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200,000 ways to tie a tie

Harsh Mathur’s “side job” in the interdisciplinary studies of arts and physics

In a talk, Professor Harsh Mathur explained how to use the knot theory to discover 200,000 ways to tie a tie.

In a talk, Professor Harsh Mathur explained how to use the knot theory to discover 200,000 ways to tie a tie.

In a talk, Professor Harsh Mathur explained how to use the knot theory to discover 200,000 ways to tie a tie.

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The marriage of art and science is not a novel concept; yet whenever such a companionship arises, it never fails to amaze people how beauty can arise from intensive study. Harsh Mathur, a professor in the Department of Physics for 20 years, brings together these two fields in an interdisciplinary union. Though the interaction between physics and art is not the central focus of his time here at CWRU, Mathur still puts forward the creative inquiry and intensive effort that both fields deserve.

In the past, Mathur spent time researching mathematical miscellany, from the patterns behind tie knots to the proposed fractals in Jason Pollock paintings. In these side endeavors, he was accompanied by Kate Brown, a former graduate student who is now a professor at Hamilton University; together they studied the physics behind these artistic entities.

Mathur recently gave a talk on the numerous ways to tie a tie. According to Mathur and Brown, there are actually 200,000 ways to tie a tie, as opposed to the comparatively paltry 85 ways that was previously thought to be the maximum number of possible tie knots. The motivations Mathur had behind researching the enormous number of tie knots is simple.

“We discovered it and never published it,” Mathur said in a recent interview. “Why did we invent them? Because it’s fun. The point is that I used to talk about the 85 ways to tie a tie just because I think it’s kind of fun to talk about.”

The lighthearted nature of the study did not evoke amusement from just Mathur and Brown. As Mathur recalls, “I talked about it and I gave a talk at Ohio State, but in that talk someone said that this [the tie knot] is really funny; you guys could win the Nobel Prize. You know about that? The Nobel Prize is the sort of joke prize that is given out for research that is kind of funny.”

Despite the nature of the research, Mathur somewhat laments not publishing the findings that he found, especially considering the circumstances surrounding this decision. Not wanting to blemish Brown’s resume, Mathur pushed off publication of the findings of the 200,000 ways to tie a tie, feeling “it would not be good for her application…. I was afraid that people who hired her would not think this was serious research.” By the time he felt it was safe to do so, the 200,000 knot ties were already published by a group of computer scientists, and it made it to the New York Times fashion section.

“I would love to be on the fashion page of The New York Times,” Mathur joked. “I guess what it shows is this is what happens in science research, if you sit around too long somebody else may find your discovery, and that is part of the game.” Mathur said compared to other people publishing his findings, he was more heartbroken for not getting on the New York Times Fashion page, “What are the odds that physics project would ever wind up on the fashion page?”

Despite the outcome of this project, Mathur still puts in time researching more about the kinds of patterns that can arise from looking at art, ties or otherwise. Mathur also has interest in the field of crystallography and how it contributes not only to traditional applications, such as in solar and space settings, but also in artistic patterns utilized by medieval Islamic art. Mathur finds it “unquestionably refreshing” to connect medieval art to a new level of mathematical understanding.

Interdisciplinary research is not the focus of Mathur’s work, or “day job,” as he describes it. Yet he approaches these subjects with a light hearted zeal and a deep interest in the research. To Mathur, making connections between art and science can provide much more insight about both. Mathur has shown that such results have yielded unique experiences that individual studies alone just can’t provide.


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200,000 ways to tie a tie