Mathematics

Complex systems may work better when their parts are not perfectly alike. Northwestern physicists found that carefully balanced variation, or “disorder,” can make networks such as power grids, ecosystems, neurons, and materials more stable. Even random differences sometimes improved stability compared with completely uniform systems. The discovery could help researchers design more resilient technologies and explain why natural systems are so rarely perfectly uniform.

A mathematical shape famous for covering a surface without ever repeating has revealed an unexpected ability to twist light into unusual chiral patterns. The discovery could lead to new ways of controlling light, polarization, and advanced optical devices.

Researchers at Binghamton University have developed a mathematical strategy that can solve Wordle with a 99% success rate. Instead of simply guessing words packed with common letters or choosing the most likely answer, the method uses Shannon entropy, a measure from information theory, to identify guesses that reveal the most useful information. Each guess is designed to rapidly shrink the pool of possible answers, even when the guessed word itself seems unlikely to be correct.

Scientists have devised a new way to switch magnetic computer memory while using far less energy than today's leading technologies. By mathematically optimizing the pulses used to flip digital bits, the method could reduce energy consumption by several orders of magnitude. Simulations suggest it may bring future memory devices surprisingly close to the fundamental physical limit for processing information. The same idea could eventually work with electrical currents or ultrafast lasers.

Harvard researchers have transformed ordinary knitting into a platform for creating fabrics that can snap between different shapes and perform useful functions. Using elastic yarns and industrial knitting techniques, the team engineered thick textiles that naturally curve and lock into multiple stable configurations, much like a light switch flipping between on and off. By adding conductive yarn, they turned these shape-shifting fabrics into soft electronic switches capable of controlling […]