A fundamental mathematical tool, conceived by Isaac Newton more than three centuries ago, has just received an update. Researchers have modernized Newton’s classic algorithm, expanding its applicability and efficiency to solve today’s complex mathematical problems, with implications ranging from logistics to artificial intelligence.
Isaac Newton’s original method, developed around the 1680s, was a cornerstone in mathematical optimization. Its genius lies in the ability to find the minimum values of functions, a process for identifying the most efficient solutions in a range of scenarios. This method is used for everything from determining the ideal location for a new airline distribution center to refining the algorithms that guide self-driving cars.
Traditionally, the algorithm operates by calculating the first derivative (which indicates the slope of a function) and the second derivative (which describes the rate of change of this slope). These calculations allow for a progressive approximation of the point where the function reaches its minimum value.
The New Frontier of Newtonian Optimization
Recently, a team of three researchers – Amir Ali Ahmadi, Abraar Chaudhry, and Jeffrey Zhang – continued Newton’s legacy. They managed to extend Newton’s method, helping to more easily find the minimum values of functions with higher exponents that follow certain characteristics making them “easier” to calculate.
This enhanced version of the algorithm stands out for its ability to reach the true minimum value of a function more directly, requiring fewer iterations compared to previously established techniques.
Sources:
https://www.quantamagazine.org/three-hundred-years-later-a-tool-from-isaac-newton-gets-an-update-20250324/ – Three Hundred Years Later, a Tool From Isaac Newton Gets an Update