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Saturday, June 23, 2018

Classic Math Problem Used for a Current Problem

  This piece is quite technical,  but love the fact that classical math is being used to drive some very modern problems. Great example for teaching?  In particular note how this problem deals with rapidly changing contexts, commonly existing in our world  Other applications?

In Quanta Magazine:

A century ago, the great mathematician David Hilbert posed a probing question in pure mathematics. A recent advance in optimization theory is bringing Hilbert’s work into a world of self-driving cars.

" ... The  future is now here. As a result of new work by Amir Ali Ahmadi and Anirudha Majumdar of Princeton University, a classical problem from pure mathematics is poised to provide iron-clad proof that drone aircraft and autonomous cars won’t crash into trees or veer into oncoming traffic.
“You get a complete 100-percent-provable guarantee that your system” will be collision-avoidant, said Georgina Hall, a final-year graduate student at Princeton who has collaborated with Ahmadi on the work.

Amir Ali Ahmadi, a professor at Princeton University, has shown how a sum-of-squares algorithm can be applied to modern optimization problems.

The guarantee comes from an unlikely place — a mathematical problem known as “sum of squares.” The problem was posed in 1900 by the great mathematician David Hilbert. He asked whether certain types of equations could always be expressed as a sum of two separate terms, each raised to the power of 2  ... "

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