Understanding the Diffie-Hellman key exchange, an example of public key cryptography

Visualize how passkeys, which rely on asymmetric cryptography to authenticate users, work

After using biometrics or a PIN to access the private key stored on a device, it is combined with a random number generated by the site to produce a cryptographic signature. This signature is verified using the site's public key, allowing a user to log in without entering a password. This reduces the risk of fraudulent messages—phishing attacks—and data breaches.

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.

Watch how the Enigma machine encrypts messages and learn about its critical design flaw

Using settings selected from a series of rotors and a plugboard that let operators swap letters with any of their choosing, the machine lit up the output letter for each letter typed. While this system could generate messages requiring any of 150 quintillion potential keys, the machine's reflector never encrypted a letter as itself, providing an entry point for exploiting the system.

A US Department of Defense research lab developed the technology for the dark web

Although encryption existed to mask the content of communications across the internet before the 1990s, those managing overseas network infrastructure could determine a spy's affiliation based on where they saw data sent to and received from. To keep this information secret, the US Naval Research Laboratory developed onion routing, which enabled anonymized web browsing. The release of the technology to the public obscured sensitive communications further by growing the volume of anonymous data.

How end-to-end encryption protects messages, even from service providers

Using symmetric and asymmetric cryptography, data is encrypted on the sender's device before being transmitted across application servers that lack the key needed to decrypt it. The message is not decrypted until it reaches the recipient's device, which uses their private key to recover the plaintext. E2EE's effectiveness has led to its adoption by WhatsApp and Signal.

Watson and Crick revealed DNA's double-helix structure using others' key findings

Their 1953 model, made from cardboard cutouts, explained how DNA stores genetic information through base pairing. Rather than experimenting and collecting their own data, they incorporated patterns and data from other scientists through trial and error.

A look at historical ciphers, from the Spartan 'scytale' to the Navajo Code Talkers

From the Greek word for "hidden writing," cryptography in Ancient Greece took the form of batons around which a long strip of leather or parchment was wrapped, after which messages were written. Recipients needed a scytale of the correct width to encircle received ribbons and reveal the message. Members of the Navajo Nation created a code that remained unbroken throughout its use in World War II.

Bitcoin explained and made simple

Bitcoin, the most popular and well-known example of a cryptocurrency, came on the scene around 2010, with its evangelists proclaiming it would eventually displace government-backed traditional cash. While the concept of a digital currency may seem straightforward, the details can be deceptively simple. This quick video overview provides the foundation for a deeper dive into the world of decentralized currency.

Watch a cybersecurity expert answers questions about hacking

From firewalls and VPNs to ransomware and viruses, IBM Distinguished Engineer Jeff Crume has seen many changes in cybersecurity during his 40 years of IT experience. In this video, he explores some of the most significant hacking events in history and provides advice on protecting yourself online.

Harry Dexter White outmaneuvered Keynes to make the dollar the center of the new global monetary system

The chief US Treasury economist at the conference, White, advocated for a dollar-centered exchange rate system over Keynes' competing idea of a new global currency, shaping the postwar economic order for decades.

It took 70 years for computer scientists to determine how to cut a cake fairly

The cake-cutting problem explores how to divide something fairly, which is not solely about cutting evenly-sized pieces. A protocol that accounted for personal preferences (e.g., a corner piece) between just three people took 16 years to develop.

An explanation of TCP/IP, which helps transmit data across the internet like a club sandwich

The system consists of several layers—application, transport, internet, and network—each responsible for specific tasks. These include interacting with a web browser, checking for errors, sending packets of data across various networks to avoid congestion on their way to a destination address, and managing the transmission of information across hardware, such as an Ethernet cable.

Mathematician David Hilbert developed general relativity equations before Einstein

Although working independently of one another, the two exchanged correspondence in the lead up to November 1915, when Hilbert submitted their gravitational field equations five days before Einstein presented their work. An error in Hilbert's formulation and its nonpublication until March 1916 would leave credit for general relativity to Einstein.

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.

The origin of chaos theory, colloquially known as the 'butterfly effect'

The theory explains that systems following well-understood physical laws can still produce unpredictable outcomes due to small variations in their initial conditions. Originally identified in weather data, elements of chaos have been observed in stock market fluctuations, cardiac arrhythmias, and the evolution of online social movements.

Bill Gates and Paul Allen were childhood friends before founding Microsoft

The two bonded over a teletype terminal at their school, which required a $40 hourly fee for computing time. They were banned from using the device after exploiting a bug that allowed them to bypass the fee, only to be later offered free computing time for finding more bugs.

Before the modern banking system, most lending resembled private credit

Before the creation of the modern banking system, the majority of loans were negotiated directly between the lender and the borrower—effectively making them private credit transactions.

How does the cocktail party effect work?

In the 1950s, British cognitive scientist Colin Cherry started to explore how we could focus our hearing on one single source, even in a noisy environment. This video animation explains the phenomenon known as the cocktail effect and how selective hearing works. Discover how our brain is on the lookout for important or personally relevant information, even as we are occupied in other discussions.

The Kennan Telegram shaped early US Cold War strategy

In 1946, diplomat George Kennan sent a long telegram from Moscow warning that the Soviet Union was inherently expansionist. His analysis laid the groundwork for the US policy of containment that defined the early Cold War.

The wild, early history of the tunnel across the English Channel

Britain and France today are connected by the Chunnel—a tunnel bored roughly 120 feet under the seabed of the notoriously choppy English Channel, which opened in 1994. The dream of integrating Britain with the rest of the continent this way began much earlier, with daring, physically impossible plans proposed as early as the 19th century. Check out the earliest plans here.

Explaining computer kernels and what makes monolithic kernels different from microkernels

A kernel is an intermediary piece of software on a device that manages the connection between software programs—the services and processes they perform to run correctly—and the available hardware resources, such as memory and computing bandwidth, including prioritizing resource allocation and managing access to specific hardware. A monolithic kernel manages all of an operating system's services, whereas a microkernel only handles essential services.

Private schools are free to experiment with teaching styles

Because they’re not beholden to national curricula, private school teachers can use different pedagogical approaches, like Harkness, which was developed at New Hampshire’s Phillips Exeter Academy. The method brings students to a large round oval table and encourages them to lead the lesson through inquiry.

Breaking down how Dickinson viewed letters as an extension of her poetry

The poet's many correspondences were dashed with playful arrangements of text, offering her pen pals surprises once they opened their envelopes. Jana Dambrogio and Daniel Starza Smith explain how Dickinson even creatively used the 19th-century security technique of letterlocking in poetic ways.

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

Superbugs evolve defenses against medication, then share them with neighbors

One reason antibiotic resistance spreads so quickly is that bacteria have multiple mechanisms allowing them to share genetic material. This short video offers a concise explanation for each of these mechanisms, and animation that helps viewers understand how antimicrobial resistance can quickly spread from one organism to another.

Why don’t we negotiate with terrorists?

Politicians in the US and the UK regularly refuse to negotiate with terrorists. Some claim that negotiating with terrorists would be inappropriate and impractical, and might encourage and legitimize terrorists around the world. But, other Western governments—including France and Spain—have negotiated with terrorist groups. So why do some governments refuse to negotiate with terrorists, while others consider it effective? This article by Chatham House breaks down the history, strategies, and arguments around negotiating with terrorists.

Elk Cloner, the first computer virus to spread in public, was written as a practical joke by Richard Skrenta, a Pittsburgh high school student.

The idea for the Federal Reserve was conceived in secret in 1910—with bankers donning duck hunt gear for disguise while traveling to a remote country club on Georgia's Jekyll Island

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.

An initial public offering or 'IPO' is the process of a private company becoming public by putting shares of the company on the stock market for purchase.

The US dollar is the most widely circulated currency in the world, and is involved in nearly 90% of global transactions

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

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 rivalry between Alexander Hamilton and Thomas Jefferson centered on federalism—the question of how much power the federal government should hold relative to the states.

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.

Memecoins are a type of cryptocurrency—a form of digital currency with a wide variety of uses—created around popular 'memes,' or viral internet jokes.

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.

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.

In 1945, Surrealist artist Salvador Dalí and legendary animator Walt Disney began collaborating on a short film that was not completed until 2003, years after both men had died.

While atoms are normally made of protons, neutrons, and electrons, exotic ones have been built with antimatter—alternate versions of normal matter that live for fractions of a second and are about a billion times as rare.

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

See how fireworks are made and learn how metals like magnesium and copper are responsible for different colors.

The story of Dollree Mapp, whose legal challenge over her 1957 conviction for possessing "obscene material" led to a major strengthening of the Fourth Amendment

Hear 50 years of iconic hip-hop samples, the genre's foundational looped tracks

See the evolution of Ebola vaccine and treatment development.

Pure water does not conduct electricity because this flow of energy requires the movement of charged particles, and water is a neutral molecule.

Fear or disgust related to clusters of holes and cracks, called trypophobia, may stem from evolutionary processes to help us avoid pathogens.

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.

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.

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