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Illuminating math and science. Supported by @SimonsFdn . 2022 Pulitzer Prize in Explanatory Reporting.

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Joined October 2012
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A new proposal says that gravitational waves and quantum technology should make it possible to detect an event closely associated with a graviton, the quantum particle of gravity. Physicists are debating what a detection would mean. @walkingthedot reports:
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It Might Be Possible to Detect Gravitons After All | Quanta Magazine

A new experimental proposal suggests detecting a particle of gravity is far easier than anyone imagined. Now physicists are debating what it would really prove.

www.quantamagazine.org
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3 years
“Real numbers can’t exist, because you can’t hide them inside black holes.” — Ahmed Almheiri, physicist at the Institute for Advanced Study.
Does Time Really Flow? New Clues Come From a Century-Old Approach to Math.

The laws of physics imply that the passage of time is an illusion. To avoid this conclusion, we might have to rethink the reality of infinitely precise numbers.

www.quantamagazine.org
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Did the universe emerge from an initial point known as a “singularity? Or, as Stephen Hawking argued, does it have no temporal beginning at all? A critique of Hawking’s “no-boundary” proposal has reignited the debate.
Physicists Debate Hawking’s Idea That the Universe Had No Beginning | Quanta Magazine

A recent challenge to Stephen Hawking’s biggest idea — about how the universe might have come from nothing — has cosmologists choosing sides.

www.quantamagazine.org
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The James Webb Space Telescope will see what — and when — its predecessors cannot see.
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For the first time, mathematicians have shown the most efficient way yet of squaring the circle — or, equivalently, of circling the square — by cutting the shapes into pieces simple enough to be visualized and then rearranging them.
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At 23 years old, Alan Turing wrote a seminal paper that helped define computation, algorithms and what came to be known as Turing machines — the theoretical foundation for modern computing.
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The James Webb Space Telescope will see what — and when — its predecessors cannot see.
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The married mathematicians Eric Larson and Isabel Vogt often found themselves discussing ideas after dinner, working through problems on the chalkboards they have in their home. The pair recently proved a centuries-old question about algebraic curves.
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Mathematicians are studying elliptic curve patterns that resemble murmurations of starlings. Nina Zubrilina, a doctoral student at Princeton, was the first to prove a formula that explains reasons for the patterns.
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Growing evidence supports what physicists have long suspected: In some way or other, space-time itself seems to fall apart at a black hole, implying that space-time is not the root level of reality, but an emergent structure from something deeper.
The Black Hole Information Paradox Comes to an End

In a landmark series of calculations, physicists have proved that black holes can shed information.

www.quantamagazine.org
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Before mathematicians used modern symbolic algebra, they would reason geometrically. For instance, these figures show the equation (𝑎 + 𝑏)² = 𝑎² + 2𝑎𝑏 + 𝑏².
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The married mathematicians Eric Larson and Isabel Vogt often found themselves discussing ideas after dinner, working through problems on the chalkboards they have in their home. The pair recently proved a centuries-old question about algebraic curves.
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The Nobel Prize in Physics 2022 has been awarded to Alain Aspect, John F. Clauser and Anton Zeilinger “for experiments with entangled photons, establishing the violation of Bell inequalities and pioneering quantum information science.”
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Before mathematicians used modern symbolic algebra, they would reason geometrically. For instance, these figures show the equation (𝑎 + 𝑏)² = 𝑎² + 2𝑎𝑏 + 𝑏².
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Peter Scholze, one of the most respected mathematicians in the world, completed an important proof entirely in his head and hungover. A computerized proof assistant later confirmed that his work was correct.
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Mathematicians are studying elliptic curve patterns that resemble murmurations of starlings. Nina Zubrilina, a doctoral student at Princeton, was the first to prove a formula that explains reasons for the patterns.
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The Fields medalist Terence Tao has championed the use of computerized proof verification tools, including the computer language called Lean. Tao recently led a collaborative effort to formalize a combinatorics proof with Lean. It took just three weeks.
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The most famous experiment in quantum physics could provide the framework for astronomers to observe the cosmos at an incredibly high resolution.
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As a grad student, Liyang Chen spent a year working out how to carve a nanowire that’s thinner than a single bacterium. Using the wire, Chen helped show that the metal it’s made from — and others like it — may carry electrical charge without electrons.
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The new James Webb Space Telescope will see what — and when — its predecessors cannot see.
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Yihong Chen, an AI researcher, recently led a study that taught a machine learning model to periodically forget its initial training. Chen and her team say the success of their approach suggests that forgetfulness may help AI generalize between languages.
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“Being able to combine laboratory experiments with mathematical models forces me to be really honest and explicit about what I think is going on.”
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Yesterday we published an article with the headline “Physicists Create a Wormhole Using a Quantum Computer.” It described the efforts by a team of physicists led by Maria Spiropulu of Caltech to implement a “wormhole teleportation protocol” on a quantum computer. (1/10)
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Michel Talagrand has been awarded the Abel Prize, one of the highest honors in mathematics, for applying tools from high-dimensional geometry to complex probability problems. @jordanacep reports:
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Behold! President Biden has unveiled the first image from the James Webb Space Telescope, which launched in December. Here, we see the deep field SMACS 0723, in which a galaxy acts as a gravitational lens, magnifying thousands of extremely distant galaxies.
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In string theory, six extra dimensions curl up at every point in our 4D universe, and their configuration determines the macroscopic laws of physics. The game plan for string theory, then, boils down to searching for the specific manifold that would describe the microstructure of
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The three-quark model of a proton may be elegant, but this simplicity comes with shortcomings. Physicists have known for decades that the proton is much more than three quarks.
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An “A-team” of mathematicians, including Terence Tao, Timothy Gowers, Ben Green and Freddie Manners, have cracked open a combinatorics problem that eluded researchers for decades.
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When photons hurtle toward a black hole, most are sucked into its depths, never to return, or gently deflected away. A few, however, skirt the hole, making a series of abrupt U-turns. Some theorists now say that this “light trap” hints at quantum gravity.
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The Arthashastra, written in 300 BCE, is the first known text on economics. In 1905, it was rediscovered by the scholar Rudrapatna Shamasastry. His great-great-granddaughter is Anima Anandkumar, now a machine learning scientist at CalTech and Nvidia.
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“Octonions are to physics what the Sirens were to Ulysses.” — particle physicist Pierre Raymond
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In 1921, David Hilbert proposed a research program for grounding mathematics in absolute certainty. A decade later, Kurt Gödel proved that math is incomplete. In 1936, work by a young Alan Turing proved that some problems can’t be solved by algorithms.
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William Gasarch, a professor of computer science at the University of Maryland, recently combined a 1916 proof by Issai Schur with a 1770 proof by Leonhard Euler to reprove that infinite prime numbers exist.
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In the simplest model of the solar system, which considers only the gravitational forces exerted by the sun, the planets follow their elliptical orbits like clockwork for eternity. Reality is far more dynamic.
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Scientists trained a language-based machine learning model to understand and solve competition-level math questions.
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The Nobel Prize in Physics 2023 has been awarded to Pierre Agostini, Ferenc Krausz and Anne L’Huillier "for experimental methods that generate attosecond pulses of light for the study of electron dynamics in matter."
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In 1930, the mathematician Frank Ramsey proved that as graphs get bigger, structure is inevitable. Ramsey died later that year at the age of 26. This work spawned Ramsey theory, which looks for inescapable patterns in a huge range of systems.
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The married mathematicians Eric Larson and Isabel Vogt often found themselves discussing ideas after dinner, working through problems on the chalkboards they have in their home. The pair recently proved a centuries-old question about algebraic curves.
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A Hamiltonian path is a route that passes through every node in a graph exactly once. Finding Hamiltonian paths can overload even the best-known algorithm for the job. Finding Eulerian paths that pass through every edge is computationally simpler.
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In 1930, the mathematician Frank Ramsey proved that as graphs get bigger, structure is inevitable. Ramsey died later that year at the age of 26. This work spawned Ramsey theory, which looks for inescapable patterns in a huge range of systems.
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1 year
When photons hurtle toward a black hole, most are sucked into its depths, never to return, or gently deflected away. A few, however, skirt the hole, making a series of abrupt U-turns. Some theorists now say that this “light trap” hints at quantum gravity.
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Scientists trained a language-based machine learning model to understand and solve competition-level math questions.
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Lee Cronin, a chemist in Scotland, co-developed a new approach for distinguishing life from nonlife. “We’re trying to make a theory that explains how life arises from chemistry, and doing it in a rigorous, empirically verifiable way.”
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This equation is often described as the most beautiful in all of mathematics. Each of its numbers, 0, 1, π, 𝑖 and 𝑒 symbolize an entire branch of math, and in that way the equation can be seen as a glorious confluence, a testament to the unity of math.
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Albert Einstein upended our view of the universe by merging space and time into a single dynamic fabric. Now, many physicists are coming to their own radical realization: The fabric of space-time seems to emerge from something else. 🧵
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In 1979, Roger Penrose said the number-one problem in general relativity is how to determine the mass within a region of space-time. A definition of angular momentum ranked second on Penrose’s list. Now both of these problems have been solved.
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The new James Webb Space Telescope will see what — and when — its predecessors cannot see.
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LaTeX, a system invented by Leslie Lamport in the 1980s, has become the standard way to typeset complex formulas and format scientific documents not only in math but in most scientific domains. It’s how we write mathematical notation in Quanta Magazine.
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Recently, Zhengyi Zhou, a mathematician at the Chinese Academy of Sciences, helped prove the existence of a certain type of sphere in dimensions seven and above. These manifolds will help mathematicians probe an infinite number of related objects.
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When the pioneers of calculus discovered that all the functions they were familiar with — like sines and cosines, along with exponential functions — could be converted into the universal currency of “power series,” they noticed startling coincidences.
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The most famous experiment in quantum physics could provide the framework for astronomers to observe the cosmos at an incredibly high resolution.
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This “living crystal” is a clump of rotating, jiggling starfish embryos in the lab of the biophysicist Nikta Fakhri. It embodies a state of matter known as an odd material that may have previously unknown biological functions.
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The supermassive black hole in the Milky Way’s center, seen in this new image released today by the Event Horizon Telescope ( @ehtelescope ), has a strong magnetic field spiraling around its edge, hinting that a jet might shoot out from it.
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Every rational number is algebraic, and some irrational numbers are too.
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The neuroscientist Nadine Dijkstra found that the brain mixes perceived images and imagery in our mind’s eye, then evaluates the result. “When this mixed signal is strong or vivid enough, we think it reflects reality.”
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@jordanacep BREAKING: June Huh, a one-time high school dropout who took six years to finish undergrad, has won the Fields Medal, math’s highest honor.
June Huh, High School Dropout, Wins the Fields Medal | Quanta Magazine

June Huh wasn’t interested in mathematics until a chance encounter during his sixth year of college. Now his profound insights connecting combinatorics and geometry have led to math’s highest honor.

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William Gasarch, a professor of computer science at the University of Maryland, recently combined a 1916 proof by Issai Schur with a 1770 proof by Leonhard Euler to reprove that infinite prime numbers exist.
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A group of physicists including one of the architects of inflation have revived the idea of a cyclic, or “ekpyrotic,” universe — one that has no beginning and no end.
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Any oscillator — a pendulum, a spring, a firefly, a human heart cell — wants to match up with its neighbors. Mathematicians recently showed that synchronization is inevitable in expander graphs, a type of network found in many areas of science.
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Yihong Chen, an AI researcher, recently led a study that taught a machine learning model to periodically forget its initial training. Chen and her team say the success of their approach suggests that forgetfulness may help AI generalize between languages.
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Peter Scholze, one of the most respected mathematicians in the world, completed an important proof entirely in his head and hungover. A computerized proof assistant has now confirmed that his work is correct.
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The three-quark model of a proton may be elegant, but this simplicity comes with shortcomings. Physicists have known for decades that the proton is much more than three quarks.
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4 years
Stephen Hawking’s black hole information paradox has been resolved, and not in Hawking’s favor.
The Black Hole Information Paradox Comes to an End

In a landmark series of calculations, physicists have proved that black holes can shed information.

www.quantamagazine.org
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Scientists have built deep neural networks that can map between infinite dimensional spaces.
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On this day 107 years ago, mathematician Paul Erdős was born in Budapest. Erdos is pictured here in 1985, teaching the then 10-year-old Terence Tao.
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The most famous experiment in quantum physics could provide the framework for astronomers to observe the cosmos at an incredibly high resolution.
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Mathematician and logician Kurt Gödel was born on this day in 1906. Gödel's famous incompleteness theorems, which ended the pursuit of a complete and consistent mathematics, were published when he was 25 years old.
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What’s inside a proton? Your answer may vary depending on how hard you hit it with electrons.
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This equation is often described as the most beautiful in all of mathematics. Each of its numbers, 0, 1, π, 𝑖 and 𝑒 symbolize an entire branch of math, and in that way the equation can be seen as a glorious confluence, a testament to the unity of math.
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Neural networks can be as unpredictable as they are powerful. Now mathematicians are beginning to reveal how a neural network’s form will influence its function. (From 2019)
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Peter Scholze, one of the most respected mathematicians in the world, completed an important proof entirely in his head and hungover. A computerized proof assistant has now confirmed that his work is correct.
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The mathematical concept of algorithmic complexity seemed inapplicable in the real world. But scientists are now using it to analyze networks and push their evolution toward optimal solutions.
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“I like to understand simple things very well, because my brain is very slow. So I think about them for a very, very long time.”
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Michel Talagrand Wins Abel Prize for Work Wrangling Randomness | Quanta Magazine

The French mathematician spent decades developing a set of tools now widely used for taming random processes.

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The path integral, devised in 1948 by Richard Feynman, gets results that are beyond dispute by summing messy quantum amplitudes with reckless abandon. “It’s like black magic,” said Yen Chin Ong, a mathematician-turned-physicist.
How Our Reality May Be a Sum of All Possible Realities | Quanta Magazine

Richard Feynman’s path integral is both a powerful prediction machine and a philosophy about how the world is. But physicists are still struggling to figure out how to use it, and what it means.

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The most famous experiment in quantum physics could provide the framework for astronomers to observe the cosmos at an incredibly high resolution.
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With the exception of a single symbol for ⅔, Ancient Egyptians’ number system could only express more complicated fractions (like ¾) as sums of unit fractions, which are fractions that feature a 1 in their numerator (½ + ¼).
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The most famous experiment in quantum physics could provide the framework for astronomers to observe the cosmos at an incredibly high resolution.
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In 1975, the Japanese physicist Yoshiki Kuramoto introduced a mathematical model that describes how synchronization occurs in collective systems. The Kuramoto model has proved useful for modeling synchronization in networks from brains to power grids.
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This equation is often described as the most beautiful in all of mathematics. Each of its numbers, 0, 1, π, 𝑖 and 𝑒 symbolize an entire branch of math, and in that way the equation can be seen as a glorious confluence, a testament to the unity of math.
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@jordanacep @EricaKlarreich BREAKING: Maryna Viazovska, a Ukrainian number theorist, has been awarded the Fields Medal, math’s highest honor. She is the second woman to receive the medal in its 86-year history. @7homaslin and @EricaKlarreich report:
Ukrainian Mathematician Maryna Viazovska Wins Fields Medal | Quanta Magazine

With her homeland mired in war, the sphere-packing number theorist Maryna Viazovska has become the second woman to win a Fields Medal in the award’s 86-year history.

www.quantamagazine.org
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How would you find the area under this curve for any value of 𝑥? A creative restructuring of this problem led a young Isaac Newton to calculate one of the first power series he ever used.
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The standard recipe for multiplying a 2-by-2 matrix requires eight multiplications. In 1969, Volker Strassen discovered a procedure that uses seven rather than eight multiplication steps. Strassen’s approach was later proved to be optimal.
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James Truman, a professor at the University of Washington, made fruit fly brain cells fluorescent so that he could track the changes in their neurons during metamorphosis. The results were startling.
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The process of multiplying any two matrices of a given size can be described by a single, unique, 3D tensor.
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3 months
Tensors are instrumental in physics, machine learning and even biology. Einstein once begged a friend to help him understand them, fearing he was going mad. Joseph Howlett explains how they work:
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2 years
Quantum chromodynamics predicts that the proton is, at high resolution, a dandelion-like cloud made up almost entirely of force-carrying particles called gluons.
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1 year
BREAKING: Pulsar data collected over decades points to a background of low-frequency ripples in space-time moving across the universe. @Astro_Jonny reports:
An Enormous Gravity ‘Hum’ Moves Through the Universe | Quanta Magazine

Astronomers have found a background din of exceptionally long-wavelength gravitational waves pervading the cosmos. The cause? Probably supermassive black hole collisions, but more exotic options...

www.quantamagazine.org
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1 year
In 1972, Bob Metcalfe presented a thesis about connecting MIT’s mainframe computer to a precursor of the internet called Arpanet. The dissertation committee failed him, saying the topic wasn’t theoretical enough. This year, he received the Turing award.
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2 years
Before dying from a duel at 20 years old, Évariste Galois uncovered the hidden structure of polynomials and helped pioneer the area of mathematical research now called group theory.
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Scientists trained a language-based machine learning model to understand and solve competition-level math questions.
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1 year
The Nobel Prize in Physiology or Medicine 2023 has been awarded to Katalin Karikó and Drew Weissman "for their discoveries concerning nucleoside base modifications that enabled the development of effective mRNA vaccines against COVID-19."
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2 years
“The importance of thinking and writing before you code needs to be taught in undergraduate computer science courses and it’s not.”
Computing Expert Says Programmers Need More Math | Quanta Magazine

Leslie Lamport revolutionized how computers talk to each other. Now he’s working on how engineers talk to their machines.

www.quantamagazine.org
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2 years
The Riemann hypothesis is one of the most important, if not *the* most important, unsolved problems in all of mathematics.
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2 years
🌊Why is the ocean blue? Indian physicist Chandrasekhara Ventaka Raman discovered the answer. #OTD 1928, he showed how light scatters when it hits particles smaller than its wavelength, called Raman scattering. He was the first Asian person to win a Nobel Prize.
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2 years
This equation is often described as the most beautiful in all of mathematics. Each of its numbers, 0, 1, π, 𝑖 and 𝑒 symbolize an entire branch of math, and in that way the equation can be seen as a glorious confluence, a testament to the unity of math.
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1 year
The Chinese-American mathematician Shing-Tung Yau has led a decades-long effort to construct definitions of mass and angular momentum within general relativity.
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3 years
Scientists have built deep neural networks that can map between infinite dimensional spaces.
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3 years
This equation is often described as the most beautiful in all of mathematics. Each of its numbers, 0, 1, π, 𝑖 and 𝑒 symbolize an entire branch of math, and in that way the equation can be seen as a glorious confluence, a testament to the unity of math.
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10 months
Today, we published our annual list of the year’s biggest discoveries in computer science. Here are a few of the stories that we included 🧵
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4 years
BREAKING: Physicists at Fermilab announced that elementary particles called muons wobbled more than expected while whipping around a magnetized ring, strongly suggesting that unknown particles of nature are giving the muons an extra push. #gminus2
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