Determining the least expensive path for a new subway line underneath a metropolis like New York City is a colossal planning challenge—involving thousands of potential routes through hundreds of city ...

The original version of this story appeared in Quanta Magazine. If you’ve been making the same commute for a long time, you’ve probably settled on what seems like the best route. But “best” is a ...

Algorithms that zero in on solutions to optimization problems are the beating heart of machine reasoning. New results reveal surprising limits. Our lives are a succession of optimization problems.

Algorithms have taken on an almost mythical significance in the modern world. They determine what you see on social media and when browsing online, help form people’s belief systems, and impact the ...