Academia vs Business
by Jeff
Image text: Some engineer out there has solved P=NP and it's locked up in an electric eggbeater calibration routine. For every 0x5f375a86 we learn about, there are thousands we never see.
This comic is a flow chart defining what would happen if this person solved an impossible problem given to him and what would happen if he were in academia or in business. The argument seems to be here that Academia is much better than business, at least for the ego.
p=NP problem is one of the great unsolved problems in computer science. The Clay Mathematics Institute has a $1 million prize to the first person or group who solves it.
EDIT: As mentioned by just about everybody in the comments, 0x5f375a86 is the algorithm to approximate the solution to the square root of an unsigned floating number, also known as fast inverse square root. The solution uses an ingenious first approximation and the difficult problem was solved without any fanfare (like in the cartoon) for the game, Quake III Arena. Thanks everyone!
Reverse Polish Sausage
by Mike
Image text: It looks good, but it needs more postfixins.
This comic is based on the Reverse Polish notation proposed for use in mathematics. It's also sometimes known as postfix notation because the operators follow all of it's operands. For example, In normal notation if you wanted to add the numbers 3, 4, and 5 you would write 3 + 4 + 5. Using reverse polish notation it would be written as 3 4 5 +.
Psychic
by Jeff
Image text: You can do a lot better than 1% if you start keeping track of the patterns in what numbers people pick.
That's two easy ones in a row. My only question is, what about the other 99% of people that you try this trick on? Is it worth it for 1% of the people to think you are a psychic and the other 99% think you are a dope?
Newton and Leibniz
by Jeff
Image meta text: YEEEEEEAAAAAAHHHHHH!
This comic is a pun on the word derivative.
First and foremost Isaac Newton and Gottfried Leibniz both invented calculus independent of each other, as the comic says, about 8 years apart. However, Newton disputed the fact that Leibniz invented calculus independent of him.
In calculus a derivative is the result of mathematical differentiation; the instantaneous change of one quantity relative to another; df(x)/dx. However, the literary word derivative means to develop from something older.
So, the pun is that Newton in the comic is claiming that Leibniz's derivative(the invention of calculus) is a derivative(developed from) his derivative(calculus).
The comic as a whole is mocking the pattern of corny one-liners that David Caruso often spurts out during the opening scenes of CSI: Miami. The one liner is followed by him dramatically pulling off his sunglasses and then the show breaks into the title sequence which starts with the word "YEEEEAAAAAAAH." This has become a popular internet meme and was used frequently most recently with Michael Jackson's death.
Make sense? Anyone have a better explanation than that?
Haiku Proof
by Mike
Image meta text: "After somewhere around 40 hours, there's no academic reason to go to the class. Only go for the hallucinations."
The Greek mathematician Euclid proved there are an infinite number of primes (though not through haiku). Basically, you start by assuming the opposite- that there are a finite number of primes. Multiply all of them together and add 1. Then you ask what are the factors of that new number. It's not divisible by any of the primes because it would yield a remainder of 1... so either there is a prime number you forgot that wasn't in your original set or this new number is prime. In either case, you just proved the set of primes can not be finite.
Also, there's no proof that after 48 hours of sleep deprivation math lectures get ANY more interesting.
Wings
by Jeff
Image meta text: Please do not try any of this and die or get arrested.
This comic references Titan, a moon of Saturn which has 14% of earth's gravity. Because the gravity is less, it takes less lift to fly on Titan.
Also, the main character uses hot glue on his wings, similar to how Icarus of Greek Mythology flew too close to the sun with wings made of wax. Just like Icarus, the character falls after subjected to high levels of heat. In the comic's case, the heat was applied by a heat lamp from xkcd's resident troublemaker "Black Hat".
Threesome
by Jeff
Image meta text: I wanted us to try finding an approximate numeric solution, but noooo.
For the three body problem, it is a math and astronomy problem about the gravity interaction between 3 different "bodies". Scholarpedia has this about the problem. "The [three body] problem is to determine the possible motions of three point masses m_1, m_2, and m_3, which attract each other according to Newton's law of inverse squares. ... While the two-body problem is integrable and its solutions completely understood, solutions of the three-body problem may be of an arbitrary complexity and are very far from being completely understood."
And obviously, with a threesome, there is literally three bodies. The comic is making a pun on that.
Extrapolating
by Jeff
Image meta text: By the third trimester, there will be hundreds of babies inside you.
The math in this comic is extrapolating that if in the period of a day to go from 0 to 1, that means that the next day you should go from 1 to 2 and so on. Extrapolating is usually used on graphs with more data points than 1!
The same can be said for the meta text. O to 1 baby, then 1 to 2 babies and so on.