Kevin Hartnett, Quanta Magazine:
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.
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.
Mathematicians settled Hilbert’s question within a few decades. Then, almost 90 years later, computer scientists and engineers discovered that this mathematical property — whether an equation can be expressed as a sum of squares — helps answer many real-world problems they’d like to solve.
Yet even as researchers realized that sum of squares could help answer many kinds of questions, they faced challenges to implementing the approach. The new work by Ahmadi and Majumdar clears away one of the biggest of those challenges — bringing an old math question squarely to bear on some of the most important technological questions of the day.