It's a simple word that has developed a sinister connotation: algorithm. For many of us, algorithms help determine what we watch, read and listen to — in the process, confirming our tastes and biases, and creating ideological echo chambers.

The word might not seem like one that would get much consideration from the Holy See. But last month in his first encyclical, Pope Leo XIV addressed the potential dangers of artificial intelligence. The word "algorithm" came up 19 times.

As part of NPR's "Word of the Week" series, we're looking at the history of the word that's defined much of modern life — and in the process, we'll blow the dust off some ancient mathematical concepts.

Where does it come from?
The etymology of the word is a strange one, according to Rob Watts, a journalist and host of RobWords, a popular YouTube channel about word origins and usage. "It just sounds like a mathematical term," he notes. Instead, it invokes a specific mathematician, he says: the 9th century Persian Muhammad ibn Musa al-Khwarizmi.

"It's actually the Latin take on that name al-Khwarizmi that we're invoking when we use the word algorithm," Watts says.

But it's taken a rather convoluted journey to reach us a dozen centuries later. The modern word algorithm traces back to the Latin algorismus through French (algorisme) and English (algorism). It also got "somewhat conflated with the term "arithmetic" before arriving in its current form, Watts says.

Who was Muhammad ibn Musa al-Khwarizmi?
Al-Khwarizmi wasn't just a mathematician — he was also an astronomer and geographer, who hailed from south of the Aral Sea in present day Uzbekistan. Part of his name is derived from Khwarazm, as the region was called.

But mathematics was where he made some of his most important contributions. Through his influential book, which roughly translates to The Compendious Book on Calculation by Completion and Balancing, he helped introduce algorithmic methods for solving mathematical problems, popularized the use of Hindu-Arabic numerals (including the concept of zero) in the West, and laid the groundwork for algebra — thus ensuring his place in the hearts of generations of ninth graders.

Al-Khwarizmi's ideas embedded themselves into modern mathematics, according to Judy Grabiner, a historian of science and professor emeritus of Pitzer College.

"This book gets translated into Latin in the 12th century more than once, because in 12th century Europe there was a revival of learning, an interest in ancient learning," she says.

Other scientific words and names, many beginning with al — Arabic for "the" — made their way into English during a flowering of Islamic science and math that began in the 8th century. Examples include words like alcohol, alkali, alchemy, and in astronomy, star names such as Altair, Alkaid, Alcor and Aldebaran.

A mathematical recipe
The algorithm made the jump from astronomy and chemistry to modern computing.

Bill Westrick, a software engineer based in Indiana, has been using algorithms in his daily work for decades. Most people may see them as a black box locked inside a computer, he acknowledges, but "an algorithm is really just a well-defined set of instructions to accomplish a task."

Think of it like a cake recipe: "You get the cake mix and it has a set of instructions," Westrick says. The recipe "tells me to put the ingredients in a particular order or mix it for a particular amount of time. I may not understand why that is, but if I follow those instructions, I should end up with a nice cake."

Long before modern computers, algorithms proved extremely useful in various fields of mathematics, such as business, surveying and navigation, says Susan McRoy, chair of the Computer Science Department at the University of Milwaukee.

"The algorithm is something that has enabled us to control really complex and wonderful technology," she says.

Take navigation: At sea, celestial navigation, which came into its own in the late 1700s, requires algorithms to crunch the inputs from a sextant that allows mariners to determine their position on the surface of a sphere. In the 1950s, a Dutch computer scientist, Edsger Dijkstra, developed what came to be known as Dijkstra's algorithm, a way of finding the shortest road distance between two points, which is key to computer-based mapping apps. And, of course, modern-day satellite-based GPS would not work without its own set of complex algorithms.

Algorithms even helped us land on the moon.

"The whole world of applied mathematics and imperialism and countries fighting at sea, not to mention linguistics, all come together in this," Grabiner observes.

So, the pope may be rightly concerned about what he described as dehumanizing algorithms that feed us a single, self-reinforcing viewpoint on social media. But it might be worth remembering that algorithms have been helping humans find their way for centuries.