To develop general relativity, Einstein relied on his college friend, Marcel Grossman

Mathematician David Hilbert developed general relativity equations before Einstein

Although working independently of one another, the two exchanged correspondence in the lead up to November 1915, when Hilbert submitted their gravitational field equations five days before Einstein presented their work. An error in Hilbert's formulation and its nonpublication until March 1916 would leave credit for general relativity to Einstein.

Explore Albert Einstein's Zürich notebook and review his notes on relativity

Within the pages are calculations, sketches and his first attempts at deriving what would be the field equations for gravity. It also documents some dead ends and the difficulties Einstein encountered as he describes part of the mathematics of what would become general relativity, describing it as "too involved."

The general theory of relativity defines gravity as the curvature of spacetime

The breakthrough that redefined Isaac Newton's picture of gravity came when Albert Einstein realized that freely falling is indistinguishable from weightlessness, leading him to the principle of equivalence between gravity and acceleration. His prediction that gravity bends light was confirmed in 1919 during a solar eclipse.

Visualizing Einstein's special relativity

Before Einstein developed his theory of general relativity, he worked out what is known as special relativity—or why time is experienced different for different observers. The breakthrough rests on his theory that light travels at a constant...

Expanding special relativity to accelerated motion led to general relativity

The specialized theory postulates the speed of light is the same for all observers and the laws of physics are identical in all settings where velocity is constant. These established the concept of spacetime, whose flexibility became even greater when used to explain gravity.

Einstein created a mathematical term for anti-gravity to keep the universe static

General relativity predicted that the gravity of all the matter in the universe would cause it to collapse, contradicting the belief at the time that the universe was constant and unchanging. Albert Einstein added the cosmological constant to his equations, which acted like anti-gravity, to "fix" his math.

Explore a visualization of curved spacetime under general relativity

While depictions involving bends in elastic fabrics are common to illustrate gravity, they are circular representations that rely on gravity in the real world to depict gravity in the model. The river model instead shows how bends in spacetime convert speed through time into speed through space, producing acceleration.

A 1919 eclipse validated general relativity and made Albert Einstein a celebrity

According to the theory, starlight should deflect around massive objects due to the warping of spacetime light travels through on its way to Earth. Comparing the locations of stars behind the Sun during the eclipse with their positions at night showed deflections that popularized Einstein's model.

How neutron stars serve as laboratories for testing Einstein's theory of gravity

Data from a 16-year study of an orbiting pair of spinning neutron stars showed that measurements of gravitational wave energy and the bending of light around the system were consistent with predictions made by general relativity to an accuracy of at least 99.99% across seven tests. (Some readers may experience a paywall.)

Understanding how gravity works at the quantum scale is physics's greatest challenge

While the theory of general relativity explains how gravity works and quantum mechanics explains interactions at the subatomic scale, the two frameworks contradict one another. Developing a model of gravity mediated by particles can help complete the Standard Model.

General relativity describes a singularity as the final moment in time

Using Penrose diagrams—mathematical structures that compress all of space and time—physicists can observe the path of light and which events can affect one another. The space-time maps help visualize the structure of black holes and describe what happens when objects fall in.

The mathematics of general relativity does not rule out the existence of wormholes

Such objects, also known as Einstein-Rosen bridges, would resemble funnel-like tunnels connecting two regions of spacetime, allowing for instant travel across the universe. However, such structures would be incredibly unstable and require undiscovered materials with negative energy to keep them open.

Explore a simplified breakdown of the Einstein field equations

Often depicted as one formula, Einstein's equation represents a suite of 16 nonlinear partial differential equations, which can be simplified to six unique ones, that relate the geometry of spacetime to the presence of mass and energy.

The first interferometric gravitational wave detector was invented in 1972

Robert Weiss completed the designs after his students asked about an earlier apparatus that used stretched aluminum cylinders to detect passing gravitational waves. Unfamiliar with general relativity and hoping to keep the course focused on experimental tests rather than mathematics, Reiss later asked his students to consider his device for homework. (Some readers may experience a paywall.)

Understanding time dilation

The faster you go, the slower time ticks for you. And the stronger the gravitational field acting on you, the slower time ticks for you. These phenomena – collectively called time dilation – were first explained by Albert Einstein’s theories of general and special relativity. In this 11-minute video, beloved astrophysicist Neil deGrasse Tyson explains them to comedian Chuck Nice.

One of Einstein's papers challenged quantum theory but helped confirm entanglement

In 1935, Einstein suggested that quantum mechanics was incomplete due to its strange implications about entangled particles. Their challenge led to decades of experiments that eventually proved distant particles could affect each other instantly.

Albert Einstein taught courses in Davos

This silent video from the 1920s shows footage of Einstein at Davos. The famous scientist spent time there, delivering public lectures on his theory of relativity as part of the town’s university courses.

Understanding how and when time began requires a theory of quantum gravity

Rewinding the universe to the big bang compresses all matter, energy, space, and time into a single point, necessitating a model that combines general relativity with quantum mechanics. Although physicists understand time to have begun when the universe did, a clear understanding of the mechanisms involved remains unclear.

Against his wishes, Albert Einstein's brain was removed before his cremation, and the pathologist responsible stored it for decades in mason jars within a beer cooler.

The ideas of Einstein and Freud combined in 'The Persistence of Memory'

The Persistence of Memory was painted on a canvas roughly the size of a sheet of paper, depicting a desolate landscape with melting clocks, ants, and a distorted figure. The piece incorporates Freud and Einstein's ideas, resulting in a haunting composition symbolizing time's fluidity and Dalí's personal anxieties.

Camus credited a teacher with his success

After winning the Nobel Prize in literature in 1957, Camus wrote a letter to Louis Germain, his former teacher, thanking the man for "the affectionate hand" he extended to Camus as a student. In the short note, he'd go on to write, "without your teaching and example, none of all this would have happened."

The greenhouse effect was discovered by analyzing Earth's temperature

Using mathematical techniques developed to analyze heat transfer, Jean-Baptiste Joseph Fourier showed that Earth should be significantly cooler if solar radiation were the only contributor to its surface temperature. By considering that the atmosphere could amplify the sun's warming effect, he formulated what became known as the greenhouse effect.

An overview on germ theory, the crucial framework developed by Louis Pasteur

Germ theory of disease is based on the concept that many diseases are caused by infections with microorganisms, typically only visualized under high magnification. Read this general overview to understand the basic framework which allowed for development of vaccines.

Mathematicians often solve problems using wordless mental processes

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.

Benjamin Graham is known as the 'father of value investing'

Graham was an investor, author, and professor who was also Warren Buffett's teacher and mentor during his time at Columbia University. Graham is still considered one of the most influential people in the world of investing today.

Computer pioneer Alan Turing was also an elite runner

Alan Turing is credited with helping to found modern computer science, in addition to cracking the Nazi code known as Enigma. Beyond these world-historical achievements, the British mathematician also nearly represented his country in the Olympics in the marathon, running just 11 minutes slower than the eventual gold recipient at the 1948 games. Read more on this lesser-known aspect of the man here.

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.

Warren Buffett's former professor Benjamin Graham is known as the 'father of value investing,' a strategy in which investors seek to buy stocks trading below their intrinsic worth.

The first image of a black hole was captured by creating an Earth-sized virtual observatory from a network of eight radio telescopes.

American dance legend Martha Graham, sometimes called 'the Picasso of dance,' refused to perform at the 1936 Olympics in Berlin and conceived the piece 'Chronicle' in response to the experience.

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.

English mathematician Ada Lovelace wrote the first computer algorithm a century before computers existed and hypothesized that computing devices would one day be able to compose music—foreseeing the generative AI systems of today.

The Brothers Grimm were lawyers before they were storytellers, and became interested in fairy tales as they began investigating how rules and customs had been passed down through cultures.

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.

While the sun's gravity keeps the planets in orbit, their gravity also pulls on the sun, causing it and everything else in the solar system to orbit around a mutual balance point called the barycenter—the true center of the solar system.

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

Objects can be 3D printed with light by projecting 2D computerized tomography (CT) scans onto rotating cylinders of resin, which solidify upon exposure.

Double world record holder Hunter Ewen helped conquer his fear of balloons, called globophobia, by training to win Guinness World Record titles for balloon inflation.

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.

In 1939, baseball star Lou Gehrig delivered his inspirational 'Luckiest Man' speech after retiring due to the health condition that now bears his name.

Stanford built a Google Maps for the Roman Empire, revealing how much it cost to travel in the ancient world

Existentialist writer Jean-Paul Sartre coined the famous phrase 'Hell is—other people' in his play 'No Exit'

'Grand Canyon of the Yellowstone,' a work by American painter Thomas Moran, inspired Congress to establish Yellowstone National Park.

The word 'jazz' evolved from 'jasm,' 19th-century American slang for 'energy'

Larger animals like giraffes, elephants, and blue whales have developed a unique defense against cancer, a phenomenon known as Peto's Paradox

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

Roughly 43 million US borrowers owe roughly $1.7T in student debt, the second-largest source of consumer debt behind mortgages.

The rivalry between Alexander Hamilton and Thomas Jefferson centered on federalism—the question of how much power the federal government should hold relative to the states.

Abraham Lincoln was almost assassinated weeks before his inauguration as he traveled from Illinois to DC through Baltimore in 1861; it took two independent claims for Lincoln to be convinced the threat was real

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.