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Discovery
Using Abstract Mathematics to Solve Real-World Problems

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Photo of two men in at a whiteboard

Roman Polyak and Igor Griva discuss mathematics in Polyak's office at George Mason University in Fairfax, Va.

Credit: Evan Cantwell, GMU


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Illustration plotting cost, feasibility constraints and possible ways to build a truss

One of the leading applications for nonlinear rescaling is the design of trusses, the complex metal frameworks that support many of the critical components of our built environment such as bridges, electrical transmission lines and radio towers. This illustration shows a mathematical plot pitting cost against the almost countless ways truss cross-beams can be arranged. The goal is to find the optimal arrangement that can be constructed at the lowest cost, while still supporting the enormous weight loads of both the equipment mounted to the truss and the truss itself.

Credit: Zina Deretsky, NSF


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Roman Polyak of George Mason University in Fairfax, Va

Roman Polyak of George Mason University in Fairfax, Va., is a leading expert on nonlinear rescaling, a mathematical approach that he developed for solving constrained optimization problems that has found use across the globe in fields ranging from structural engineering to medicine.

Credit: Evan Cantwell, GMU


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