An interview with James Yorke, the man who coined the mathematical term 'chaos'

The life of Edward Lorenz, who originally used a seagull in his 'butterfly effect' metaphor

By accidentally finding that rounding one variable to its third decimal place and re-running a weather simulation produced a drastically different two-month forecast, the American mathematician established the field of chaos theory. His paper—"Predictability: Does the Flap of a Butterfly's Wings in Brazil Set off a Tornado in Texas?"—introduced the well-known metaphor for the behavior of chaotic systems. (Some readers may experience a paywall.)

Learn how natural systems exhibit characteristics of chaos theory

In biology, some mathematical models of ecosystem populations and heart irregularities show strong sensitivity to initial conditions, which scientists can simulate to determine quantitative tipping points at which these systems become unstable. Within the social sciences, crowd behavior and the virality of social media posts have shown how human behavior fits within the framework of chaos theory.

A mathematical and visual analysis distinguishing chaos from randomness

Random systems lack any underlying pattern or causal relationships, while chaos is mathematically deterministic because the behavior follows established laws of nature. In 3D plots, chaotic systems produce outputs that approximate a mathematical function, while random points appear as statistical noise.

The story of two female programmers running the simulations behind chaos theory's discovery

Margaret Hamilton and Ellen Fetter worked on MIT's 800-pound Royal McBee LGP-30 computer, which was fed binary code on paper tape to perform computations. Among the computations performed were those involving equations describing the motion of gas in a circulating fluid for Edward Lorenz, widely considered the father of chaos theory.

Chaos theory—informally known as the butterfly effect—is the reason why weather forecasts are presented with probabilities rather than certainties.

Mathematics proves turbulence's chaos creates super diffusion

Turbulent flow is responsible for the rapid scattering of dandelion seeds, volcanic ash, and untied balloons. Its swirling behavior accelerates particle scattering faster than other mixing methods, as particles acquire energy from the interactions of eddies.

Visualize chaos with the orbit of three or more objects bound by gravity

In this simulation, users can simulate randomized and preset orbital configurations for up to 10 celestial bodies to observe the system's evolution in an interactive 3D space. The same configurations can produce different orbital behavior—a feature of chaos—by making small changes to an object's mass under advanced settings.

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 universe only evolves toward increasing disorder, providing a direction to time

Within physics, the second law of thermodynamics states that entropy always increases, as seen by a concentrated drop of dye slowly diffusing throughout a cup of water, increasing disorder. Because such processes do not unfold in reverse, entropy may be what provides time with a single direction, unlike space.

How upheavals in accepted scientific theories helped popularize the term 'paradigm'

When Thomas Kuhn published "The Structure of Scientific Revolutions" in 1962, he described the history of science as comprising periods of "normal science" where these accepted frameworks—paradigms—gradually accumulate anomalies until they cannot describe nature. Revolutionary science, such as the development of a new theory, results in a paradigm shift, another term Kuhn helped popularize. (Some readers may experience a paywall.)

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.

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.

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

A "no math" primer on quantum mechanics

Quantum mechanics may not immediately grasped, but it can be slowly understood through the experiments and discussions offered here by writer Dr. Miguel F. Morales. A professor of physics at the University of Washington in Seattle, Dr. Morales makes understanding the basics of quantum mechanics fun with a promised "no math" approach.

Time magazine ran a cover story titled 'The End of the World as We Know it?' in January 1999

In January 1999, Time published a dramatic Y2K cover with apocalyptic imagery and dire headlines. The portrayal likely exacerbated public fear and magnified the crisis in the popular imagination, turning a technical issue into a cultural panic.

How a brain injury created a mathematical mind

In 2002, two men savagely attacked Jason Padgett outside a karaoke bar, leaving him with a severe concussion--and turning Padgett into a mathematical genius.

How Jim Chanos used a Wall Street Journal article to uncover Enron's fraud

After seeing an article in the Wall Street Journal about the unclear financials of energy companies, Chanos' firm Kynikos Associates began investigating the finances and accounting of Enron, an American energy corporation that was the seventh-largest company at the time. The firm ended up making $500M on its short positions against Enron.

There are more chess game variations than observable atoms in the universe

Mathematician Claude Shannon estimated there are 10 to the 120th power variations of chess games possible. Known as the "Shannon number," this is more than the estimated number of atoms in the cosmos.

Proponents argue that abandoning the rules-based order risks a return to the chaos that led to 2 world wars

Brookings scholar Robert Kagan warns that if China and Russia gain regional dominance, the world could return to the unstable conditions of the late 19th century—the same chaos that led to two devastating world wars.

The surprisingly poetic origins of the phrase 'March Madness'

When legendary sportscaster Brent Musberger called the 1982 NCAA basketball tournament "March Madness," the term stuck and helped popularize the annual event. But he wasn't the first to use the phrase. This Time magazine article explores the contributions of Henry V. Porter, who originally used "March madness" in a 1939 article about the Illinois State basketball tournament, and later in a 1942 poem called "Basketball Ides of March."

What it means to call something 'Lynchian'

David Lynch was one of American cinema's most influential directors. He brought a singular, unsettling vision to the silver screen. Critics, however, have trouble pinning down what it means when other artists try to recreate that vision. This essay untangles his influence, tracing the word "Lynchian" back to its earliest utterances and attempting to define a notoriously slippery term.

What is space-time?

Space-time is a complex subject, but this Livescience article makes an effort to disentangle the topic. Somewhat akin to a sheet of rubber that can be warped and bent in parts, space-time is a bit more involved that that. However, the analogy makes this and other aspects of the concept simpler to grasp.

The history of the periodic table and how it hinted at atoms possessing internal structure

In 1869, more than two decades before the discovery of electrons, Russian chemist Dmitrii Mendeleev organized known elements by atomic weight and chemical properties using index cards. His organization revealed previously undiscovered elements and identified patterns in the reactivity of elements, which would later be linked to each element's outermost electron shell. (Some readers may experience a paywall.)

CEO Gary Tan explains Y Combinators guiding philosophy

Hear YC President and CEO Garry Tan talk about why he values earnesty and excellent communication skills in YC founders, his thoughts on AI, and more in this unexpectedly deep and in-depth interview.

A theory about Pink Floyd and 'The Wizard of Oz' was popularized by a 19-year-old

Pink Floyd’s seminal album “Dark Side of the Moon” eerily synchronizes with “The Wizard of Oz,” offering a psychedelic soundtrack for the movie. Journalist Charlie Savage popularized the phenomenon when he was 19. He’d go on to write for the Boston Globe and New York Times winning a Pulitzer Prize.

Understanding college basketball's guru, UCLA's John Wooden

John Wooden coached UCLA to an unprecedented 10 NCAA titles, including seven straight from 1967 to 1973. He studied the characteristics that made people successful and, in 1948, created his iconic triangular diagram with 25 common behaviors. This article unpacks the 25-block framework that makes the "Pyramid of Success" and shows how Wooden's off-court wisdom shaped future champs like Bill Walton and Steve Kerr.

The Lucasian Chair is among the most prestigious academic positions in science

Once held by icons like Newton, Dirac, and Hawking, the position was founded in 1663. "Star Trek" imagined the Lucasian Chair’s future holder as the android Data, cementing its mythos across scientific and science fiction realms.

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.

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.

The word 'jazz' evolved from 'jasm,' 19th-century American slang for 'energy'

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.

The first robot in literature may have been a 'mechanical man' in 1907's 'Ozma of Oz,' a book in L Frank Baum's 'Wizard of Oz' series.

The name 'Silicon Valley' arose from the founding of Shockley Semiconductor Laboratory in Fairchild Semiconductor in 1956-57, founded near Stanford University in Palo Alto

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

Radioactive elements can introduce software errors because the ionizing radiation they produce can detach electrons from atoms, and computer code relies on the distribution of electrons.

Exploring the Larry Bird punch that almost changed March Madness

A Yale student wrote a profound essay about the consulting industry's influence on elite college students that was published in a book of her writing after she died in a post-graduation car accident.

Mid-century modern graphic designers, known for their bright colors and bold lines in advertising, also found success with children's books.

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.

Search a massive database of over 4 decades of clues from the TV quiz show 'Jeopardy!'

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.

A researcher recently discovered an interview from 1967 between groundbreaking journalist Joan Didion and the Grateful Dead, years before the band became an institution.

See a ranking of the best (and worst) Federal Reserve Chairs since 1914 out of the 16 men and women who have held the office since.

One disco producer saw 'Star Wars' four times on its opening weekend and was so inspired that he recorded the album 'Star Wars and Other Intergalactic Funk,' which produced a chart-topping single.

How the most famous Ebola book, The Hot Zone, which sold 3.5 million copies and was translated into 30 languages, got aspects of the disease so wrong.

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

How Amazon operates a 'flywheel' business model, a self-reinforcing cycle that drives continuous growth

'Grand Canyon of the Yellowstone,' a work by American painter Thomas Moran, inspired Congress to establish Yellowstone National Park.

The hormonal disorder PCOS was renamed PMOS in 2026, a move designed to improve care and research by shifting the focus to the hormonal causes of this condition that affects 1 in 8 women.

Children are now three times more likely to say they want to be a YouTuber when they grow up than an astronaut, with some even attending 'YouTube camps' that teach kids how to create content for the platform.