Unraveling the Mystery of Mathematics Through the Power of Knots
Mathematician Colin Adams has spent the majority of his career exciting and enlightening students and the general public about the power of mathematics using an age-old venue that most of us, quite frankly, have taken for granted: knots.
Think about it, says Colin, a day doesn't go by that we don't use or deal with knots – from tying our shoes in the morning or untangling an extension cord to tying a ribbon around a present -- knots are an integral part of our lives.
"And it's been that way for very long time, adds Colin, professor of Mathematics at Williams College in Williamstown, MA. "Knot theory itself is over a century old and today is one of the most active areas of modern mathematics." In addition, the study of knots has led to important applications in DNA research and the synthesis of new molecules, and has had a significant impact on statistical mechanics and quantum field theory, he explains.
From his class lectures at Williams College and the books he has written on knot theory to the public presentations he conducts on the subject across the nation, Colin is known for making mathematics come alive via his engaging hands-on approach to exploring problems and theorems through knots.
"The mathematical theory of knots was actually born out of attempts to model the atom," says Colin, who, as a researcher, is particularly interested in studying how the theory applies to hyperbolic geometry. His other research pursuits in mathematics include hyperbolic three-manifolds. "Near the end of the nineteenth century," he continues, "Lord Kelvin suggested that different atoms were actually different knots tied in the ether that was believed to permeate all of space. Physicists and mathematicians set to work making a table of distinct knots, believing they were making a table of the elements."
In the 1980s, chemists and biochemists again became intrigued with the theory of knots – applying it, among other things, to further unravel the mystery behind the structure of the molecule deoxyribonucleic acid (DNA). Says Colin: "DNA consists of millions of atoms that together form a blueprint for life. Although it is in the shape of a double helix, we can think of it as a very long thin string packed into the nucleus of a cell, like 200 kilometers of fishing line tangled up inside a soccer ball."
Breaking down such information for his audiences in exciting, entertaining ways is where Colin especially excels. For example, his 1994 book, "The Knot Book: An Elementary Introduction to the Mathematical Theory of Knots" still remains popular for its style in explaining complex knot theory problems in lively, accessible terms, as well as explaining how this work is applied to DNA research and synthetic chemistry.
His other books for students and the public also come highly rated, including "How to Ace Calculus: The Streetwise Guide" (co-authored with Joel Hass and Abigail Thompson), which is an irreverent tongue-in-cheek supplement to calculus that makes learning calculus fun.
In addition, Colin is author of the mathematical humor column called "Mathematically Bent" which appears in the Mathematical Intelligencer. His current public lecture -- "Blown Away: What Knot to Do When Sailing" – is being well received across the country. This tale of adventure on the high seas relates how Colin's understanding of the mathematical theory of knots saved his bacon from doom and destruction.
Colin, who has been teaching at Williams College since 1985, received a B.S. in mathematics from the Massachusetts Institute of Technology in 1978, and a Ph.D. in mathematics from the University of Wisconsin-Madison in 1983. He has also held positions at Oregon State University, the Universities of California at Santa Barbara and Davis, and the Mathematical Sciences Research Institute in Berkeley.
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