Contains the first sporadic groups discovered by far: 11 and 12 in 1861, and 22, 23 and 24 in 1973. And therefore presumably the simplest! The next sporadic ones discovered were the Janko groups, only in 1965!
Each is a permutation group on elements. There isn't an obvious algorithmic relationship between and the actual group.
TODO initial motivation? Why did Mathieu care about k-transitive groups?
Their; k-transitive group properties seem to be the main characterization, according to Wikipedia:Looking at the classification of k-transitive groups we see that the Mathieu groups are the only families of 4 and 5 transitive groups other than symmetric groups and alternating groups. 3-transitive is not as nice, so let's just say it is the stabilizer of and be done with it.
- 22 is 3-transitive but not 4-transitive.
- four of them (11, 12, 23 and 24) are the only sporadic 4-transitive groups as per the classification of 4-transitive groups (no known simpler proof as of 2021), which sounds like a reasonable characterization. Note that 12 and 25 are also 5 transitive.
Mathieu group section of Why Do Sporadic Groups Exist? by Another Roof (2023)
Source. Only discusses Mathieu group but is very good at that.These are the final equations that you derive from the Lagrangian via the Euler-Lagrange equation which specify how the system evolves with time.
Video "1984 Macintosh advertisement by Apple (1984)" comes to mind.
TODO year. This was a reply to Microsoft anti-Linux propaganda it seems: www.ubuntubuzz.com/2012/03/truth-happens-redhats-legendary-reply.html
Trascript from: www.dailymotion.com/video/xw3ws
The world is flat. Earth is the centre of the universe. Fact - until proven otherwise.
Despite ignorance. Despite ridicule. Despite opposition. Truth happens.Despite ignorance.
The telephone has too many shortcomings to be seriously considered as a means of communication. /Western Union 1876/
In 1899 the US Patent Commissioner stated, everything that can be invented has been invented.Despite ridicule.
The phonograph has no commercial value at all. /Thomas Edison 1880/
The radio craze will die out in time. /Thomas Edison 1922/
The automobile has practically reached the limit of its development. /Scientific American 1909/Despite it all truth happens.
Man will not fly for fifty years. /Orville Wright 1901/
The rocket will never leave the Earth's atomosphere. /New York Times 1936/
There is a world market for maybe five computers. /IBM's Thomas Watson 1943/
640K Ought to be enough for anybody. /Bill Gates 1981/First they ignore you...
Linux is the hype du jour. /Gartner Group 1999/Then they laugh at you...
We think of linux as competitor in the student and hobbyist market. But I really don't think in the commercial market we'll see it in any significant way. /Bill Gates 2001/Then they fight you...
Linux isn't going away. Linux is a serious competitor. We will rise to this challenge. /Steve Ballmer 2003/Then you win... /Mohandas Gandhi/You are here.
Red Hat Linux. IBM.
Truth Happens advertisement by Red Hat
. Source. Rich people who create charitable prizes are often crooked Updated 2025-01-10 +Created 1970-01-01
A friend of mine who's a rich man - he invented some kind of simple digital switch - tells me about these people who contribute money to make prizes or give lectures: "You always look at them carefully to find out what crookery they're trying to absolve their conscience of."
TODO who was he talking about? Robert Noyce or Gordon Moore feel likely candidates:
But do you know what, Cirism is totally fine with taking indulgences to absolve someone from their past sins, so long as they have repented. Everyone deserves a second chance.
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