The term 'algorithm' originated from the Latinized name of al-Khwārizmī, a 9th-century mathematician whose works introduced Arabic numerals and the decimal-based numeral system to Europe and whose treatise 'Al-Jabr' gave algebra its name.

Abaci, the plural of abacus, allowed individuals to perform arithmetic and tally quantities by moving pebbles called calculi, from which the word 'calculator' is derived.

The first commercially successful calculating machine—the arithmometer—was patented in 1820 but not mass-produced for over three decades, likely because its inventor was focused on his insurance business.

English mathematician Ada Lovelace wrote the first computer algorithm a century before computers existed and hypothesized that computing devices would one day be able to compose music—foreseeing the generative AI systems of today.

The Ishango bone suggests mathematics was born about 20,000 years ago

Ancient civilizations developed mathematical systems for various purposes, including the Egyptians for the construction of the pyramids and the Ancient Greeks for logical reasoning in theorems. However, these systems were predated by the Ishango bone—found in the Democratic Republic of the Congo—whose notches suggest a base ten system, prime numbers, and simple mathematical operations.

One of the first mechanical calculators—the Pascaline—was built in the 1640s by French mathematician Blaise Pascal to help his father, who worked as a tax collector.

The first algorithmic random number generator was developed in 1946

Although previous methods of randomness involved physical tools with limited outcomes, such as dice, or relied on chaotic variables for number generation, such as electronic noise, John Von Neumann's middle-square method turned the problem into a mathematical computation. It has since been replaced by methods that generate numbers from unique initial values, such as the time on a clock.

Mathematical breakthroughs influenced Shakespeare’s stories

New ideas in math were transforming Europe at the time Shakespeare penned his plays, including newly popular conceptions of zero via philosophers Descartes and Leibniz.

The term 'alcohol' has Arabic origins

Linguistic research reveals a lot about the ancient origins of alcohol. For example, studying various languages reveals that "mead," an alcoholic beverage made from honey, came even before wine.

Trade and conquest carried chess into Europe by the 11th century

After spreading through Persia, chess traveled along Islamic military and trade routes into North Africa and Moorish Spain by the 10th century. By the 11th century, it had taken root across much of Europe, flourishing in courts and monasteries.

An overview of 12 fundamental types of algorithms and the uses for each

These include search algorithms to quickly process and find important information, cryptographic algorithms to secure communications, randomized algorithms—such as Monte Carlo simulations for estimating probabilities of outcomes—and greedy algorithms, which make optimal choices based on available data in a step-by-step fashion, as seen in navigation apps.

The Middle Ages produced inventions that still affect our lives today, like coffee houses and improved agricultural techniques.

From the Greek for 'star taker,' the astrolabe allowed individuals to tell time and determine their latitude based on the position of the sun or other stars, as well as calculate the height of objects.

The Antikythera mechanism: The oldest-known analog computer

A device now considered the world's oldest computer was pulled from a shipwreck more than 120 years ago. Known as the "Antikythera Mechanism," it is now believed to have allowed precise tracking of astronomical positions, and its sophistication overturned understanding of Ancient Greek capabilities.

A breakdown of algorithms, how they are constructed, and their applications

Algorithms are instructions for accomplishing a goal and typically take the form of a step-by-step procedure. Given the conditions, these procedures can take various paths, increasing an algorithm's complexity. While traditional computer algorithms are programmed to account for all possible scenarios within a given process, machine learning systems build their own rules from data-driven patterns.

The first compiler to facilitate communication with computers was developed by Grace Hopper

The A-0 program linker automatically translated mathematical symbols into machine-readable binary code. Although it took two years for computer executives to get on board with the idea, the technology was foundational to future programming languages that allowed computers to understand commands written in word-based languages.

Before alarm clocks, people relied more heavily on their circadian rhythms, humans hired to wake them, and on tools such as candle clocks that dropped pins in metal trays at roughly set intervals.

The scientific name for northern lights came from two Greco-Roman gods

Although cave paintings may have depicted them millennia earlier, one of the oldest known references to auroras is a Babylonian cuneiform tablet from about 600 BCE. In 1619, Galileo Galilei named the phenomenon in the northern hemisphere "aurora borealis" after the Roman goddess of dawn—Aurora—and the Greek god of the north wind—Boreas.

The idea of a check—or promissory note—goes back to antiquity

As long as traders have looked to pay in cash or coin, the idea of an IOU has been close behind. Clay tablets from ancient Mesopotamia (roughly modern Iraq) and Persia (Iran) suggest proto-checks were used at the time. Islamic traders innovated "sakks" in the 9th century, leading to the broader adoption during the Middle Ages in Europe.

More than 2,000 years ago, a hand-powered model of the solar system called the Antikythera mechanism—the oldest example of an analog computer—could predict solar eclipses.

Slide rules—ruler-sized mechanical calculators with a component that slides out to show relationships between numbers—were used by engineers at NASA during the Apollo missions.

In 1822, French scholar Jean-François Champollion deciphered Egyptian hieroglyphs using the Rosetta Stone.

Look up the date of any Islamic holiday going back to 622 CE

The US Naval Observatory's calculator converts Hijri calendar dates to Gregorian and vice versa, covering Islamic holidays from the first year of the Islamic calendar through the present. The resource helps show how much Ramadan's dates shift year over year and allows readers to find out when Ramadan would have fallen in a certain year.

As of 2025, the College Board has banned the use of calculators with computer algebra systems on the SAT and PSAT.

Designed in 1937 by Harvard graduate student Howard H. Aiken, the 'Harvard Calculator' was used by the US Navy to solve advanced physics problems.

Among the smallest mass-produced mechanical calculators in history, the Curta was designed by Austrian engineer Curt Herzstark while imprisoned in a Nazi concentration camp during World War II.

A readable narrative account of how Muhammad first received the Quran

The story behind Ramadan's origins involves a lesser-known layer of personal drama for Muhammad, who fled the Cave of Hira in fear thinking he had been possessed by the angel communicating with him. Only his wife, Khadijah, was able to reassure him. The first revelation came during Ramadan in 610 CE, but the full Quran took 23 years for the angel Jibril (or Gabriel) to deliver.

An explanation of Turing machines—the foundations of digital algorithms and computers

The device reads data, overwrites or ignores it, and then moves on to the next piece of data based on a set of programmed rules. By imagining this data as zeros and ones—binary that makes up computer code—Turing machines became the theoretical models for how any algorithm could be run on a computer if the procedure could be coded into a set of digital rules.

Ancient Greek astronomer Hipparchus created accurate maps of the night sky way ahead of his time, with coordinates sometimes within a single degree of modern values.

The hour originated from an ancient Egyptian astronomical system

The movements of astronomical objects, measured in a day and a year, form the foundation of our sense of time. The Egyptians divided each day and night into 12 time eras, using arbitrarily selected stars as references rather than movements of specific celestial objects.

The work of Claude Shannon, for whom Anthropic's AI chatbot is named

Known as the father of information theory, Claude Shannon applied Boolean algebra—a subset of mathematics that quantifies true or false statements as 1 or 0, respectively—to circuit design to develop the concept of a binary digit. His paper "A Mathematical Theory of Communication" (1948) laid the groundwork for all modern digital systems.

A 14-year-old "human calculator" shatters six mathematical world records in one day

A teenage prodigy from Maharashtra, India named Aaryan Shukla set the record for the fastest time to mentally add 50 five-digit numbers. He did so in just 25.19 seconds–roughly equivalent to one addition every 0.5 seconds. The math whiz said he practices calculations for around five to six hours a day.

Early 20th-century debates about horses with 'paranormal mathematical abilities' helped shape modern approaches to psychological research.

The QWERTY layout first appeared in the Sholes and Glidden typewriter, sold starting in 1874 by the E. Remington and Sons gun manufacturer, which was looking to diversify after the Civil War.

Mathematicians often solve problems using wordless mental processes

It's a common technique among expert mathematicians, where thinkers rely on intuition, blurry perceptions and subconscious work—no writing, no formulas. The state is distinct from daydreaming, and often relies on sudden illuminations stemming from extended periods of subconscious reflection.

How a competition honoring a king's birthday uncovered history's first chaotic system

A committee established a contest for King Oscar II's 60th birthday, featuring four unsolved problems in mathematics, including one on proving the stability of a system of more than two objects held together by gravity. Focusing on three celestial objects, Henri Poincaré won the prize for his proof, which he later learned was incorrect and, upon correcting it, instead proved these systems to be unstable.

The foundation for computer viruses was published after its creator's death

In the late 1940s, Hungarian American mathematician, scientist, and engineer John von Neumann gave a series of lectures where he explained the theoretical framework for a computer program that could replicate itself—the von Neumann Universal Constructor. His lectures were later compiled and published in 1966, nine years after his death from cancer.

Chess traces its roots to chaturanga in sixth-century India

The earliest form of chess, known as chaturanga, emerged in India around the sixth century. The game simulated four divisions of the military—infantry, cavalry, elephants, and chariots—and laid the foundation for modern chess’ structure and strategy.

How the months of the year got named

Curious about how the months got their names? This article from The Old Farmer's Almanac explores the origins of today’s Gregorian calendar. Based on the ancient Roman lunar calendar, the months were named after Roman gods until winter when the names changed to numerical titles. Read along to learn the significance and intentions behind labeling each lunar cycle.

Computer pioneer Alan Turing was also an elite runner

Alan Turing is credited with helping to found modern computer science, in addition to cracking the Nazi code known as Enigma. Beyond these world-historical achievements, the British mathematician also nearly represented his country in the Olympics in the marathon, running just 11 minutes slower than the eventual gold recipient at the 1948 games. Read more on this lesser-known aspect of the man here.

Sudoku was originally called 'Number Place'

While there are earlier variations on the game, the modern version appeared in 1979, though it was then called "Number Place." The game was slightly altered and renamed in Japan.

Coffee brewing likely originated in Ethiopa and on the Arabian Peninsula.

The fast Fourier transform breaks down wave signals into discrete components

The algorithm was initially discovered by German mathematician Carl Friedrich Gauss in 1805, but his notes were not found until after his death. Today, FFTs form the basis for most compression software in media and are essential to technologies such as radar, sonar, and telecommunications.

The origin of shortest-path algorithms and how they became optimized for navigation apps

In 1956, Dutch programmer Edsger Dijkstra spent about 20 minutes developing an algorithm to demonstrate how computers could quickly determine the shortest route between Rotterdam and Groningen. Since then, modified versions of Dijkstra's formulation comprise the processing backbone of systems such as Google Maps and Apple Maps.

The Royal Game of Ur, which dates back as far as 2600 BCE, is believed to be one of the oldest board games in the world.

The science of cryptography, including methods to encrypt data and how to break encryption

Monoalphabetic ciphers use a set of rules to replace each letter with another consistently, making them susceptible to brute force attacks that try every kind of replacement. While more complex ciphers can transform text in less obvious ways, because certain letters are used more often than others, an analysis of letter frequency may reveal patterns that help uncover the rules that make up a cipher.

The ancient Roman origins of the leap year

The earth's orbit around the sun takes about 365.2422 days, leaving farmer almanacs the awful job of pretending the calendar year fits into a whole number. This article explores the modern origins of the civil solar calendar and its leap year. The Julian calendar, named after the Roman emperor Julius Caesar, cut the calendar year into 365.25 days, gifting the public an extra day every four years. Learn more of the history here.

How Byzantine scholars supercharged Renaissance Italy

A brief survey of how Byzantine scholars changed the course of the Renaissance by introducing Classical Greek literature to Italy. These scholars and their students were responsible for translating, interpreting, and printing many of the most fundamental texts in the Western tradition. Without their efforts, the Italian Renaissance and Western thought would have been immeasurably poorer.

FLOW-MATIC was the first programming language resembling the English language

As part of the team working on UNIVAC—the first commercially produced electronic digital computer in the US—Grace Hopper helped develop the system that enabled nonprogrammers and businesspeople without a strong mathematics background to use the machine effectively, thereby enhancing the computer's commercial viability.

How the ancients calculated Earth's size correctly

Watch this seven-minute video to hear Carl Sagan explain how ancient Greek polymath Eratosthenes correctly calculated the size of the Earth in the third century BCE. At some point, Eratosthenes noticed a discrepancy in the length of shadows cast in different cities during the summer solstice. This observation grew into a simple experiment that enabled Eratosthenes, the head librarian at the Library of Alexandria, to calculate the Earth's size precisely.

Early timekeeping tools included sundials, water clocks, and astrolabes

Astrolabes also provided a person's latitude based on the height of the stars in the sky, thus aiding in navigation. Incense and candle clocks relied on the constant burning rate of fire to track the passage of time based on premarked locations with equal-interval spacing.