The fast Fourier transform breaks down wave signals into discrete components

Differences in seismic wave speeds let scientists determine an earthquake’s location

Because primary waves are faster than secondary waves, seismic stations will detect longer gaps between these waves’ arrivals the farther an earthquake is. Calculating the distance to the earthquake from three stations allows its origin to be triangulated.

Ultrasound machines emit and collect high-frequency sound waves to construct images

Before its use in medical imaging, the technology was employed in World War I for submarine detection, the same way bats use sound for echolocation of obstacles. Differences in the penetrating power of different frequencies allow medical professionals to detect different structures in the body.

The greenhouse effect was discovered by analyzing Earth's temperature

Using mathematical techniques developed to analyze heat transfer, Jean-Baptiste Joseph Fourier showed that Earth should be significantly cooler if solar radiation were the only contributor to its surface temperature. By considering that the atmosphere could amplify the sun's warming effect, he formulated what became known as the greenhouse effect.

The first interferometric gravitational wave detector was invented in 1972

Robert Weiss completed the designs after his students asked about an earlier apparatus that used stretched aluminum cylinders to detect passing gravitational waves. Unfamiliar with general relativity and hoping to keep the course focused on experimental tests rather than mathematics, Reiss later asked his students to consider his device for homework. (Some readers may experience a paywall.)

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.

The Fair, Isaac and Company (FICO) was founded in 1956

When they created FICO, William Fair, an engineer, and his cofounder, Earl Isaac, reasoned that financial data could help a wide variety of companies improve business decisions. FICO created the first credit scoring system to help lenders be more objective.

Researchers identify a hidden instability pattern in simple ocean wave models

Stokes waves—a solution to the mathematics of water waves—were once assumed to be stable. Italian mathematicians have proven disturbances cause these waves to collapse and such collapses follow an infinite repeating pattern. To complete the proof, the team offered a $100 donation to solicit online help.

Quantum field theory, which has made predictions accurate to 12 decimal places, explained

Instead of being made of indivisible particles, all visible matter in the universe is built from underlying quantum fields—smooth, invisible entities that behave like waves and extend throughout space and time. The theory suggests these fields are fundamental, and particles are disturbances that move through them.

Tone Transfer recreates any piece of audio into instrumental recreations

Using machine learning models and Differentiable Digital Signal Processing, this tool can transform any 15-second sound clip into a flute, saxophone, trumpet, or violin reproduction. Researchers behind the open-source experiment hope the technology will enable musical creation through creative sound combinations.

View how AES—the global standard for symmetric encryption—works

Established by the National Institute of Standards and Technology in 2001, the Advanced Encryption Standard transforms plaintext into ciphertext using multiple rounds of processing, including substitution, transposition, and mixing. Larger keys undergo more rounds to produce 16-byte blocks of scrambled data, with 256-bit AES keys taking 3.31 × 10⁵⁶ years to decrypt via brute force.

'FAST': An acronym to remember stroke symptoms to look for

The primary factor in surviving a stroke is how quickly one gets the appropriate medical treatment. “FAST” refers to the four most noticeable symptoms of a stroke: face-dropping ("F"), arm weakness ("A"), speech difficulty ("S"), and "time to call 911" ("T").

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 golden ratio is believed to underlie patterns in nature and beauty

The irrational mathematical constant has been cited in art, architecture, and nature since its origins in ancient Greece. Its connection to the Fibonacci sequence has associated it with spiral patterns in pineapples, pinecones, and other plants.

Scientists use ground-based radar data to detect turbulence within clouds

NCAR developed the NEXRAD Turbulence Detection Algorithm and the Graphical Turbulence Guidance system to provide forecasts up to 18 hours ahead using ground-based Doppler radar data. Software systems also utilize an automated observation and reporting package—the EDR system—found on Delta, United, and Southwest Airlines aircraft.

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 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.

X-rays earned the very first Nobel Prize in physics for revealing hidden worlds

In 1895, Wilhelm Conrad Röntgen discovered X-rays, which could pass through solid objects and make unseen structures visible. Today’s X-ray tools continue to advance science and medicine, including capturing real-time images of proteins.

Why Edwin Armstrong developed FM radio

AM radio was popular but prone to interference and static, which could be frustrating for listeners. In 1933, Armstrong, a Columbia University professor, discovered that a clearer signal could be broadcast by revising how it was captured.

Fracking originated in the American Civil War

After witnessing how artillery created fissures in narrow water channels, a Civil War veteran wondered if the process could be replicated in underground wells to extract oil. He patented an "exploding torpedo" for this purpose, which became the foundation for future fracking techniques.

Visualize the components of fireworks

This article provides animated diagrams depicting how different parts of fireworks function. The elements work together through timed mechanisms to produce desired effects.

Moore's Law came from observing exponential computing growth in the 1960s

In 1965, Gordon Moore, cofounder of Intel Corporation, observed a four-year trend of constant growth rate in computing power. Hypothesizing the trend would continue, his observation became the benchmark that the computing industry has worked to maintain for 60 years.

CUDA was Nvidia’s first step into artificial intelligence

CUDA (Compute Unified Device Architecture) is a parallel computing platform that was developed by Nvidia in the mid-2000s. By letting people perform computations in parallel, rather than sequentially, CUDA allowed people to compute large amounts of data quickly. CUDA has been used to build machine-learning models as well.

Glowing chemicals allow scientists to read DNA like a barcode

The process of determining the order of nitrogenous bases in DNA involves first cutting the DNA into fragments, which are duplicated multiple times using bacteria. Fluorescently labeled terminator bases are added to fragments, which are sorted by length and read via laser to reconstruct the sequence.

The transatlantic cable allowed for communications between North America and Europe

It had significant impacts on just about every industry, including finance. Specifically, the transatlantic cable made it so that real-time financial transactions could take place across the Atlantic, and allowed for much faster sharing of information that increased global market accuracy.

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.

Listen to the sounds of pulsars, which emit radio pulses up to hundreds of times a second

Just as figure skaters spin faster by tucking in their arms, these celestial objects acquire high rates of spin from the collapse of the cores of massive stars. The star's rotation spins its magnetic field, generating beams of radio waves from its magnetic poles. If either of these poles faces a detector, the signals can be picked up and converted to audio signals.

Freud and Jung were once friends. What drove them to break up?

Austrian psychologist Sigmund Freud and Swiss psychiatrist Carl Jung were fast friends, immediately hitting it off the first time they met in 1907. This four-minute video dives into the intellectual divide that drove them apart.

Fireworks make a loud booming sound after exploding due to air expanding faster than the speed of sound.

A small portion of The Winstons' 'Amen, Brother,' an obscure '60s gospel record, is the basis for thousands of hip-hop tracks, making it one of the most sampled records ever that's informally known as 'the Amen break.'

The history of many kitchen appliances involves unexpected discoveries and applications, including wartime radar turned hamster defroster and replacing an 'ice king' with heat-stealing boxes.

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.

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

While the first exchange-traded fund (a 'basket' of different assets that can be bought and sold on a stock exchange) in the US only launched in 1993, the global ETF market has grown to more than $10T in the short time since.

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.

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

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.

Calculate how much of your tax dollars go to each federal program based on your income, filing status, and number of children

The concept of phantom limbs, the perception that amputated limbs are still present, dates back to a French military surgeon in the 16th century.

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

Long before Major League Baseball began allowing instant replay for balls and strikes, an umpire reluctantly used the technology to determine whether a hit was a home run, a move that inadvertently ushered in a new era for the sport.

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.

A century of Billboard issues documenting the evolution of popular music.

Waves off the coast of Nazaré, Portugal, can reach over 100 feet and are caused by the area's deep underwater canyon geography

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.

Trace how the Bill of Rights, inspired by centuries of political theory, took shape between 1774 and 1789.

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

Visualize the path of every solar eclipse from 1900 to 2099 and see what each looks like when observed from different locations on Earth.

Gerrymandering works through two techniques: cracking opposing voters across districts to dilute their power, and packing them into a few to waste their votes in lopsided majorities.

Graffiti dates back to at least ancient Pompeii, where citizens scrawled messages to one another on public walls