Mathematical breakthroughs influenced Shakespeare’s stories

Linguists proved Shakespeare wrote his plays

In the 1800s, linguist Wincenty Lutoslawski invented a method of linguistics analysis called stylometry to help certify literary authorship. Stylometrists concluded that Shakespeare wrote his plays, and likely collaborated with Christopher Marlowe for some.

Shakespeare’s storytelling uses intricate, intertwining narratives

According to one professor, readers return to Shakespeare’s plays, not for his storylines, but to learn how things unfold. In the process, they often use his plays to understand why humans act the way they do.

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 Shakespeare changed the sonnet

A sonnet is a rigid poetic form from the Renaissance, featuring 14 lines, a consistent meter (or beat) and rhyme scheme, and a noticeable thematic shift known as a "volta." Shakespeare popularized a form featuring three four-line stanzas and a rhyming couplet, departing from the Petrarchan two-part structure of eight- and six-line stanzas.

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.

Enlightenment ideals of reason informed the foundation of the Revolution

From the 17th to 19th centuries, an intellectual movement took place in Europe and its colonies that emphasized reason over authority. Following the Scientific Revolution, thinkers like Descartes, Kant, and Locke sought to explain the world in rational—rather than religious—terms. The movement caused a paradigm shift in how societies are organized and how people perceive themselves.

The magic angle to skip a spinning stone is 20 degrees

The traditional shoreside activity—reputedly practiced by luminaries Shakespeare and Homer—can be broken down into its bare physics, from hydrodynamics and momentum to gravity.

Galileo’s discovery of Jupiter’s moons led to multiple scientific advancements

Beyond challenging Earth-centric views upon their discovery in 1610, the Galilean moons were also later analyzed to contribute to early astrometry and astronomical interferometry. Measurements of eclipses were also used to estimate the speed of light.

Theater of the Absurd brought existentialist ideas to the stage

In the 1950s, playwrights horrified by the events of World War II and inspired by existentialism’s response to it began staging plays that brought many of the philosophy's ideas to center stage. Critic Martin Esslin coined the term “Theater of the Absurd” in 1960, citing the plays of Samuel Beckett, Arthur Adamov, and Eugene Ionesco as indicative of a new theatrical style that rejected realism and standard plot.

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.

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.

Shakespeare included a reference to toasting in ‘The Merry Wives of Windsor’

At one point in the 1602 play, the character Falstaff calls for a quart of wine, asking for toast to be placed in it, as was customary at the time.

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.

The history of the 10 axioms of Zermelo–Fraenkel set theory with choice, regarded as the most universal foundations of math

Like postulates in geometry—accepted truths that form the logical building blocks for formal proofs of more complex theorems—axioms cannot be proven, but set the underlying logic and rules for systems. The ZFC axioms resulted from painstaking work to identify the underlying rules of mathematics and are built on the premise of sets, or well-defined collections of elements.

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.

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 role stories play in mass economic trends like bitcoin, crashes

Economics is dominated by numbers, but stories play a huge role in the emotional shifts seen within macroeconomic trends. For example, bitcoin is not just a cost-benefit winner, but a compelling tale of decentralization and independence. This is a 20-minute summary of Nobel prize-winning economist Robert Shiller's "Narrative Economics."

The most bizarre numbers in the universe

Even for math-y types, some numbers are incomprehensible. This article dives into several kinds of numbers more complicated than even irrational numbers with endless decimals like "pi" or Euler's number: Noncomputable numbers. Read the bizarre...

William Blake may be best known as a poet, but he was also a painter

The author of "Songs of Innocence and of Experience" was a romantic poet and painter. "Newton," one of his better-known pieces, satirizes Isaac Newton, whom he saw as too concerned with the empiricism of science and, as a result, lacking an understanding of nature.

Despite his disability, Stephen Hawking reshaped our understanding of black holes

His theoretical work—especially on black holes emitting radiation, now known as Hawking radiation—challenged long-held ideas. He also brought complex physics to the public through bestselling books like "A Brief History of Time."

How quantum computers can empower Shor's algorithm to break digital encryption

Secure communications largely rely on numeric keys generated by multiplying two enormous prime numbers together, and it is computationally impractical to determine these primes by trying to divide by every possible one. While Shor's algorithm can provide better guesses for this brute-force approach, it relies on a number that is difficult to determine on classical computers but much easier to calculate using the simultaneous computations enabled by quantum superposition.

The man who created Settlers of Catan was inspired by Viking tales about the journey to Iceland.

Klaus Teuber invented the game when he was in his 30s, and had his wife and children act as early test players. Published in 1995, the game has now sold over 45 million units.

Lewis Carroll's 'Alice's Adventures in Wonderland' turned the fantasy genre upside down

A lot of 19th-century British fantasy was often stiff; its children’s literature was often overly didactic. Carroll’s novel—about a young girl who falls into an unusual world full—was neither, offering vivid, psychedelic imagery and seemingly nonsensical word games.

Clever Hans was a 1900s horse that was believed to be able to solve math equations, tell time, and read and comprehend German, until a psychology student discovered how he got his answers.

Handel's 1741 'Messiah' saved him from financial ruin

The piece is widely recognized as a masterpiece and a perennial expression of highbrow culture during the holiday season. The biblically based, English text also broke from opera norms at the time, rewarding him for his risky innovations.

The Medicis of Italy innovated 'bills of exchange,' precursors to checks

At the time, lending money for interest (also known as usury) was banned in much of the Christian world. The enterprising Medicis developed bills of exchange to allow merchants to promise payment without cash or coin (with some discrete means of earning interest woven in). Learn more about how this family laid the foundation for modern banking.

The South Sea Bubble was an 18th-century scandal that redefined speculation

This video illustrates how the South Sea Company in Britain sparked a stock boom in 1720, with promises of huge trading profits, driving shares to unprecedented heights before a sudden crash wiped out the fortunes of investors—including Isaac Newton, who lost an estimated £20K.

Jane Austen by the numbers

This feature from the Guardian takes a unique approach to Austen's literature, breaking her life, work, and fandom down into data. The slide deck includes comparative analyses of character employment, net worth, and age. Below is a breakdown of Austen's unexpected posthumous rise to fame.

Volcanic activity may have triggered the Black Death by spewing gases that led to crop failures in Europe, thus forcing the import of grain ships with plague-infested fleas.

The Brothers Grimm were lawyers before they were storytellers, and became interested in fairy tales as they began investigating how rules and customs had been passed down through cultures.

As of 2025, the most cited papers in science include a review of graphene, methods to improve image recognition, streamlining electron density calculations, and optimizing protein studies.

Stanford built a Google Maps for the Roman Empire, revealing how much it cost to travel in the ancient world

Learn more about the history of fireworks, which dates back to an accidental invention during an alchemist's quest for information about immortality.

After the Boston Tea Party, colonists switched to coffee, which became the main morning drink for revolutionaries.

For centuries, it was common to sleep in two shifts: a few hours at the beginning of the night, and a longer period beginning around midnight

Walt Disney's early film 'Alice's Wonderland' was a groundbreaking innovation in the silent film era

Exploring the Larry Bird punch that almost changed March Madness

Explore chaos in this simulation of two double pendulums, where small differences in the release angles produce wildly different outcomes.

Existentialist writer Jean-Paul Sartre coined the famous phrase 'Hell is—other people' in his play 'No Exit'

The Mona Lisa's celebrity status and repeated restorations have obscured what made the painting so revolutionary for its time

Browse a detailed visual analysis of over 200,000 similes—comparisons that often use 'like' or 'as'—from popular fiction to see how frequently writers the same idiomatic expressions.

American dance legend Martha Graham, sometimes called 'the Picasso of dance,' refused to perform at the 1936 Olympics in Berlin and conceived the piece 'Chronicle' in response to the experience.

Play the role of a student in a game where you try to navigate college and remain debt-free, selecting different income levels, high school experience, race, ethnicity, and more.

According to the physics of black holes, our 4D reality may be a hologram—a projection of information coded on a 2D surface on the edge of the universe.

Alzheimer's can lead to brain shrinkage, with an average of around 2% of volume reduction per year

Warren Buffett's former professor Benjamin Graham is known as the 'father of value investing,' a strategy in which investors seek to buy stocks trading below their intrinsic worth.

'Shogun,' a 1980s TV series, helped popularize sushi in the US by stimulating an American interest in Japanese culture.

Mark Twain spent decades feuding with the US Postal Service, convinced its costs and regulations were bureaucratic overreach.

Some coin denominations have ridges etched on their sides, partly to prevent counterfeiting, in a practice called 'reeding.'

El Niño, Spanish for 'the boy,' was named after Jesus Christ because the phenomenon resembled the weather changes observed around Christmastime.