Mathematically, these problems get translated into a search for the minimum values of functions. But in all these scenarios, the functions are too complicated to assess directly. Researchers have to approximate the minimal values instead.

It turns out that one of the best ways to do this is by using an algorithm that Isaac Newton developed over 300 years ago. This algorithm is fairly simple. It’s a little like searching, blindfolded, for the lowest point in an unfamiliar landscape. As you put one foot in front of the other, the only information you need is whether you’re going uphill or downhill, and whether the grade is increasing or decreasing. Using that information, you can get a good approximation of the minimum relatively quickly.

Although enormously powerful — centuries later, Newton’s method is still crucial for solving present-day problems in logistics, finance, computer vision and even pure math — it also has a significant shortcoming. It doesn’t work well on all functions. So mathematicians have continued to study the technique, figuring out different ways to broaden its scope without sacrificing efficiency.

Last summer, three researchers announced the latest improvement to Newton’s method. Amir Ali Ahmadi of Princeton University, along with his former students Abraar Chaudhry (now at the Georgia Institute of Technology) and Jeffrey Zhang (now at Yale University), extended Newton’s method to work efficiently on the broadest class of functions yet.

Read the full story here: https://www.quantamagazine.org/three-hundred-years-later-a-tool-from-isaac-newton-gets-an-update-20250324/