Mathematicians often solve problems using wordless mental processes

How a brain injury created a mathematical mind

In 2002, two men savagely attacked Jason Padgett outside a karaoke bar, leaving him with a severe concussion--and turning Padgett into a mathematical genius.

What is the brain up to when the mind wanders?

As you stare into the distance while washing your home's seemingly never-ending pile of dishes, the brain activates its default mode network. This collection of "task-negative" brain regions associated with memory, reward, action consideration, and prediction alight with activity when humans mentally turn inward, possibly giving rise to the brain's ability to wander and humans' ability to construct internal narratives about the world.

Mathematical breakthroughs influenced Shakespeare’s stories

New ideas in math were transforming Europe at the time Shakespeare penned his plays, including newly popular conceptions of zero via philosophers Descartes and Leibniz.

How metaphors shape the way we think

A metaphor is often viewed as a form of art, deployed only in special circumstances to help an audience grasp something complex or unique. But metaphors are far more fundamental than that, shaping much of how we think about our relationship to others and the world. This article explores how a focus on the metaphors we use can clarify and strengthen our thinking. Learn more here.

The sophisticated math jokes of 'The Simpsons'

"The Simpsons" has always been a slyly sophisticated show and has featured more than a few references to complex mathematical concepts. That's largely due to its writers' room, which has featured more than one writer who studied math before transitioning to comedy.

The science of optical illusions

The human brain has developed cognitive shortcuts to help us navigate in a world where our visual senses are constantly bombarded of information. But these shortcuts can also be exploited, tricking the brain into telling us something is happening when it really isn't. This short video unpacks the neuroscience behind some of the most common (but perplexing) optical illusions.

Researchers believe the brain consolidates memories, processes emotions, and plans for the future during dream states

Binary mathematics represented as switches allows silicon rocks to do math

Each switch is assigned a zero or a one based on whether it is open or closed, and logic gates are built from these switches that let the system perform mathematical operations. Modern software builds upon these operations to perform increasingly complex tasks.

A "no math" primer on quantum mechanics

Quantum mechanics may not immediately grasped, but it can be slowly understood through the experiments and discussions offered here by writer Dr. Miguel F. Morales. A professor of physics at the University of Washington in Seattle, Dr. Morales makes understanding the basics of quantum mechanics fun with a promised "no math" approach.

'Imagination is more important than knowledge. For knowledge is limited, whereas imagination embraces the entire world.'

- Albert Einstein

How your subconscious influences your decisions

How much of your desires and daily choices are truly yours? One of the most effective ways to influence someone's subconscious is when they're asleep. To study this possibility, researchers trained participants to be able to dream lucidly, a phenomenon that occurs when a dreamer knows they're dreaming.

Explore over 30,000 Olympiad-level math problems

Users can browse questions from 47 countries and 17 languages, sorted by topic across categories that include algebra, geometry, discrete mathematics, and number theory. Each problem is accompanied by at least one solution, with both authored in LaTeX that can be copied over to other platforms.

Some people really cannot imagine. Literally.

There are many people who are astonished to discover that their complete lack of ability to picture visual imagery is different from the norm.

Ray Dalio credits much of his success to his transcendental meditation practice

Dalio took up transcendental meditation after learning that The Beatles practiced it on a trip to India in 1968. He says the practice allows him to clear his mind, be more creative, and unlock his subconscious.

Within mathematics, some infinities are bigger than others

While the concept of infinity refers to a countless set of items, these infinite sets can be compared to one another by matching an item from one set to an item in another, one by one. This analysis shows that certain sets must be larger than others because some infinite sets have leftover, unmatched items.

A 14-year-old "human calculator" shatters six mathematical world records in one day

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.

Jazz musicians use different melodic approaches to produce improvised performances

While jazz musicians are known for their improvisational skills, they rely on years of training and a complex understanding of compositions to inform their improvised solos, using a song's structure and chords to make their in-the-moment choices. Although jazz artists could, in theory, play whatever they wanted, musicians often employ common melodic approaches—such as scalar improvisation and arpeggios—to generate solos.

AI systems identify patterns involving physics and time through 'world models'

These realistic virtual environments, such as driving simulations seen in video games, allow these systems to "learn" properties about reality beyond what can be captured in samples of text, images, and videos. Training AI in these simulated environments can help develop "physical AI" for automated robotic systems. (Some readers may experience a paywall.)

How legendary artists overcame creative block

For most artists, creative block—the unfortunate experience when new ideas suddenly disappear—is inevitable. This Artsy article looks at six artists (including Picasso, Monet, and O’Keeffe) who dealt with creative block and overcame it by experimenting with new media, moving to a new place, or by sheer willpower. It also highlights one artist, Chuck Close, who claims that he never dealt with creative block because he simply viewed his artistic practice as any other job.

Why the nature of consciousness is such a difficult problem

David Chalmers is one of the leading philosophers of consciousness. In this video, he outlines some of the major questions in this field, including the "hard problem of consciousness," which seeks to find neural correlate for every conscious experience.

Clever Hans was a 1900s horse that was believed to be able to solve math equations, tell time, and read and comprehend German, until a psychology student discovered how he got his answers.

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.

Some art critics believe that Liminalism, a form of art exploring the uncanny yet familiar, defines our present moment

While analyzing images of abandoned malls or empty hallways, art historians and critics argue that this style captures the feelings of this moment in time. Liminalism, they propose, expresses prominent themes in our age like anonymity, alienation, and anxiety.

Problem solving, problem recognition, and learning ability makes up intelligence

Psychologists have several theories from which the concept of intelligence is explained, including general and multiple intelligences. Although IQ is used to quantify intelligence, issues like its cultural biases have spurred debate.

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.

Japanese artist Tatsuo Horiuchi creates masterpieces using Microsoft Excel

Upon retiring, he wanted to get into art, but found the materials to be expensive. Since 2000, he has created art pieces using the line tool and other features the software provides before printing and taping together various spreadsheets that make up a completed work.

Short-term memory is a temporary space for limited, newly learned information

Short-term memory stores info for 15 to 30 seconds and is managed by the prefrontal cortex. Though they're often confused, short-term memory stores information, while working memory actively uses it to help you reason, learn, and solve problems, such as a math equation.

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.

Chaos theory—informally known as the butterfly effect—is the reason why weather forecasts are presented with probabilities rather than certainties.

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.

According to the physics of black holes, our 4D reality may be a hologram—a projection of information coded on a 2D surface on the edge of the universe.

Alzheimer's can lead to brain shrinkage, with an average of around 2% of volume reduction per year

Browse a detailed visual analysis of over 200,000 similes—comparisons that often use 'like' or 'as'—from popular fiction to see how frequently writers the same idiomatic expressions.

Use this calculator to find the dollar value of your mental load, from meal planning to coordinating after-school care for your children.

While atoms are normally made of protons, neutrons, and electrons, exotic ones have been built with antimatter—alternate versions of normal matter that live for fractions of a second and are about a billion times as rare.

Apeirophobia is an overwhelming fear of living forever, perhaps stemming from the brain's inability to conceptualize an infinite life.

Gerrymandering works through two techniques: cracking opposing voters across districts to dilute their power, and packing them into a few to waste their votes in lopsided majorities.

As of 2025, the most cited papers in science include a review of graphene, methods to improve image recognition, streamlining electron density calculations, and optimizing protein studies.

Art theft is the third-largest source of criminal revenues worldwide, thanks in part to the subjective nature of valuing a work of art.

SpongeBob exemplifies Aristotle's philosophy for living well because he understands that happiness doesn't come from external factors like money, recognition, or power.

Memecoins are a type of cryptocurrency—a form of digital currency with a wide variety of uses—created around popular 'memes,' or viral internet jokes.

A Yale student wrote a profound essay about the consulting industry's influence on elite college students that was published in a book of her writing after she died in a post-graduation car accident.

In 1945, Surrealist artist Salvador Dalí and legendary animator Walt Disney began collaborating on a short film that was not completed until 2003, years after both men had died.

The idea for the Federal Reserve was conceived in secret in 1910—with bankers donning duck hunt gear for disguise while traveling to a remote country club on Georgia's Jekyll Island

The concept of phantom limbs, the perception that amputated limbs are still present, dates back to a French military surgeon in the 16th century.

Legendary architect Frank Lloyd Wright designed the SC Johnson headquarters in Wisconsin, aiming to make a cathedral-like workplace

Explore the animals that populate the depths of the ocean, from fish and coral in the first few hundred feet, all the way down to the bottom of the Mariana Trench.

Watch this video that uses Lego bricks to explain how venture capital works.

NBA superstar Victor Wembanyama spent the 2025 summer training with monks in central China to enhance his body and mind.

'Silent' fireworks have gained more interest in recent years as a quieter celebratory option.