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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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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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2 years

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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5 months

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 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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3 years

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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2 years

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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2 years

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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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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“Octonions are to physics what the Sirens were to Ulysses.” — particle physicist Pierre Raymond

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8 months

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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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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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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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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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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8 months

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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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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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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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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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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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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The new James Webb Space Telescope will see what — and when — its predecessors cannot see.

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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 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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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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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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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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2 years

@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.

www.quantamagazine.org

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Every rational number is algebraic, and some irrational numbers are too.

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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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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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1 year

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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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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Scientists have built deep neural networks that can map between infinite dimensional spaces.

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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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3 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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2 years

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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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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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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What’s inside a proton? Your answer may vary depending on how hard you hit it with electrons.

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3 years

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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“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.”

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.

www.quantamagazine.org

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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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@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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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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11 months

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.

www.quantamagazine.org

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6 months

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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9 months

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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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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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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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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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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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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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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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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Scientists trained a language-based machine learning model to understand and solve competition-level math questions.

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“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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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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The Riemann hypothesis is one of the most important, if not *the* most important, unsolved problems in all of mathematics.

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While a quantum internet still seems decades away, an optical telescope network linked with quantum hard drives could be in closer reach. (From 2021)

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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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Quantum superpositions allow for simultaneous possibilities, while general relativity suggests that space and time are malleable. Paired together, these radical features imply that causality is indefinite.

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🌊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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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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Scientists have built deep neural networks that can map between infinite dimensional spaces.

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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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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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In 1973, the legendary mathematician Paul Erdős asked if it’s possible to build a hypergraph with two seemingly incompatible properties. In a 50-page proof, a quartet of mathematicians recently showed that it is.

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By chopping up large numbers into smaller ones, researchers have rewritten a fundamental mathematical speed limit. (From 2019)

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In 2023, neuroscientists uncovered that our brain distinguishes reality from imagination on a gradient, with a threshold marking the jump from one state to another. Learn about the biological breakthroughs of 2023:

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In 1974, Mary K. Gaillard and Ben Lee used the then-unnamed strategy of naturalness to predict the mass of the still-hypothetical charm quark. Three months later, the charm quark was found, ushering work that helped complete the Standard Model.

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Mathematicians seek geometric “foams” that fill high-dimensional space optimally, the way hexagons fill space in a honeycomb.

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