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.

In a standard deck of 52 cards, shuffling produces one of approximately 8.07 × 10⁶⁷ potential card orders—a number about as large as the number of atoms in the Milky Way.

NSF-funded research into matching algorithms improved the success of organ transplants

Investigations in game theory, including concepts focused on creating mutually beneficial partnerships—matching theory—led to the design of computer systems that efficiently matched kidney recipients and live donors, resulting in higher-quality matches. By 2019, these matching algorithms were used for multi-organ exchanges.

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.

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.

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.

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.

When modeling the fastest way to board passengers onto an airplane, research shows that random boarding is often faster than boarding in groups.

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.

Emergency room evaluations may be improved with AI algorithms

Emergency room care teams must make fast and crucial decisions. They must determine if patients need to be admitted or discharged and when to order more tests or not. Researchers have been exploring how often patients died in the week after they were sent home and evaluating how this and other aspects of emergency care decision-making could be improved with AI algorithms to assist decision-makers.

Connected technology improves infrastructure efficiency in smart cities

Through information and communication technologies, smart cities can provide enhanced public services and improved quality of life by managing traffic and dynamic safety policies. They can also promote sustainability by automating energy use and redirecting resources according to need.

In the 1950s, Alan Turing developed a mathematical model to explain why animals have stripes, spots, and other patterns based on differences in how quickly two interacting chemicals spread throughout a developing organism.

Microchips in payment cards improve security by generating unique transaction codes

Magnetic strips store unchanging data that is easily cloned, but microchips act as miniature computers that encrypt sensitive data. They also resist fraud by creating data unique to each transaction, preventing duplication.

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.

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.

Turbulence has been called the most important unsolved problem in classical physics

Despite being the most common type of fluid flow in our world, scientists have struggled to model turbulent flow accurately. Though behaving unpredictably, understanding inertia and viscosity can help determine whether turbulence will occur.

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.

Cells modify their internal spacing to improve biochemical reaction efficiencies

Studies involving microscopy and genetic engineering tools in yeast and human cells show ribosomes act as crowding agents—much like packing peanuts—and their concentrations are actively tuned to alter the rate of cellular functions. However, these concentrations and cell crowding levels vary across different tissues and cell types.

Quantum computers can simulate nature more effectively than classical computers

Ordinary computers struggle to simulate quantum fields due to entanglement, but systems built from those elements can model the complexity. Systems using particle in more than two states—qudits—have successfully modeled 2D electromagnetic fields and done so more efficiently.

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.

How the number 15 solved a longstanding math challenge

The “packing coloring” problem asks how many numbers are needed to fill an infinite grid so that identical numbers never get too close to one another. A new computer-assisted proof finds a surprisingly straightforward answer—only 15. While...

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.

When experiencing turbulence, fluid elements undergo stretching and folding

Simulations show patches of fluid particles, such as splashes of milk, bend under turbulent flow, creating curvature that grows linearly then exponentially. This accelerated deformation enhances folding and mixing faster than other methods, such as stirring or beating.

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.

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.

Grace Hopper warned against prioritizing hardware purchases in future computing

Foreseeing the rising volume of data and the increasing demand for its processing and access, she advocated that organizations first map the total flow of information they require and then choose infrastructure to support it, rather than wastefully spending on the fastest computing technology and forcing software to compensate for unnecessary hardware or incorrect data.

The 'butterfly effect' is the informal name for chaos theory

In mathematics, chaos theory involves complex systems that are highly sensitive to their initial conditions. Originally discovered when analyzing weather data, slight variations in the data input into such systems create drastically different results, despite following known physical laws.

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.

Taxi and ambulance drivers appear to have the lowest risk of dying from Alzheimer's disease out of 443 occupations, which suggests that constant real-time navigation work strengthens the hippocampus and may help protect against the disease.

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.

In 2000, the Clay Mathematics Institute placed million-dollar bounties on seven unsolved problems in mathematics—the Millennium Prize Problems—in the hopes of spurring solutions.

Microbial research suggests shifts in diverse populations may help an invasive species establish itself

In 1958, English ecologist Charles Elton suggested that diverse ecosystems should be more resistant to invasive species because gaining a foothold would be more challenging when resources are more thinly spread. However, in lab-grown microbial ecosystems with greater biodiversity, population volatility opened more ecological roles that invasive species could easily fill.

Face and neck massages improve the removal of brain cell waste products in mice

A study identified that massaging mice and monkeys' faces and necks enhanced the flow of cerebrospinal fluid. Because CSF has been shown to flush out proteins linked to Alzheimer's and Parkinson's, the research hints at non-invasive treatments to reduce the severity of these diseases.

How math whizzes exploit sportsbooks

Chris Dirkus is a professional sports bettor who approaches the hobby as a math problem, not from a fan's perspective. He focuses on mispriced odds in popular games where many fans are betting for high liquidity. He's one of a rare segment of sports bettors exploiting slow models and human mistakes.

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.)

An analysis of the logistic map, which shows how chaos can emerge from simple equations

When modeling systems such as the predator-prey cycle of an organism's population in an ecosystem, the logistic map function shows the population normally settles into an equilibrium value. However, at high reproduction and starvation rates, multiple such values arise, making it difficult to accurately model long-term population growth in some environments.

Chip technology replaced magstripes to stop easy card cloning and fraud

The magstripe on bank cards always gives the same data, making it simple to copy using a device called a grabber. In contrast, embedded chips create a unique code with every transaction, making it much harder to clone or steal card information.