Illuminating math and science. Supported by @SimonsFdn. 2022 Pulitzer Prize in Explanatory Reporting.
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The human genome is no blueprint or algorithm — it’s something else entirely, something living with promiscuous logic. Can new genomic AI models, such as Evo 2 and AlphaGenome, untangle these tricky knots or will the genome confound them, too? quantamagazine.org/why-the-h…
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“Real numbers can’t exist, because you can’t hide them inside black holes.” — Ahmed Almheiri, physicist at the Institute for Advanced Study. quantamagazine.org/does-time…
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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. quantamagazine.org/physicist…
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Earlier this year, a 17-year-old high school student named Hannah Cairo solved a 40-year-old mystery about how waves behave, surprising and exciting mathematicians. @KSHartnett reports: quantamagazine.org/at-17-han…
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The James Webb Space Telescope will see what — and when — its predecessors cannot see. quantamagazine.org/why-nasas…
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In 1956, 26-year-old Edgar Dijkstra invented a classic path-finding algorithm while out with his fiancée at a café in Amsterdam. It all happened in his head: “Without pencil and paper you are almost forced to avoid all avoidable complexities,” he said. quantamagazine.org/computer-…
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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. quantamagazine.org/an-ancien…
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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. quantamagazine.org/alan-turi…
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The James Webb Space Telescope will see what — and when — its predecessors cannot see. quantamagazine.org/why-nasas…
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Dijkstra’s algorithm doesn’t just tell you the fastest route to one destination. Instead, it gives you an ordered list of travel times from your current location to every other point that you might want to visit — a solution to what researchers call the single-source shortest-paths problem.
quantamagazine.org/computer-…
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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. quantamagazine.org/old-probl…
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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. quantamagazine.org/elliptic-…
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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. quantamagazine.org/the-most-…
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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. quantamagazine.org/the-scand…
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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. quantamagazine.org/old-probl…
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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. quantamagazine.org/the-scand…
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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. quantamagazine.org/lean-comp…
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As a child, Hannah Cairo learned math by taking online lessons from Khan Academy. By the time she was 14, she had taught herself the equivalent of an advanced undergraduate math degree.
quantamagazine.org/at-17-han…
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Andrew Barto and Richard Sutton have won the A.M. Turing Award for developing the theoretical foundations of reinforcement learning, a key method behind many major breakthroughs in artificial intelligence. 🧵
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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. quantamagazine.org/elliptic-…
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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. quantamagazine.org/a-team-of…
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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. quantamagazine.org/meet-stra…
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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. quantamagazine.org/famous-qu…
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The new James Webb Space Telescope will see what — and when — its predecessors cannot see. quantamagazine.org/why-nasas…
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Alexander Mordvintsev, a research scientist at Google, has created complex cell-based digital systems that use only neighbor-to-neighbor communication. These “neural cellular automata” could have promising applications in biology, computing and robotics. quantamagazine.org/self-asse…
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Recently, computer scientist Binghui Peng and his team proved mathematically that there may be a hard limit to LLMs’ compositional task-solving abilities. quantamagazine.org/chatbot-s…
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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. trib.al/OGGxfOA
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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.” quantamagazine.org/holly-moe…
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In 1974, the mathematician Douglas Hofstadter used a graphing calculator to find a fractal pattern in how electrons behave. His adviser dismissed it as numerology. The fractal, called the Hofstadter butterfly, is now known to be a real-life phenomenon. quantamagazine.org/ten-marti…
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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: quantamagazine.org/michel-ta…
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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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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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Dijkstra’s algorithm doesn’t just tell you the fastest route to one destination. Instead, it gives you an ordered list of travel times from your current location to every other point that you might want to visit — a solution to what researchers call the single-source shortest-paths problem.
quantamagazine.org/computer-…
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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. quantamagazine.org/elliptic-…
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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 space-time in our universe. quantamagazine.org/ai-starts…
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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. quantamagazine.org/inside-th…
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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. quantamagazine.org/a-team-of…
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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. quantamagazine.org/black-hol…
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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: quantamagazine.org/the-geome…
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In 1965, the mathematical physicist Roger Penrose proved that, given two simple assumptions, space-time must end at points called singularities. The paper has been called “the most important paper in general relativity” since Einstein’s. quantamagazine.org/singulari…
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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. quantamagazine.org/the-ai-re…
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“Octonions are to physics what the Sirens were to Ulysses.” — particle physicist Pierre Raymond quantamagazine.org/the-octon…
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One hundred years ago, a 23-year-old postdoc named Werner Heisenberg completed a calculation that would become the heart of quantum mechanics, a radical yet stunningly accurate theory of the atomic and subatomic world. quantamagazine.org/its-a-mes…
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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. quantamagazine.org/complexit…
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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. quantamagazine.org/new-proof…
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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. quantamagazine.org/new-math-…
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Scientists trained a language-based machine learning model to understand and solve competition-level math questions. quantamagazine.org/to-teach-…
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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: quantamagazine.org/the-geome…
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During the pandemic, Carolina Figueiredo, a grad student at Princeton, was inspired by the YouTube lectures of Nima Arkani-Hamed, a theoretical physicist. Later, as part of a team that included Arkani-Hamed, Figueiredo leveraged a new geometric approach to quantum physics to discover a secret relationship between real-world particles. quantamagazine.org/physicist…
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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 brain is a dense, thorny network of neurons, which come in many flavors and whose behaviors are controlled by a menagerie of molecules released on precise timescales. It is staggeringly more complex than an AI algorithm. quantamagazine.org/ai-is-not…
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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. quantamagazine.org/after-nea…
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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. quantamagazine.org/old-probl…
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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. quantamagazine.org/complexit…
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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. quantamagazine.org/after-nea…
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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. quantamagazine.org/black-hol…
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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.” quantamagazine.org/a-new-the…
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Scientists trained a language-based machine learning model to understand and solve competition-level math questions. quantamagazine.org/to-teach-…
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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. quantamagazine.org/how-infin…
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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. quantamagazine.org/mass-and-…
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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. quantamagazine.org/computing…
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The new James Webb Space Telescope will see what — and when — its predecessors cannot see. quantamagazine.org/why-nasas…
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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. quantamagazine.org/in-the-wi…
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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. quantamagazine.org/how-infin…
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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. quantamagazine.org/famous-qu…
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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. quantamagazine.org/starfish-…
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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.” quantamagazine.org/is-it-rea…
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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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In 1965, the mathematical physicist Roger Penrose proved that, given two simple assumptions, space-time must end at points called singularities. The paper has been called “the most important paper in general relativity” since Einstein’s. quantamagazine.org/singulari…
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Every rational number is algebraic, and some irrational numbers are too. quantamagazine.org/recountin…
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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.
quantamagazine.org/june-huh-…
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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. quantamagazine.org/new-proof…
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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.
quantamagazine.org/big-bounc…
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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. quantamagazine.org/new-proof…
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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. trib.al/a9jIEKO
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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. quantamagazine.org/lean-comp…
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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. quantamagazine.org/new-proof…
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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. quantamagazine.org/inside-th…
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Since she was in graduate school, Laura Monk has been developing mathematical theories that Maryam Mirzakhani didn’t have a chance to finish before her death. Monk feels she’s gotten to know the mathematician through her proofs. quantamagazine.org/years-aft…
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Since late 2017, Ashwin Sah and Mehtaab Sawhney have written a mind-boggling 57 math proofs together, many of them profound advances in various fields. Their latest findings are no exception: quantamagazine.org/grad-stud…
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Stephen Hawking’s black hole information paradox has been resolved, and not in Hawking’s favor. quantamagazine.org/the-black…
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During the pandemic, Carolina Figueiredo, a grad student at Princeton, was inspired by the YouTube lectures of Nima Arkani-Hamed, a theoretical physicist. Later, as part of a team that included Arkani-Hamed, Figueiredo leveraged a new geometric approach to quantum physics to discover a secret relationship between real-world particles. quantamagazine.org/physicist…
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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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Scientists have built deep neural networks that can map between infinite dimensional spaces. quantamagazine.org/new-neura…
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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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The most famous experiment in quantum physics could provide the framework for astronomers to observe the cosmos at an incredibly high resolution. quantamagazine.org/famous-qu…
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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. quantamagazine.org/complexit…
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What’s inside a proton? Your answer may vary depending on how hard you hit it with electrons. quantamagazine.org/inside-th…
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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. quantamagazine.org/how-infin…
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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) quantamagazine.org/foundatio…
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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. quantamagazine.org/lean-comp…
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The simplex method is an algorithm that turns an optimization problem, like setting up an investment portfolio, into a geometry problem. Recently, the scientists Sophie Huiberts (left) and Eleon Bach reduced the runtime of the simplex method. quantamagazine.org/researche…
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In 1956, 26-year-old Edsger Dijkstra invented a classic path-finding algorithm while out with his fiancée at a café in Amsterdam. It all happened in his head: “Without pencil and paper you are almost forced to avoid all avoidable complexities,” he said. quantamagazine.org/computer-…
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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. quantamagazine.org/computer-…
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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.”
quantamagazine.org/michel-ta…
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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. quantamagazine.org/how-our-r…
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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. quantamagazine.org/famous-qu…
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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). quantamagazine.org/maths-old…
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