# Mili Shah Will Solve Your (Math) Problems

POSTED ON: January 31, 2019

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Mili Shah, 2019. Photo by Joao Enxuto / The Cooper Union

Mili Shah, the newly-arrived associate professor of mathematics at the Albert Nerken School of Engineering, loves to solve “math problems.” But not the kind most of us recall from our grade school days. In fact, back in high school, Shah was rather indifferent to those kind of math problems and would have likely laughed if you had suggested she would become a mathematician. Now she says, “I love interacting with people and finding out what types of problems they have and figuring out ways I can help them using math.”

In college Shah considered studying art history, in spite of growing up in a STEM-focused family. Her father was the local doctor in the town of Tifton, Georgia, where she grew up. Her mother, who trained as a chemist, ran the front office of the practice. Her brother has become an ophthalmologist. She recalls her college sophomore differential equations course as being eye-opening. “It was full of applications,” she says. “It had a lot of environmental problems like what are known as predator-prey problems modeling the populations of different animals and how they relate to each other. The following summer I did a Research Experience for Undergraduates program in environmental math and saw how you can apply mathematics to solving ground water contamination, using it to explain the phenomena of how contaminants flow down a river, for example.”

After graduating Shah immediately began to pursue a Ph.D. in applied mathematics. For her thesis she worked on an algorithm known as a, “symmetry-preserving singular-value decomposition.” If you don’t know what that is, Mili Shah is the perfect person to ask because she will get a big smile on her face and, without a hint of condescension, give you an easy-to-understand explanation that shares her enthusiasm. “The group we were working with was interested in the problem of how to preserve symmetric motions in molecular dynamics simulations.  What was fun was that the work was applicable to other types of problems. For example in facial recognition we were able to mathematically prove that if you wanted to create the best symmetric approximation of someone’s face you can flip the left side to the right and the right side to the left and average the two.”

Shah arrived at the school of engineering after teaching for over ten years at Loyola University in Maryland. She started here in the Fall of 2018 teaching Calculus 1 and Linear Algebra. This semester she co-teaches an industrial robotics course. “I am really excited,” she says. “We have a nice robotic arm and are about to install a motion-capture system. We’ll be showing how to use that and describing the math underlying everything.”

When not teaching Shah has been working with the National Institute of Standards and Technology, a government-funded lab in Gaithersburg, MD. “They are trying to come up with math-based metrics to evaluate different types of robots, be it robotic arms or exoskeletons or what have you, to evaluate which one is better than the other one. This was an area of research I knew nothing about but again, math is a universal language. It’s been fun applying mathematics to this area.”

In Shah’s spare time … well … she thinks about math. She has had an equation on the chalkboard in her office since moving there. “This is based on the problem of having a robot with different sensors, like a camera and a lidar, and figuring out how to combine them into a common-coordinate frame. Mathematically it turns out to be a really clean problem. But in a practical sense there is always noise. So a lot of times you do equality to build up your intuition and then, if you can solve it for equality, you can take it to the next step for minimizing the real-world difference. That’s the beauty of being an applied mathematician. You have your ideals but you always continue to add realistic elements to it. I’m always open to new ideas and new problems. If you have any type of problem come talk to me and I will try to figure out how math can help you.”

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