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.

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.

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 odds of a perfect March Madness bracket are worse than finding one specific grain of sand on Earth

With 63 games to predict, random guessing produces odds of 1 in 9.2 quintillion. Even an informed picker who gets 67% of games right faces odds of about 1 in 120 billion, meaning if every American filled out a unique bracket, we'd expect a perfect one in roughly 366 years.

The arrow of time—the concept that time only moves in the forward direction—is thought to result from the universe progressing toward greater disorder, or entropy.

Lining up every microbe on Earth would stretch to about 105,000 light-years

There are about 10²⁷ such organisms on the planet, many of which are adapted to produce energy through uncommon reactions in unconventional environments, such as within rocks or near volcanoes on the ocean floor. Studies of these organisms have reframed astrobiologists' search for life beyond Earth by broadening the parameters under which life can exist.

Modern physics suggests that many universes with different physical laws could exist

Physicists suggest that quantum fluctuations in the early universe could have given rise to these universes. Ancient Greek philosophers like Chrysippus proposed a version of the multiverse over 2,000 years ago—millennia before its adoption into various theoretical frameworks today.

There may be 74,963 kinds of ice, resulting from water molecules rearranging themselves

The theoretical limit greatly expands the known types of ice, with type Iₕ being the most common on Earth and forming hexagonal crystals. The extreme environments of planets like Uranus and Neptune can create a variety of ice with unique structures and properties, as these conditions can reshape these crystals into new geometries.

The most bizarre numbers in the universe

Even for math-y types, some numbers are incomprehensible. This article dives into several kinds of numbers more complicated than even irrational numbers with endless decimals like "pi" or Euler's number: Noncomputable numbers. Read the bizarre...

Scientists are experimenting with ways to probe the multiverse theory

Researchers are simulating vacuum bubbles—the theorized starting points of universes—using quantum computers, digital models, and exotic lab setups to study how they form, expand, and possibly collide. One experiment aims to "blow" artificial universe-like bubbles inside ultra-cold quantum gases, potentially capturing real-time glimpses of cosmic birth processes in a lab.

Chess is played by an estimated 600 million people worldwide

Chess remains one of the most popular games in history, with roughly 600 million players across the globe. The game thrives casually in homes, schools, and parks, while also sustaining robust online communities and professional tournaments.

More than 40 quintillion black holes are estimated to exist in the universe, including about 100 million in the Milky Way, each with masses up to hundreds of times that of the sun.

The entire observable universe in one map

Scientists believe we’ve only discovered about 5% of the universe. Here’s a map of what we’ve found so far, visualized using a log scale.

Even in an infinite universe, its limited age prevents a sky full of starlight

Olbers' paradox asks why the sky would ever appear dark if the universe is full of stars in all directions emitting light everywhere. Light from the farthest stars requires more time to reach our skies than the universe's age.

Antimatter's rarity across the cosmos is one of the biggest problems in modern physics because the high-energy environment of the early universe should have produced equal amounts of matter and antimatter.

Research suggests that about 1% of all matter in the universe is locked inside black holes, millions of which are likely to lurk undetected near us in space.

Explore a visualization of the scale of objects across the universe, from an astronaut and planets to stars and galaxy clusters, in this interactive adventure.

How many galaxies are there? (Hint: a lot)

The universe is considered by some to be infinite, while others find comfort in the fact that it may have an end. Click for more.

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...

Light takes approximately eight minutes to travel from the sun's surface to Earth, but it takes thousands of years to reach the star's surface from its core—a distance more than 200 times shorter.

The observable universe has a mass of 100 sexdecillion kilograms

The amount of visible matter in the universe is most accurately determined by measuring the cosmic microwave background. Quantities of dark matter and dark energy are calculated through the observed bending of light around galaxies and the expansion of the universe, respectively.

Within quantum physics, the order of events across time may not follow causality

Although time is considered a fixed, ordered mapping of events, where the past affects the future, quantum superposition breaks down causality, suggesting that future events can occur simultaneously with past ones. Within the quantum model, the notion of cause and effect is not a fundamental feature of our universe.

You are 65,000 times more likely to be struck by lightning than to be hit by space trash

In 2023, about 1,500 pieces of space junk fell to Earth, with most consisting of payload fragmentation debris. The vast majority that falls back to Earth burns up before reaching the surface, making it three times less likely to be struck by space trash than by a meteorite.

There may be as many as 300 million potentially habitable planets in our galaxy

The estimate comes from a study using data from the Kepler space telescope—a project aimed at finding exoplanets—and considers exoplanets similar in size to Earth around sun-like stars. These have a greater potential to possess liquid water.

About 85% of the matter in the universe is dark matter—an invisible substance that only interacts with its surroundings through gravity.

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.

Universes with stronger dark energy may be more common than ours

Research shows that while universes with slightly weaker dark energy form stars more efficiently, universes with stronger dark energy are statistically more common and can still support star formation. This challenges the anthropic logic that our universe must have ideal conditions for life because we exist to observe them.

Watch what would happen if you literally had all the money in the world.

The universe may have been reborn from a state of emptiness

Some physicists propose the universe might be the latest in an eternal cycle of universes, each emerging from the empty remains of the one before. This model is inspired partly by Norse and Egyptian myth, suggesting the universe is a cosmic ouroboros—a self-consuming serpent representing an eternal return.

Ring galaxies, the rarest kind in the universe

Galaxies come in different sizes, but when it comes to shapes there are just four kinds: spiral, elliptical, irregular, and the rarest kind, ring. Ring galaxies only form in the event of a small galaxy passing through a large one, but there's more to them that that. This page explores these rare and beautiful heavenly bodies.

The cosmic dark ages: before stars existed

The theories behind the Big Bang suggest the process of the universe beginning to the creation of stable, neutral atoms took just half a million years. But the transition from such atoms to star formation took surprisingly much longer, upwards of 100 million years. Why? This deep dive explores the science behind the unique physical composition of the so-called cosmic dark ages.

Because some models of the universe do not incorporate time, it may be an emergent property born from our limited perception of the universe, rather than a fundamental property of reality.

What happens to golf balls after they're used?

With over 1 billion golf balls produced annually, an estimated 300 million to 1.5 billion are lost worldwide. On average, thousands of balls are left behind on each course, often ending up in ponds, forests, and beaches. While many golf courses recover and reuse some of these balls, studies suggest countless remain unretrieved.

View the composition of the universe, dominated by dark energy and dark matter

About 95% of the observable universe is made of substances whose composition is unknown, but most of what remains (4%) is in the form of clouds of hydrogen and helium, followed by gases and plasma within stars (0.5%) and neutrinos created in nuclear reactions (0.3%).

The Standard Model reveals an underlying organization to the universe

Using the framework of quantum field theory, it structures all known particles into 12 matter particles, alongside five particles that carry three of the four fundamental forces. Although remarkably precise and predictive, it cannot yet explain gravity, dark matter, or dark energy.

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.

The universe might have emerged from a quantum fluctuation—not absolute nothing

Traditional physics breaks down at the moment of the Big Bang, but quantum theory suggests that “empty” space is never truly empty. In 1973, physicist Edward Tryon proposed that our universe began from a quantum energy blip in the quantum vacuum.

View a timeline of the universe's major events, according to the Big Bang model.

The heat death of the universe will mark the perceptive end of time

Under this scenario, all matter and energy will be scattered as far out as possible, with no stars left to produce measurable light between objects. With no way of observing changes or increasing the disorder of the universe further, events could not be distinguished from one another, and time would lose meaning.

After the Big Bang, the universe's current composition was built in stages

The Big Bang theory describes the universe beginning 13.7 billion years ago as an ultradense point, followed by stages, like the radiation- and matter-dominated eras. Each era was responsible for a unique element, such as the cosmic microwave background and atomic nuclei.

From the Big Bang to present—a timeline

A timeline for everything, from the Big Bang to the beginnings of life on Earth. This article lays out, in spans of billions of years, what was happening in the universe as it became the universe. Starting from the Planck era, the earliest known meaningful time, to the probable "Big Crunch" 30 billion years from now, see how the universe has existed and persisted.

As of 2025, the Standard Model has at least five unresolved problems

Among the issues with the most successful theory of the universe at subatomic scales is its inability to explain the extreme imbalance observed between visible matter and antimatter, since both should be roughly equal. The Standard Model also omits gravity and cannot account for the observed rate of cosmic expansion.

Magic: the Gathering was inspired by baseball cards

Richard Garfield originally pitched a game publisher on a more complex game about programming robots, but he was told that they were looking for something less expensive and more portable. Inspired by the way baseball cards were collected and traded, he came up with the idea for Magic: the Gathering, which gave players packets of random cards, effectively pieces of the whole game, rather than the entire deck.

As of 2022, scientists estimate that 117 billion people have been born on Earth

Although no demographic data exist for more than 99% of the time humans have existed, this value can be estimated by tracking approximate population sizes over different periods and the birth rates within those periods. In 2022, about 6.8% of humans that have ever been born were alive.

Time disappears when encompassing all quantum configurations across the universe

The Wheeler-DeWitt equation, a modified version of the Schödinger equation—the formula that describes the evolution of the quantum configuration of a system—describes the quantum state of space-time across the universe. The transformation causes the variable of time to disappear, suggesting it is not a fundamental, physical parameter of the cosmos.

If a sheet of standard printer paper could be folded 42 times, it would have the same thickness as the distance from the Earth to the moon.

Infinity can come in different sizes and be ordered by these sizes

Russian mathematician Georg Cantor demonstrated that certain sets of numbers (e.g., the natural numbers) form countable infinities, while others cannot be counted (e.g., the real numbers) and are therefore uncountable, representing larger versions of infinity. Through the axiom of choice, German mathematician Ernst Zermelo proved this concept of ordering infinities.

Due to dark energy, the universe is expected to end as a dark, sparse place

While the sun is expected to continue shining for another five billion years, the expansion of the universe will cause nearby stars and galaxies to become ever more distant, until they are too far to observe. Once the last old, red, dim stars cool into darkness after trillions of years, the universe will settle into a state of eternal, dark emptiness.

'Scorigami' attempts to chart every NFL game score

The rules of the sport set bounds on possible final outcomes, so this adept statistician mined some fascinating takeaways. Some scores are impossible (like 5 to 1) and some are more common (like 20-17, occurring over 300 times since 1944). Watch for a deluge of numbers.

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.

A scale of the universe, from atoms to cosmos

Can you really appreciate just how small protons are, or how massive the universe is? To attempt to grasp it, watch this short video which zooms out from a young woman in California to the very limits of the cosmos using established scales. Then, dive deep into the atoms of her white blood cells for a fully-rounded effect.