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Algebraic geometry
Algebraic geometry is a branch of mathematics which, combines abstract algebra, especially commutative algebra, with geometry. It can be seen as the study of solution sets of systems of polynomials. When there is more than one variable, geometric considerations enter and are important to understand the phenomenon. One can say that the subject starts where equation solving leaves off, and it becomes at least as important to understand the totality of solutions of a system of equations as to find some solution; this does lead into some of the deepest waters in the whole of mathematics, both conceptually and in terms of technique.
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Computers & Math News
September 16, 2026
Sep. 15, 2026 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 ...
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Sep. 13, 2026 Researchers have experimentally demonstrated the optical Magnus effect for the first time, revealing that a tightly focused laser interacts most strongly with an atom slightly away from the beam’s center. The unexpected shift is similar to the ...
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Sep. 12, 2026 Researchers at Harvard have demonstrated a way to protect quantum information using microscopic sound waves. By continuously surrounding a diamond-based qubit with mechanical vibrations, they extended its coherence time by roughly threefold. The ...
Sep. 12, 2026 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 ...
Sep. 11, 2026 Scientists have created an ultra-small nanolaser that could eventually allow microchips to transmit information with light instead of electricity, potentially making computers faster while cutting energy use roughly in half. Thousands of the lasers ...
Sep. 11, 2026 Researchers have found a way to perform certain quantum operations more than 1,000 times faster, cutting thousands of repeated control cycles down to just one. The advance could reduce errors and bring reliable, fault-tolerant quantum computers ...
Sep. 7, 2026 A more realistic quantum model has revealed evidence that strange, nearly immobile quasiparticles called fractons could exist in solid materials. Their inability to move freely could make them promising building blocks for unusually robust quantum ...
Sep. 6, 2026 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, ...
Sep. 6, 2026 Princeton researchers have tested an AI system that can monitor and control fusion plasma in milliseconds, reacting far faster than a human operator. In one experiment, it predicted a damaging instability about 200 milliseconds before it appeared ...
Sep. 4, 2026 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 ...
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Sep. 4, 2026 MIT researchers have created bacterial “transistors” that can be wired together into living circuits capable of performing calculations and directing chemical signals. One day, these biological ...
Sep. 3, 2026 Scientists at Carnegie Mellon University have discovered an unexpected form of the Hall effect, overturning the long-held assumption that this electrical response only appears when a magnetic field ...
Aug. 31, 2026 Scientists have uncovered hidden complexity inside two ultrathin superconductors that seemed much simpler than they really are. Niobium diselenide and tantalum disulfide appeared to have a single ...
Aug. 31, 2026 Physicists have demonstrated a new way to entangle distant quantum bits without the constant measurements and active control normally required. The team created a “quantum bath,” a shared ...
Aug. 30, 2026 Physicists have mathematically captured a bizarre “spacetime crystal” that can either dissolve or collapse into a microscopic black hole after only a tiny change in energy. Their breakthrough ...
Aug. 30, 2026 IBM and University of Chicago researchers have completed a quantum computation that leading classical methods could not practically reproduce. The system used 70 error-corrected logical qubits and ...
Aug. 27, 2026 Researchers used AI to search through more than 100 million possible settings for 3D-printing a high-performance NASA alloy. After only 40 ...
Aug. 27, 2026 Scientists have found a surprising way to potentially switch on an unusual form of magnetism in ruthenium dioxide, a material that normally appears ...
Aug. 26, 2026 NASA has successfully tested a system that allows satellites to navigate without GPS by using other spacecraft and debris as landmarks in orbit. In just three days, FALCON also improved the known ...
Aug. 24, 2026 Researchers have created a tiny chip that produces a stable “rainbow” of light capable of generating multiple high-frequency signals at once, potentially boosting the speed and capacity of future ...