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Introduction to Knot Theory
Hailed by the Bulletin of the American Mathematical Society as "a very welcome addition to the mathematical literature," this text is appropriate for advanced undergraduates and graduate students. Written by two internationally renowned mathematicians, it offers an accessible treatment that requires no previous knowledge of algebraic topology. 1963 edition.
- GenresMathematicsScience
182 pages, Hardcover
First published January 1, 1963
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July 5, 2013
In case you didn't know, there is a branch of mathematics which is concerned with the study of knots. It's a subfield of algebraic topology, which I was vaguely interested in for a few years. I never got to be any good at it, but I read a few books, of which this was perhaps the most exciting.
It's been sitting on my shelf for ages, looking rather lonely. Somehow it ended up close to my Nabokov novels; I guess they didn't have much to say to each other. I picked it up just now and flipped through it, to see how much of it had stuck. Unfortunately, very little. I was clearly never going to be a knot theorist. But I was reminded of one quite amusing point. The authors bring in all this heavy-duty math, so that they can classify knots. They define a bunch of complicated algebraic objects. And then, right at the end, they consider the problem of distinguishing a granny knot from a square knot, and tell you that it can't be done using the methods developed in this book.
Who would have imagined? It's pretending to be a math text, but it turns out to be a shaggy dog story.
_______________________________
Rereading Smolin's The Trouble With Physics, and I'd completely forgotten that knot theory got started when Kelvin thought atoms might be knots in magnetic field lines. As Smolin says: it turned out that knot theory is an interesting and fruitful part of pure mathematics, but that doesn't mean Kelvin's idea was any good. In point of fact, it was just imaginative nonsense.
He does come up with clever ways to tease the string theorists. No wonder they're furious.
_______________________________
So this guy walks into a bar with a dog and a cat.
"I'm sorry," says the bartender, "we don't allow animals in here."
"Look," says the guy, "these are very special animals. They're knot theorists."
"Oh yeah?" says the bartender. "Prove it."
"Right!" says the guy and looks at the cat. "Name a knot invariant."
"Mu! Mu!" says the cat.
"Okay," he says and looks at the dog. "Name a knot invariant."
"Arf! Arf!" says the dog.
The bartender calls the bouncer and tells him to get rid of these lunatics. Out on the street, the dog looks at the man and says, "Should I have said 'the Jones polynomial?'"
It's been sitting on my shelf for ages, looking rather lonely. Somehow it ended up close to my Nabokov novels; I guess they didn't have much to say to each other. I picked it up just now and flipped through it, to see how much of it had stuck. Unfortunately, very little. I was clearly never going to be a knot theorist. But I was reminded of one quite amusing point. The authors bring in all this heavy-duty math, so that they can classify knots. They define a bunch of complicated algebraic objects. And then, right at the end, they consider the problem of distinguishing a granny knot from a square knot, and tell you that it can't be done using the methods developed in this book.
Who would have imagined? It's pretending to be a math text, but it turns out to be a shaggy dog story.
_______________________________
Rereading Smolin's The Trouble With Physics, and I'd completely forgotten that knot theory got started when Kelvin thought atoms might be knots in magnetic field lines. As Smolin says: it turned out that knot theory is an interesting and fruitful part of pure mathematics, but that doesn't mean Kelvin's idea was any good. In point of fact, it was just imaginative nonsense.
He does come up with clever ways to tease the string theorists. No wonder they're furious.
_______________________________
So this guy walks into a bar with a dog and a cat.
"I'm sorry," says the bartender, "we don't allow animals in here."
"Look," says the guy, "these are very special animals. They're knot theorists."
"Oh yeah?" says the bartender. "Prove it."
"Right!" says the guy and looks at the cat. "Name a knot invariant."
"Mu! Mu!" says the cat.
"Okay," he says and looks at the dog. "Name a knot invariant."
"Arf! Arf!" says the dog.
The bartender calls the bouncer and tells him to get rid of these lunatics. Out on the street, the dog looks at the man and says, "Should I have said 'the Jones polynomial?'"
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