Mathematician David Hilbert developed general relativity equations before Einstein

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

Recognizing the mathematical complexities of generalizing special relativity with a new picture of gravity and acceleration, Albert Einstein had Grossman introduce him to tensor calculus. Years before developing the precursor to GR together, Einstein would use Grossman's lecture notes to prepare for his exams.

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...

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.

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."

A breakdown of the experimental test results supporting the general theory of relativity

Besides accurately explaining the slight wobble observed in Mercury's orbit, general relativity predicted that light would bend around massive objects by an amount matching what was observed when background starlight bent around the sun during an eclipse. The theory also predicted the existence of gravitational waves and black holes decades before they were found.

How a solar eclipse proved Einstein's theory of gravity

For hundreds of years, Isaac Newton's laws of gravity and motion accurately predicted every observation and measurement involving orbits. With the advance of technology, more precise measurements revealed anomalies, including the orbit of Mercury, which Albert Einstein's general theory of relativity could explain. This article details the two frameworks and how they went head-to-head during an eclipse for gravitational supremacy.

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.

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.

Albert Einstein's equations predicted black holes decades before their discovery

For nearly 50 years, scientists dismissed black holes as implausible oddities, despite solutions to the equations indicating their existence. But the 1970s discovery of intense X-rays from Cygnus X-1 and its massive hidden companion flipped the consensus.

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.

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.

During his 'miraculous year,' Einstein published four groundbreaking papers

The 1905 "annus mirabilis" papers explained the photoelectric effect, Brownian motion, the absolutism of the speed of light, and mass-energy equivalence, revolutionizing scientists' understandings of space, time, mass, and energy. For the discovery of the photoelectric effect, Einstein won the 1921 Nobel Prize in Physics.

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.

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.)

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.

A Belgian Catholic priest was the first to come up with the idea for the Big Bang

In 1931, Georges Lemaître presented his radical idea that the universe came from a “primeval atom,” challenging the long-held belief that the universe had always existed. Einstein initially dismissed Lemaître’s work as having “abominable” physical insight, only to accept it later.

Cecilia Payne-Gaposchkin discovered stars are mostly made of hydrogen and helium

At 25, her doctoral thesis challenged the then-common belief that stars were composed similarly to Earth. Several years later, Henry Norris Russell, who had initially dismissed her findings, independently made the same discovery and received credit for it.

There are statistically significant discrepancies in measured universal expansion

Using data from the cosmic microwave background, which allows astronomers to model the universe's conditions since its earliest moments, yields a rate of expansion—the Hubble constant—lower than values obtained from multiple techniques measured locally at more recent timescales. Reconciling the discrepancy, known as the Hubble tension, will require a third independent measurement method between the two scales

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.

The story of two female programmers running the simulations behind chaos theory's discovery

Margaret Hamilton and Ellen Fetter worked on MIT's 800-pound Royal McBee LGP-30 computer, which was fed binary code on paper tape to perform computations. Among the computations performed were those involving equations describing the motion of gas in a circulating fluid for Edward Lorenz, widely considered the father of chaos theory.

Despite the discovery of dark matter, Vera Rubin never won a Nobel Prize

In the 1970s, Rubin and collaborator Kent Ford revealed that galaxies rotate in a way only explainable by vast amounts of unseen mass, now known as dark matter. The transformative discovery did not warrant a Nobel Prize, which was only awarded to two women in physics from 1901 to 2017.

Earth's core is about 2.5 years younger than its surface according to relativity

Due to differences in where objects are located within gravitational fields, time will run at different rates, which has major impacts on technology that relies on synchronization. For example, GPS satellites run about 38 microseconds faster every day than clocks on Earth's surface, resulting in GPS discrepancies of about six miles, were it not for software corrections.

Italian physicist Enrico Fermi (1901–1954) on the Standard Model

"If I could remember the name of all these particles, I'd be a botanist."

Listen to the audiobook version of 'A Brief History of Time'

First published in 1988, Stephen Hawking's most famous novel has sold more than 25 million copies in 40 languages. Through non-technical terminology, Hawking discusses the nature of space and time, general relativity, quantum mechanics, gravity, black holes, and cosmology.

Meet Hipparchus, the Greek astronomer who created the world's first star map

Astronomer Hipparchus created accurate maps of the night sky way ahead of his time, with coordinates sometimes within a single degree of modern values. Hipparchus founded a new theory of star motion, modeling the sky as a celestial sphere with coordinates similar to latitude and longitude—concepts only recently created in Hipparchus' time.

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

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.

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 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.

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.

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.

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

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

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.

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

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.

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.

Before writing 'Walden,' transcendentalist Henry David Thoreau nearly burned down his hometown with a campfire that grew out of control.

Meet the 56 signers of the Declaration of Independence—most of whom didn't put pen to paper until August 2, 1776—and see their original signatures.

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

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.

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

Electrical grids worldwide must double their power delivery capacity by 2050 to meet surging demand from AI and electric vehicles.

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.

While the first exchange-traded fund (a 'basket' of different assets that can be bought and sold on a stock exchange) in the US only launched in 1993, the global ETF market has grown to more than $10T in the short time since.

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.

The name 'Silicon Valley' arose from the founding of Shockley Semiconductor Laboratory in Fairchild Semiconductor in 1956-57, founded near Stanford University in Palo Alto

Volcanic activity may have triggered the Black Death by spewing gases that led to crop failures in Europe, thus forcing the import of grain ships with plague-infested fleas.

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

Iran's Revolutionary Guard Corps is independent of Iran's regular army and is one of the most powerful and influential military-political organizations in the Middle East.