M and modular functions, with applications in theoretical physics, see Wikipedia [0] for a summary. [0] https://en.wikipedia.org/wiki/Monstrous_moonshine https://en.wikipedia.org/wiki/Monstrous_moonshine

by sndean 7y ago

QuesnayJr 7y ago

The Monster group is fascinating because we know it exists without quite knowing why it exists. There's a pattern that we can sense but it still escapes our understanding. There's just enough structure that you can imagine future generations someday saying, "Of course, of course."

DonHopkins 7y ago

TIL John Conway's son was once known as "the baby monster", and that Jupiter has a whole lot of elementary particles, but I can't quite grasp the rest of what I just read. http://www.ams.org/notices/200209/what-is.pdf http://www.ams.org/notices/200209/what-is.pdf >What is... The Monster? By Richard E. Borcherds. >When I was a graduate student, my supervisor John Conway would bring into the department his one year-old son, who was soon known as the baby monster. A more serious answer to the title question is that the monster is the largest of the (known) sporadic simple groups. Its name comes from its size: The number of elements is 8080, 17424, 79451, 28758, 86459, 90496, 17107, 57005, 75436, 80000, 00000 = 2^46 . 3^20 . 5^9 . 7^6 . 11^2 . 13^3 . 17 . 19 . 23 . 29 . 31 . 41 . 47 . 59 . 71, about equal to the number of elementary particles in the planet Jupiter.

QuesnayJr 7y ago
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?
segfaultbuserr 7y ago
It's an introduction to Monstrous Moonshine, an unexpected connection between the monster group M and modular functions, with applications in theoretical physics, see Wikipedia [0] for a summary. [0] https://en.wikipedia.org/wiki/Monstrous_moonshine https://en.wikipedia.org/wiki/Monstrous_moonshine