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

Algorithms are instructions for accomplishing a goal and typically take the form of a step-by-step procedure. Given the conditions, these procedures can take various paths, increasing an algorithm's complexity. While traditional computer algorithms are programmed to account for all possible scenarios within a given process, machine learning systems build their own rules from data-driven patterns.

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.

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

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.

Watch how 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.

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.

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.

The origin of shortest-path algorithms and how they became optimized for navigation apps

In 1956, Dutch programmer Edsger Dijkstra spent about 20 minutes developing an algorithm to demonstrate how computers could quickly determine the shortest route between Rotterdam and Groningen. Since then, modified versions of Dijkstra's formulation comprise the processing backbone of systems such as Google Maps and Apple Maps.

Traffic flow can be improved through research into card shuffling

Card-shuffling mathematics has been applied to solving problems in biology to estimate the evolutionary distance between organisms and in computer science to determine the optimal distribution of files and folders in databases.

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.

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.

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.

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.

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.

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.

The first social media platforms date back to the late 1990s, and their algorithms were typically chronological, with entities like MySpace and Facebook feeding users content from the most recent posts to the oldest.

YouTube's recommendation algorithm relies on over 80 billion daily pieces of information

These signals include which videos a user has watched, searched for, and liked, as well as channel subscriptions and feedback selections, such as videos marked "not interested." Each user's viewing habits are compared with those of other users with similar habits, and this information is used to suggest additional content.

Facebook's algorithm chooses content to display on the News Feed based on user data

It employs machine learning to prioritize posts and ads based on user interactions, content type, and post timeliness, creating a personalized, engaging experience for each user.

20 of the most common cyberattacks

While there are dozens of different types of cyber attacks, this article explains the top 20 most common network attack examples, including phishing, whale-phishing, and spear-phishing attacks. Learn how to best protect yourself.

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.

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.

Advance genetic research by playing these scientific video games

Computers produce so much information that researchers can’t properly analyze all the data produced, and the overload can also lead computers to make mistakes. Researchers are increasingly turning to citizen scientists—members of the public who are willing to volunteer—to help them make sense of data when computers can’t. This article details a few of the ways you can contribute to genetics research by playing video games.

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.

Artificial intelligence may further enhance smart city data analysis

Identifying patterns within systems in the Internet of Things may enable AI tools to make informed decisions regarding transportation, safety, and sustainability without human intervention. However, such tools will also need to successfully address concerns about privacy, digital equity, and algorithmic bias.

Why Google Search's ranking system combines filters, signals, and machine learning layers

Rather than static rankings, dynamic tools continually shift search results in real time. These include Twiddlers, which adjust ranking positions based on document traits and search context, and FreshnessNode, which reshuffles top results to prioritize timely informational content.

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.

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.

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.

Modern antivirus software searches for malicious behavior alongside malicious code

The first viral infections were identified by comparing the computer code of programs and files with a database of known virus codes, a method known as signature detection. The ongoing creation of new malware made databases continuously outdated, leading to the development of systems that detect patterns consistent with known viral activity.

Social media platforms benefit not just from ensuring they have satisfied users, but also from the personal data they scoop up and can then sell to online advertisers.

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.

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.

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.

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.

What we learned about Google

Google processes over 8.5 billion searches every day—more than the number of people on Earth. This short breakdown covers how the company evolved from a Stanford research project into a global tech leader, with products like YouTube, Gmail, and Android reaching billions worldwide.

Explore over 30,000 Olympiad-level math problems from around the world.

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.