In a quiet corner of the University of Massachusetts Boston, a team led by Joanna Ruhl, Vanja Dunjko, and Maxim Olshanii tackles a stubborn puzzle: even in perfectly solvable waves, quantum jitters refuse to stay quiet. Their subject is a one-dimensional Bose gas described by the nonlinear Schrödinger equation, the same equation that makes optical…
Mathematicians don’t just chase abstract shapes; they follow rules that feel almost musical, where symmetry, space, and time compose a single score. The latest work on pluriclosed metrics on compact semisimple Lie groups sweeps us into that score, showing how a precise algebra of roots and tori can pin down a whole family of geometric…
The 3x + 1 problem, as famous for its stubborn simplicity as for its stubbornness, keeps outsmarting us with every new numerical trick and heuristic. Yet Leonard Ben Aurel Brauer, presenting under the banner of an Independent Researcher, turns the lens inward. Instead of chasing a universal invariant or a probabilistic canopy over endless sequences,…
Exams are more than a snapshot of a student’s memory on one Tuesday afternoon. They’re also a fleet of tiny data-storms, each school generating its own rush of responses, each test a potential trail of personal information. In a world where privacy laws tighten like a drawstring and schools share concerns about gatekeeping and fairness,…
The Large Hadron Collider never runs out of surprises, and this time the surprise wears a tiny, fast-moving cloak: charm quarks. These are heavy enough to be born in the initial hammer blows of a proton–proton collision, and light enough to be cradled into ordinary hadrons within the blink of a detector’s eye. In the…
Two groups can walk through the same city on two different maps and still arrive at the same skyline. They can look different on the ground, yet their faraway footprints brush the same corners of a landscape. That paradox sits at the heart of a bold new mathematical framework that rethinks how we compare infinite…
Every time you read about a network—whether it’s a social graph, a road map, or a circuit layout—you’re glimpsing a version of a classic math problem: can we trace a loop that visits every node exactly once? That is the essence of a Hamiltonian cycle. For a long time, mathematicians treated this as a deeply…
Magnetic specks ride turbulence to learn its secrets
Three-dimensional quantum matter hides strange creatures called fractons, excitations so oddly tethered to their surroundings that they barely move unless they team up with others. In the wild world of fracton phases, some particles can glide within planes, others crawl along lines, and some are stuck unless they’re joined with the right partners. The paper…
Passive investing has become the default setting for many of us who want exposure to the market without paying up for active pick-and-pick strategies. Fees shrink, simplicity shines, and the math seems to back a straightforward claim: track the index, stay near zero tracking error, and you win. But a careful look at the plumbing…
Data in health research rarely arrives neat and complete. Observational studies chase causal questions, but missing data is a constant companion. Exposures people forget to report, confounders researchers wish they had, outcomes that arrive long after the study begins. The standard workaround is multiple imputation, a practical patch that smooths over gaps as if they…
Geometric shapes aren’t just pretty ornaments on a chalkboard. In optimization, they’re enormous, living laboratories where tiny binary decisions ripple into sweeping consequences. The CUT(n) polytope—the convex hull of cut vectors of a complete graph Kn—has loomed as a central but stubborn mystery: its vertices are famously elusive to describe with a neat, closed-form formula….
Predicting how a material behaves at the scale of atoms is a little like forecasting the weather for molecules: it needs to reckon with countless moving parts, from tiny shifts in electron clouds to subtle shifts in how atoms cling to one another. If you could teach a machine to read those interactions, you could…
Banach spaces are the mathematical playgrounds where infinity meets structure. They’re the kind of spaces that let you talk about convergence, continuity, and the delicate dance between algebra and analysis. For decades, researchers have tried to stitch together two such spaces into a single, coherent object called a tensor product. The reward would be a…
Astronomers are used to thinking of galaxies as quiet neighborhoods where stars drift by and black holes hide in the basements. But the real drama happens when gas, gravity, and gravity’s most charismatic resident—the supermassive black hole at a galaxy’s center—dance together. A large new study led by Miguel Parra Tello of Pontificia Universidad Católica…
In a world of data, not all lists are created equal. Some are clean and predictable, others resemble a crowded shelf where a handful of titles fill the page while thousands of tiny volumes hide in the margins. Real systems—languages, city sizes, baby names, or scientific citations—follow patterns that look simple at a glance but…
Mathematicians love puzzles that look deceptively simple on the surface and only reveal their depth when you try to actualize them. The stage for one such drama is a complete graph, a mathematical city where every vertex is connected to every other by a road. If you label the towns 0 through p−1 around a…
Language in science has always evolved—glimpses of new terms, shifts in tone, and the slowly changing cadence of scholarly prose. But a recent study from Florida State University suggests something striking: the shifts triggered by AI-enabled writing tools aren’t just speeding up a few words here and there. They’re reshaping how scientists talk about ideas…
The Dirichlet divisor problem lives at the intersection of curiosity and calculation. It asks a deceptively simple question: when you count how many ways a number can be written as a product of two factors, what does the total sum look like as you sweep up to a large x? The generalised version widens the…
Tech culture has spent years imagining a future where AI writes papers for us, but the quieter tremor is in the way science talks to itself. A study led by Abdulkareem Alsudais at Prince Sattam bin Abdulaziz University in Saudi Arabia asks a simple, unsettling question: has the rise of accessible language models nudged the…