You’ve heard of string theory. What about knot theory?

UB knot theorist Bill Menasco holding a string of beads.

UB knot theorist Bill Menasco. The whiteboard in the background depicts drawings of mathematical knots and surfaces that Menasco created from memory. Credit: Douglas Levere

Esoteric to many, the study of knots in mathematics could help solve problems in biology, security and more

Release Date: February 10, 2016

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“It seems to be somehow buried in our humanity that we’re interested in these things. ”
Bill Menasco, professor of mathematics
University at Buffalo

Video: Menasco presents a knot puzzle

Bill Menasco presenting a knot puzzle.

BUFFALO, N.Y. — You may not have heard of knot theory.

But take it from Bill Menasco, a knot theorist of 35 years: This field of mathematics, rich in aesthetic beauty and intellectual challenges, has come a long way since he got into it.

It involves the study of mathematical knots, which differ from real-world knots in that they have no ends. You can think of each one as a string that crosses over itself a given number of times, and then reconnects with itself to form a closed loop.

“It was considered a very esoteric field when I started in it, but it has grown immensely and grown in all different directions,” says Menasco, a professor of mathematics in the University at Buffalo College of Arts and Sciences.

Today, we know the study of knots could have applications in surprising areas. It could enable security firms to create better encryption systems, or elucidate the mysteries of how the body unravels DNA, Menasco says.

He’s a researcher who loves what he does: His office is filled with knot paraphernalia, and he can draw and build 3-D versions of complex knots from memory. Neighbors know him by his license plate: KNOTPROF. But in the world of mathematics, Menasco is perhaps best known, with Morwen Thistlethwaite, for solving the Tait Flyping Conjecture, one of three famous problems posed in the late 1800s by Peter Guthrie Tait, a father of knot theory.

Below, Menasco reflects on the evolution of knot theory, from its whimsical, 19th-century beginnings to its uses in the modern world.

Q&A:

Additional photos:

Research tool

Two interlocking strings of beads.

Blue and sea green beads form two interlocking knots. UB knot theorist Bill Menasco uses the beads, which can be snapped apart and rejoined, to research the structure of different knot formations. “It’s a very physical thing,” he says, regarding the study of knots. Credit: Douglas Levere

Marine knots

A framed series of drawings of nautical knots.

A series of drawings of nautical knots. This conversation piece, which hangs in UB knot theorist Bill Menasco’s office, was a gift from his antique-collecting father. Knots play a prominent role in sailing culture, as well as in many other cultures around the world. “It seems to be somehow buried in our humanity that we’re interested in these things,” Menasco says. Credit: Douglas Levere

Bookshelf

A bookshelf featuring titles on math and science.

UB knot theorist Bill Menasco’s bookshelf. Credit: Douglas Levere

Personalized license plate

A personalized license plate that says, "KNOTPROF".

UB knot theorist Bill Menasco’s personalized license plate. Credit: Douglas Levere

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