There are over 43 quintillion possible configurations for a Rubik's Cube, but it takes no more than 20 moves—known as God's number—to solve each.

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.

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...

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 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.

Google used its 53-qubit processor on an extremely difficult problem for traditional computers to simulate to showcase quantum supremacy. IBM later challenged Google’s claim by arguing that its Summit supercomputer could solve the same problem in just 2.5 days using a more efficient method.

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.

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.

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...

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.

Unlike regular computers, where each bit is either 0 or 1, quantum computers use qubits, which can simultaneously be both—allowing for massive parallel processing power. Google’s quantum processor once solved a problem in seconds that would have taken a supercomputer 47 years.

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 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.

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.

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.

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 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.

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.

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.

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.

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.

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.

It's a common technique among expert mathematicians, where thinkers rely on intuition, blurry perceptions and subconscious work—no writing, no formulas. The state is distinct from daydreaming, and often relies on sudden illuminations stemming from extended periods of subconscious reflection.

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.

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.

Using settings selected from a series of rotors and a plugboard that let operators swap letters with any of their choosing, the machine lit up the output letter for each letter typed. While this system could generate messages requiring any of 150 quintillion potential keys, the machine's reflector never encrypted a letter as itself, providing an entry point for exploiting the system.

In 1989, Ivan Nikolić and Goran Arsović played a marathon 269-move match in Belgrade. Lasting more than 20 hours, the game ended in a draw.

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.

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.

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.

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.