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The Science of Problem Solving

Whether we’re aware of it or not, complex mathematical systems flow through our lives, but you don’t need to understand differential equations to appreciate the power of math.


“Mathematics really is like another language, but I try to talk about it in terms anyone can follow,” says Ray Treinen, an associate professor of mathematics at Texas State University.

As a researcher, his specialty is exploring the mathematics of fluid mechanics at the very small scale. Think about the single drop of water dangling from your faucet. A more advanced challenge is explaining how liquids, under the right conditions, can defy gravity and move up a tube without an external pumping force.

“At the super small scale, the effects of gravity (on liquids) get really exotic,” he says. “It’s amazing.”

water droplets cling to a clear surface
Water droplets clinging to a surface or dangling from a faucet are simple examples of capillarity, one of the areas of fluid mechanics studied by mathematicians. At the very small scale, liquids can appear to defy gravity.

Deciphering these mathematic puzzles may open the door to new discoveries in fields as diverse as nanotechnology, oil exploration, and space travel.

While his own research seeks to expand the boundaries of math, Treinen also uses his applied math expertise to aid researchers in other disciplines.

For example, he recently worked with a psychologist to develop mathematical models for analyzing specific patterns in human behavior.

“People in other fields want to use this type of modeling, but they usually don’t have the math to do it themselves. We can build the models and it gives them another tool for their research,” Treinen says.


ray reviews his work on a chalkboard
water droplets cling to a piece of clear glass
ray writes out equations on the chalkboard in front of his class