Every Rubik's Cube can be solved by repeating the exact sequence of moves used to scramble it a finite number of times.

The Rubik's Cube is the most popular puzzle toy in the world, with over 350 million sold since its invention in 1975. Originally created as a tool to teach three-dimensional movement, the colorful problem-solving game skyrocketed in popularity, spawning speedcubing competitions and becoming a fixture of global toy culture.

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.

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...

The solution time of 0.103 seconds is a Guinness World Record. A robot created by Mitsubishi Electric engineers held the previous record of 0.305 seconds.

He broke a world record, completing the task in the sky in just 23.333 seconds.

As of 2025, many figure skaters feature jumps with four spins in their routines by achieving rotation rates of 400 RPM over 20 inches off the ground. By increasing one's rotation rate to about 430 RPM or jumping closer to three feet off the ground—a height reached by NBA players—five spins are possible.

Unlike traditional crystals—whose atomic structures cause them to look identical no matter how you look at them in space—time crystals exhibit this behavior through time, where the motion of atoms will bring them to the same positions relative to one another regularly.

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...

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.

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 Maya numerical system used dots for 1, bars for 5, and a shell symbol for zero. This interactive resource lets users practice counting with the Maya base-20 system using the same symbols once common in the Yucatán.

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.

Chess begins with two players facing off on a checkered 64-square board. Each controls 16 pieces—king, queen, rooks, bishops, knights, and pawns—with the goal of checkmating the opposing king.

A sofa with the largest possible area that can make a 90-degree turn is known as Gerver's sofa, named after the mathematician who determined the shape in 1992. In 2025, a 119-page paper provided the proof confirming this shape.

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.

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.

In one of the world's most classic memory games, flip over cards and find the eight matching pairs. Accuracy is rewarded, so try not to guess too much.

If the genome is made up of microscopic chromosomes, how do scientists actually sequence it? Here's a 5-minute video explaining one of the most common processes.

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.

A teenage prodigy from Maharashtra, India named Aaryan Shukla set the record for the fastest time to mentally add 50 five-digit numbers. He did so in just 25.19 seconds–roughly equivalent to one addition every 0.5 seconds. The math whiz said he practices calculations for around five to six hours a day.

Repeated visual cues like shapes or lines derive from the brain's innate compulsion to identify faces, places, bodies, and more. With repeated shapes, the brain seeks out resolution to the subtle variations between them. See examples in art and music.

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.

Although costly and less efficient for simpler tasks, as of 2025, DNA could hold 455 exabytes of data with near limitless parallel computation potential in small data centers. Every movie ever made would fit inside the volume of a single sugar cube.

Each stage plays a key role in memory, repair, restoration, and other key biological functions. The full cycle generally proceeds from light sleep and deep rest into vivid REM dreaming, which repeats between three and five times nightly.

Resulting from a mutation on the X chromosome, the rare genetic condition causes individuals to possess an additional type of photoreceptor cell, typically sensitive to the orange range, located between the standard red and green cones. This enables the perception of approximately 100 million colors.

This form of asymmetric cryptography uses mathematical functions that rely on the product of two large prime numbers. Because traditional computers struggle to factor such products, obtaining the private keys needed to decrypt messages becomes effectively impossible. This security can be reinforced with larger prime numbers, though this makes encryption more computationally taxing.

In 1994, Peter Shor introduced an algorithm that showed a quantum computer could efficiently factor the product of two very large prime numbers, undermining the mathematics that makes RSA so secure. While using larger keys can delay the decryption time of quantum computers, this solution increases the time it takes to encrypt data, which may become impractical.

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.

There are four bases—adenine, thymine, cytosine, and guanine—which keep the two strands of DNA connected via chemical bonds between them. Connections between thymine and adenine require two hydrogen bonds, while those between cytosine and guanine need three hydrogen bonds. These differences in bond number prevent non-complementary pairings.