Mathematics

Researchers are applying evolutionary theory to cancer by changing treatments before tumors have time to develop resistance. Mathematical models suggest that rapid, carefully timed switches between multiple therapies could improve cure rates.

A team of mathematicians used whimsical "silly sprinklers" to solve a physics mystery that has puzzled scientists for decades. Their experiments showed that the rotation of both normal and reverse sprinklers is driven by the momentum of flowing water, not by the outside water flow or other long-standing theories. The results finally provide a clear answer to Feynman’s famous sprinkler problem. They could also help engineers design more efficient fluid-powered machines.

Scientists have combined machine learning with quantum physics to discover two new superconductors and create a much faster way to search for many more. The technique could bring researchers significantly closer to the long-sought goal of a room-temperature superconductor.

Quantum mechanics has journeyed from a strange and controversial idea to the foundation of some of humanity’s most advanced technologies. Now researchers are pushing its boundaries even further, with potential breakthroughs in energy, medicine, computing, and our understanding of the universe.

Researchers developed a Wordle-solving strategy that succeeds 99% of the time by focusing on information gain rather than likely answers. The method uses Shannon entropy to identify guesses that reveal the most about the hidden word. Each guess is designed to slash uncertainty and narrow the possibilities faster. The result significantly outperformed more traditional Wordle tactics.

Researchers have finally resolved a key problem in a 100-year-old theory of color, showing that the qualities we perceive in colors are intrinsic to the mathematics of color space itself. The discovery sharpens our understanding of human vision and could lead to more precise color technologies and visualizations.

Scientists have uncovered a hidden mathematical secret inside the leaves of the Chinese money plant: a naturally occurring geometric pattern known as a Voronoi diagram, something typically associated with city planning, computer science, and network design. By mapping tiny pores and looping veins in the plant’s leaves, researchers discovered that the plant organizes itself using the same kind of elegant spatial logic humans use to solve complex distance problems — without ever “measuring” anything.

Penn researchers have developed a smarter AI method for solving notoriously difficult inverse equations, which help scientists uncover hidden causes behind observable effects. By introducing “mollifier layers” that smooth noisy data, they’ve made these calculations more stable and far less computationally demanding. This could transform fields like genetics, where understanding how DNA behaves is key to disease research.

In a breakthrough experiment, scientists directly imaged how particles pair up in a system that mimics superconductors. Instead of behaving independently, the pairs moved in a synchronized, dance-like pattern—something never predicted before. This suggests a major gap in the classic theory of superconductivity.

A 150-year-old rule in geometry has been proven wrong. Mathematicians found two different doughnut-shaped surfaces that look identical when measured locally but are actually different overall. For decades, researchers suspected this might be possible but couldn’t prove it—until now. The breakthrough reshapes how mathematicians understand the relationship between local measurements and global form.

In crowded environments, more robots don’t always mean faster results—in fact, too many can bring everything to a standstill. Harvard researchers discovered a surprising fix: adding a bit of randomness to how robots move can actually prevent gridlock and boost efficiency. By allowing robots to “wiggle” slightly instead of marching in straight lines, they can slip past each other and keep tasks flowing smoothly.

Scientists have found a clever way to supercharge ultra-thin semiconductors by reshaping the space beneath them rather than altering the material itself. By placing a single-atom-thick layer of tungsten disulfide over tiny air cavities carved into a crystal, they created miniature “light traps” that dramatically boost brightness and optical effects—up to 20 times stronger emission and 25 times stronger nonlinear signals. These hollow structures, called Mie voids, concentrate light exactly where the material sits, overcoming a major limitation of atomically thin devices.

As AI systems began acing traditional tests, researchers realized those benchmarks were no longer tough enough. In response, nearly 1,000 experts created Humanity’s Last Exam, a massive 2,500-question challenge covering highly specialized topics across many fields. The exam was engineered so that any question solvable by current AI models was removed. Early results show even the most advanced systems still struggle — revealing a surprisingly large gap between AI performance and true expert-level knowledge.

Twisting atomically thin magnetic layers does more than reshape their electronics—it can create giant, topological magnetic textures. In chromium triiodide, researchers observed skyrmion-like patterns stretching far beyond the expected moiré scale, reaching hundreds of nanometers. Even more surprising, their size doesn’t simply follow the twist pattern but peaks at a specific angle. This twist-controlled magnetism could pave the way for low-power spintronic devices built from geometry alone.

A century after Erwin Schrödinger sketched out a bold vision for how we perceive color, scientists have finally filled in the missing pieces. A Los Alamos team used advanced geometry to show that hue, saturation, and lightness aren’t shaped by culture or experience — they’re built directly into the mathematical structure of how we see color. By defining a crucial missing element known as the “neutral axis,” the researchers repaired a long-standing flaw in Schrödinger’s model and even corrected tricky visual quirks like the way brightness can subtly shift perceived hue.

Neuromorphic computers modeled after the human brain can now solve the complex equations behind physics simulations — something once thought possible only with energy-hungry supercomputers. The breakthrough could lead to powerful, low-energy supercomputers while revealing new secrets about how our brains process information.

Inspired by the shape-shifting skin of octopuses, Penn State researchers developed a smart hydrogel that can change appearance, texture, and shape on command. The material is programmed using a special printing technique that embeds digital instructions directly into the skin. Images and information can remain invisible until triggered by heat, liquids, or stretching.

Researchers have discovered a hidden quantum geometry inside materials that subtly steers electrons, echoing how gravity warps light in space. Once thought to exist only on paper, this effect has now been observed experimentally in a popular quantum material. The finding reveals a new way to understand and control how materials conduct electricity and interact with light. It could help power future ultra-fast electronics and quantum technologies.

Foams were once thought to behave like glass, with bubbles frozen in place at the microscopic level. But new simulations reveal that foam bubbles are always shifting, even while the foam keeps its overall shape. Remarkably, this restless motion follows the same math used to train artificial intelligence. The finding hints that learning-like behavior may be a fundamental principle shared by materials, machines, and living cells.

A generative AI system can now analyze blood cells with greater accuracy and confidence than human experts, detecting subtle signs of diseases like leukemia. It not only spots rare abnormalities but also recognizes its own uncertainty, making it a powerful support tool for clinicians.

Tessellations aren’t just eye-catching patterns—they can be used to crack complex mathematical problems. By repeatedly reflecting shapes to tile a surface, researchers uncovered a method that links geometry, symmetry, and problem-solving. The technique works in both ordinary flat space and curved hyperbolic worlds used in theoretical physics. Its blend of beauty and precision could influence everything from engineering to digital design.

A new AI developed at Duke University can uncover simple, readable rules behind extremely complex systems. It studies how systems evolve over time and reduces thousands of variables into compact equations that still capture real behavior. The method works across physics, engineering, climate science, and biology. Researchers say it could help scientists understand systems where traditional equations are missing or too complicated to write down.

Ramanujan’s elegant formulas for calculating pi, developed more than a century ago, have unexpectedly resurfaced at the heart of modern physics. Researchers at IISc discovered that the same mathematical structures behind these formulas also describe real-world phenomena like turbulence, percolation, and even black holes. What once seemed like pure mathematics now appears deeply intertwined with the physical laws governing the universe.

A researcher from the University of Tokyo and a U.S.-based structural engineer developed a new computational form-finding method that could change how architects and engineers design lightweight and free-form structures covering large spaces. The technique specifically helps create gridshells, thin, curved surfaces whose members form a networked grid. The method makes use of NURBS surfaces, a widely used surface representation format in computer-aided design (CAD). It also drastically reduces computation cost — a task that previously took 90 hours on a high-end GPU completes in about 90 minutes on a standard CPU.

Researchers have created a prediction method that comes startlingly close to real-world results. It works by aiming for strong alignment with actual values rather than simply reducing mistakes. Tests on medical and health data showed it often outperforms classic approaches. The discovery could reshape how scientists make reliable forecasts.

UC Santa Barbara physicists have engineered entangled spin systems in diamond that surpass classical sensing limits through quantum squeezing. Their breakthrough enables next-generation quantum sensors that are powerful, compact, and ready for real-world use.

A team at the University at Buffalo has made it possible to simulate complex quantum systems without needing a supercomputer. By expanding the truncated Wigner approximation, they’ve created an accessible, efficient way to model real-world quantum behavior. Their method translates dense equations into a ready-to-use format that runs on ordinary computers. It could transform how physicists explore quantum phenomena.

A team of engineers at North Carolina State University has designed a polymer “Chinese lantern” that can rapidly snap into multiple stable 3D shapes—including a lantern, a spinning top, and more—by compression or twisting. By adding a magnetic layer, they achieved remote control of the shape-shifting process, allowing the lanterns to act as grippers, filters, or expandable mechanisms.

In a remarkable leap for quantum physics, researchers in Japan have uncovered how weak magnetic fields can reverse tiny electrical currents in kagome metals—quantum materials with a woven atomic structure that frustrates electrons into forming complex patterns. These reversals amplify the metal’s electrical asymmetry, creating a diode-like effect up to 100 times stronger than expected. The team’s theoretical explanation finally clarifies a mysterious phenomenon first observed in 2020, revealing that quantum geometry and spontaneous symmetry breaking are key to this strange behavior.

A new wearable device, a-Heal, combines AI, imaging, and bioelectronics to speed up wound recovery. It continuously monitors wounds, diagnoses healing stages, and applies personalized treatments like medicine or electric fields. Preclinical tests showed healing about 25% faster than standard care, highlighting potential for chronic wound therapy.

A sweeping investigation has revealed widespread fraud in mathematics publishing, where commercial metrics and rankings have incentivized the mass production of meaningless or flawed papers. The study highlights shocking distortions—such as a university without a math department ranked as having the most top mathematicians—and the explosion of megajournals willing to publish anything for a fee.

Scientists in Korea have engineered magnetic nanohelices that can control electron spin with extraordinary precision at room temperature. By combining structural chirality and magnetism, these nanoscale helices can filter spins without complex circuitry or cooling. The breakthrough not only demonstrates a way to program handedness in inorganic nanomaterials but also opens the door to scalable, energy-efficient spintronic devices that could revolutionize computing.

A hidden quantum geometry that distorts electron paths has finally been observed in real materials. This “quantum metric,” once thought purely theoretical, may revolutionize electronics, superconductivity, and ultrafast devices.

Rice University physicists confirmed that flat electronic bands in kagome superconductors aren’t just theoretical, they actively shape superconductivity and magnetism. This breakthrough could guide the design of next-generation quantum materials and technologies.

Scientists may have uncovered the missing piece of quantum computing by reviving a particle once dismissed as useless. This particle, called the neglecton, could give fragile quantum systems the full power they need by working alongside Ising anyons. What was once considered mathematical waste may now hold the key to building universal quantum computers, turning discarded theory into a pathway toward the future of technology.

Researchers at Harvard have created a groundbreaking metasurface that can replace bulky and complex optical components used in quantum computing with a single, ultra-thin, nanostructured layer. This innovation could make quantum networks far more scalable, stable, and compact. By harnessing the power of graph theory, the team simplified the design of these quantum metasurfaces, enabling them to generate entangled photons and perform sophisticated quantum operations — all on a chip thinner than a human hair. It's a radical leap forward for room-temperature quantum technology and photonics.

AI is revolutionizing the job landscape, prompting nations worldwide to prepare their workforces for dramatic changes. A University of Georgia study evaluated 50 countries’ national AI strategies and found significant differences in how governments prioritize education and workforce training. While many jobs could disappear in the coming decades, new careers requiring advanced AI skills are emerging. Countries like Germany and Spain are leading with early education and cultural support for AI, but few emphasize developing essential human soft skills like creativity and communication—qualities AI can't replace.

AI researchers in Switzerland have found a way to dramatically cut cement s carbon footprint by redesigning its recipe. Their system simulates thousands of ingredient combinations, pinpointing those that keep cement strong while emitting far less CO2 all in seconds.

A new study integrated mathematical modeling with advanced imaging to discover that the physical shape of the fruit fly egg chamber, combined with chemical signals, significantly influences how cells move. Cell migration is critical in wound healing, immune responses, and cancer metastasis, so the work has potential to advance a range of medical treatments.

Scientists have developed a unified theory for mathematical parameters known as gauge freedoms. Their new formulas will allow researchers to interpret research results much faster and with greater confidence. The development could prove fundamental for future efforts in agriculture, drug discovery, and beyond.

Miniature organs on a chip could allow us to do scientific studies with great precision, without having to resort to animal testing. The main problem, however, is that artificial tissue needs blood vessels, and they are very hard to create. Now, new technology has been developed to create reproducible blood vessels using high-precision laser pulses. Tissue has been created that acts like natural tissue.

Researchers developed a faster, more stable way to simulate the swirling electric fields inside industrial plasmas -- the kind used to make microchips and coat materials. The improved method could lead to better tools for chip manufacturing and fusion research.

Scientists found that neural networks cannot yet forecast 'gray swan' weather events, which might not appear in existing training data but could still happen -- like 200-year floods or massive hurricanes.

By twisting atom-thin sheets of graphene in just the right way, Rutgers researchers created intercrystals, a new form of matter where geometry alone controls electron behavior. These strange materials could power quantum computers, ultra-efficient circuits, and greener technologies.

A surprising connection has been found, between two seemingly very different classes of superconductors. In a new material, atoms are distributed irregularly, but still manage to create long-range magnetic order.

Researchers have created a method that makes virtual reality (VR) more accessible to people with mobility limitations.

A mathematician has built an algebraic solution to an equation that was once believed impossible to solve.

New research demonstrates how mathematical modeling can predict outbreaks of toxic fungi in Texas corn crops -- offering a potential lifeline to farmers facing billions in harvest losses.

With the assumption that students are going to use artificial intelligence and large language models such as ChatGPT to do their homework, researchers set out to learn how well the free version of ChatGPT would compare with human students in a semester-long undergraduate control systems course.

Working memory is like a mental chalkboard we use to store temporary information while executing other tasks. Scientists worked with more than 200 elementary students to test their working memory, assess its role in word-problem solving and if interventions could boost it and thereby improve their word problem solving skills. Results showed that improving working memory helped both students with and without math difficulties and can help educators more effectively by helping teach the science of math, study authors argue.

Researchers have demonstrated a significant performance increase in cooling technology for high-power electronic devices. They designed novel capillary geometries that push the boundaries of thermal transfer efficiency. This study could play a crucial role in the development of next-generation technology.

How gravity causes a perfectly spherical ball to roll down an inclined plane is part of elementary school physics canon. But the world is messier than a textbook. Scientists have sought to quantitatively describe the much more complex rolling physics of real-world objects. They have now combined theory, simulations, and experiments to understand what happens when an imperfect, spherical object is placed on an inclined plane.

A new method significantly advances 3D imaging of reflective surfaces. The approach integrates techniques known from high-precision optical 3D metrology and computer vision, and could benefit applications ranging from industrial inspection and medical imaging to virtual reality and cultural heritage preservation.

At hypersonic speeds, complexities occur when the gases interact with the surface of the vehicle such as boundary layers and shock waves. Researchers were able to observe new disturbances in simulations conducted for the first time in 3D.

A tiny magnetic robot which can take 3D scans from deep within the body, that could revolutionize early cancer detection, has been developed by researchers. The team say this is the first time it has been possible to generate high-resolution three-dimensional ultrasound images taken from a probe deep inside the gastrointestinal tract, or gut.

A flower-shaped structure only a few micrometres in size made of a nickel-iron alloy can concentrate and locally enhance magnetic fields. The size of the effect can be controlled by varying the geometry and number of 'petals'. This magnetic metamaterial developed by Dr Anna Palau's group at the Institut de Ciencia de Materials de Barcelona (ICMAB) in collaboration with her partners of the CHIST-ERA MetaMagIC project, has now been studied at BESSY II in collaboration with Dr Sergio Valencia. Such a device can be used to increase the sensitivity of magnetic sensors, to reduce the energy required for creating local magnetic fields, but also, at the PEEM experimental station, to study samples under much higher magnetic fields than currently possible.

Unveiling Dynamic Shape-Morphing Smartphone sized OLED Panel with Built-In Speaker -- All While Maintaining Ultra-Thin Flexibility.

Scientists investigated whether email interventions informed by behavioral science could help teachers help students learn math.

Mathematicians studied the flow of human crowds and developed a way to predict when pedestrian paths will transition from orderly to entangled. Their findings may help inform the design of public spaces that promote safe and efficient thoroughfares.

Some of the world's most advanced AI systems struggle to tell the time and work out dates on calendars, a study suggests.