Every algorithm on your phone is named after a man, and the name is really an address. Al-Khwarizmi means "the one from Khwarazm," a region on the Amu Darya delta, south of the old Aral Sea, now split between Uzbekistan and Turkmenistan.

Muhammad ibn Musa al-Khwarizmi lived from about 780 to about 850. Around 820 he worked at the House of Wisdom in Baghdad, a major center of scholarship. He wrote on astronomy and geography, but two of his books changed European mathematics.

The one people usually credit is al-Jabr, his treatise on solving equations. Its title gave English the word algebra, from al-jabr, "restoration." But algorithm comes from a different book. Around 825 he wrote on calculating with Hindu numerals, the place-value digits we now call Arabic numerals.

In the 12th century that arithmetic book was translated into Latin. A Latin manuscript of his work opens with Dixit Algorizmi, "Thus spoke al-Khwarizmi." One translation is known as Algoritmi de numero Indorum, "Al-Khwarizmi on the Hindu art of reckoning." His name, mangled into Latin, came to stand for the method itself. Algorismus meant the new way of calculating with place-value digits.

English picked it up early. Middle English had algorism by the early 13th century, via Old French algorisme. For centuries it meant simply "arithmetic with Arabic numerals."

The modern spelling came from a mistake. Scholars connected the word with Greek arithmos, "number," and reshaped it to match. Etymonline dates English algorithm to the 1690s, and Wikipedia cites a use by the mathematician Thomas Hood in 1596. Either way, the new spelling carries a th that al-Khwarizmi's name never had.

The meaning then widened. An algorithm became any step-by-step method of computation. From the middle of the 20th century it has meant, above all, a procedure for a computer to follow.

Spanish kept a different trace of the same man. There the word guarismo means a digit. So one mathematician's home region lives on in the name of a numeral, a branch of mathematics next door, and the instructions that run the internet.