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

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.

Algorithms can be designed to train themselves and self-improve without human input, to the point where the optimized code is too complex for programmers to understand.

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.

Bias can manifest in algorithmic decisions because the program follows rules that may have been written by individuals unaware of their own biases.

Machine learning lets computers learn from data instead of relying on programming

ML is a core part of artificial intelligence and is foundational to applications like chatbots, fraud detection, and self-driving cars. Businesses are also adopting it to improve efficiency and identify patterns in data, though the latter may be inaccurate.

Computational and biological systems share fundamental principles, like randomness

Proposed by Alan Turing and John von Neumann, the concept originates from how DNA and computers run by executing encoded instructions in parallel. The advent of AI and the temperature parameter has seen neural networks mimic the randomness of protein encoding.

Machine learning and deep learning are successive subsets of artificial intelligence

ML allows systems to learn from data, while DL uses complex neural networks to analyze large amounts of unstructured data. Neural networks enable capabilities like image and speech recognition through their use of algorithms to identify patterns in data.

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.

AI vs. machine learning vs. deep learning

Machine learning is best understood with visuals. A collection of the best 9 images, videos and flowcharts that explain what it is and how it works.

Logic gates—digital versions of conditional statements, such as 'if 0 and 1, then 1'—are specialized circuits that combine multiple digital signals, like the binary code representing numbers, into a single output, thereby allowing machines to perform math.

All computers are defined by their ability to input, store, process, and output data

From wooden machines to wearable tech, computers have changed a lot in appearance, but they all still perform the same essential tasks. Early computers were made of wood and metal—some were so big that they filled entire rooms just to solve simple math problems.

Visualize how data becomes organized through a variety of sorting algorithms

This interactive shows how different algorithms shift elements in a randomized set to order them from smallest to largest. By comparing the different procedures and their corresponding functions, users can explore how runtimes vary across algorithms that complete the same task.

Turing machines consist of an infinite tape, a read-write mechanism and instructions

Based on the information the mechanism reads on the tape, the machine follows the applicable instruction (e.g., if you read a 1, write a 0) and may proceed to the next cell of data. Given enough time and memory, Alan Turing proposed such a machine could perform any computation.

Understanding how Claude Code and other AI coding agents function

Under human oversight, a supervising large language model interprets user tasks and delegates work to subordinate LLMs, which can generate code, fix bugs, and run tests, often most effectively for proofs of concept. Incremental backups and versioning are crucial when using such agents, which can lose details during their work as a result of compressing context history to work around memory limitations.

Compression algorithms can reduce file sizes without losing quality by consolidating repeated data or replacing blocks of code with more compact representations, thereby reducing storage demands and improving data transmission rates.

Through prompt injection attacks, bad actors provide deceptive prompts to generative AI systems in order to manipulate their outputs and acquire sensitive data.

With many smaller computing cores, graphics processing units process many identical tasks in parallel, whereas central processing units have fewer, larger cores built to handle a wide variety of more complex tasks sequentially.

How algorithmic redistricting works

Computational methods are convincing a number of judges that some state district maps are drawn illegally. Here's a simple overview of how it works.

Scientists increasingly can't predict what AI will do

Most AI systems are so-called "black box" models, where we only see inputs and outputs while the inner workings remain obscure. This piece, written prior to the launch of ChatGPT, cautions developers to know why and how a system produces its results, and not to sacrifice explainability for accuracy.

Unlike generative AI systems, such as chatbots that do not take follow-up actions after generating their output, agentic AI systems proactively take steps to achieve goals without continuous user input.

The internet explained at five levels of difficulty, from protocols to internet flattening

Resembling a roadway with traffic laws that all cars must follow, the internet is the hardware that connects a source to a destination, and these connections must follow specific software rules. Although data had to travel through about 10 networks to reach a destination in the past, data centers increasingly consolidate traffic, just as a highway does for cars, to improve data speeds.

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.

Anthropic's interpretability team discusses how AI models' thinking mimics biology

Just as humans engage in complex behaviors to survive and reproduce, teams of experts in neuroscience, virology, mathematics, and other disciplines argue that large language models develop complex mechanisms to achieve their goals. These mechanisms can be manipulated to assess how they modify outputs—much like stimulating individual neurons—to uncover how LLMs "think."

When you complete a CAPTCHA on a website to prove you are human, you may be unknowingly training algorithms for self-driving cars, whose systems require training data to help identify crosswalks, bicycles, and other outdoor objects.

Create your own cipher by combining mathematical operations and encryption protocols

This tool allows users to build an encryption workflow in which the output of one customizable function becomes the input to another, thereby creating undiscovered methods for obscuring information via a series of ciphers.

A brief history of artificial intelligence

The concept of artificial intelligence and what it may mean for humanity has evolved as computer technologies have grown increasingly powerful through the decades. Beginning with the first (massive) computers in the 1940s, scientists have sought to make the machines as intelligent as humans. But it wasn't until computing power made exponential gains have computers begun to imitate human behavior.

Creating malware requires more than knowledge of programming languages

Because computer viruses, worms, and other malicious software reside within a computer's operating system, which manages computer hardware and software, cybercriminals writing effective malicious code must understand how the OS manages input and output, permissions, memory, etc. Knowledge of credentials and network access also helps create malware that easily spreads.

What does it mean for AI to "understand" something?

This Quanta article discusses how programmers are working to create a reliable test for the depth and extent of the knowledge of machines. What does AI know and how does it know it, if it knows anything at all? There's been progress, but it hasn't been easy. Even humans can still be fooled some of the time.

Learn how the algorithms behind Tinder, Bumble, Hinge, and other dating apps work

Formerly based on the Elo rating system, which ranks chess players, the Tinder algorithm is built on user data, with more time spent on the app providing more data on user preferences from which to customize potential matches. OkCupid's match percentage algorithm relies on overlaps in users' search preferences and responses to a subset of over 4,000 questions.

Smart pricing algorithms can unintentionally work together to raise prices

Researchers have found that, through trial and error, algorithms designed to adjust prices based on market data can learn to mimic price-fixing tactics, even without explicit programming to do so. Over time, they "learn" that it is more profitable to avoid price wars and keep prices high when competitors lower prices.

Different types of malware are categorized by how they spread or operate

Computer viruses require user interaction to execute a file and spread, whereas worms can self-replicate across systems without human intervention. Ransomware locks systems until a key is provided, spyware tracks and reports user activity to a third party, and trojans disguise various types of malware as legitimate software.

A visual guide to how bitcoin transactions work and rely on cryptography

The "crypto-" in cryptocurrencies like bitcoin refers to the mathematical functions that generate pairs of public and private keys and encrypt data in blocks. When combined, these systems secure transactions on the network, verify digital asset and token transfers, and contribute to end-user anonymity.

Explore interactive simulations of strange attractors, the graphs that help visualize chaos

Although simple, linear equations reach an explicit value for a given input, such as *f(x) \= x* + 1 equaling 4 when *x* equals 3, some chaotic, nonlinear systems tend to evolve towards multiple values simultaneously. These simulations allow users to observe the unusual mathematical artifacts created by systems as their outputs evolve toward these distinct values.

What are neural networks and why do they matter?

Learn how a neural network works, why it matters, and how it can be trained to recognize patterns, classify data, and forecast future events.

LLMs are the backbone of AI tools that process and generate natural language

Large language models identify patterns in massive datasets of books, code, and unlabeled text from which to generate coherent responses. GPT-3 was trained on about 45 terabytes of data and uses 175 billion parameters—each parameter being a value the model adjusts as it learns.

LLMs explained simply and quickly

Large language models generate responses by predicting one token at a time, based on patterns they’ve learned from massive datasets. This explainer covers their core components: data, architecture, training, and how transformer models use context to simulate conversation.

Dynamic pricing algorithms allow online businesses or box stores with electronic price tags to change prices in real time based on supply, demand, time, location, and competitor prices.

Computer systems create artificial voices by stitching together phonemes—individual sounds that make up speech, such as 't,' 'long a,' and 'k' to say 'take.'

How generative AI differs from machine learning

Compared to machine learning - which is sort of like teaching a toddler how to recognize what a dog looks like by showing them images of one - generative AI is like teaching that same child how to actually draw a dog. Unlike machine learning, generative AI can actually generate. Read this article for a more in-depth comparison between these two types of artificial intelligence.

An overview of Linux, from the foundational program to its related operating systems

The Linux kernel, which bridges hardware and software, serves as the basis for many fully customizable operating systems, whose components can be modified or removed to optimize performance or reduce bloat on devices with limited resources. This has made these OSes useful for low-power devices like smart thermostats, as well as for powerful supercomputers that require computational efficiency.

Quantum computers harness weird physics to explore unsolvable problems

Classical computers manipulate bits as either 0 or 1, but quantum computers use qubits to hold combinations of both, enabling new algorithms. This new approach could one day help with breakthroughs in medicine, chemistry, and AI.

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.

The AI that creates any picture you want and how it works

Since January 2021, advances in AI research produced a plethora of deep-learning models capable of generating original images from simple text prompts. Researchers at OpenAI, Google, Facebook, and others have developed yet to be released text-to-image tools, and similar models have proliferated online. This video is a primer on how we got here, how the technology works, and its implications.

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.

Malware has transitioned from notoriety-driven to profit- and data-driven

Many of the first researchers and hobbyists who created viruses and worms showed a natural curiosity in experimenting with and designing such software to make a name for themselves and advance the field of computer science. In the future, AI-augmented malware may adapt in real-time or design enhanced cryptojackers, infostealers, and ransomware for cybercriminals.

As occurred during the 2026 hack of an AI platform by OpenAI, agentic AI may exploit a system vulnerability to access sensitive data if that information enables it to complete its assigned task.

Graphics processing units, which process large amounts of data in parallel, have become the foundational hardware for AI systems that rely on hardware capable of processing millions of text parameters simultaneously.

Transformer architecture can recognize and predict patterns in language

The underlying software powering text generation in AI tools associates each word or subword—called a token—with a set of values corresponding to how often it appears near other tokens. By recognizing these associations in prompts, the LLM can infer meaning.

A simple explanation of semiconductors

Semiconductor chips are electronic devices that store and process information. Today they can contain billions of microscopic switches on a chip smaller than a fingernail. The article provides a quick overview of how the devices work and how they've provided the backbone of the computer age.

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.