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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
January 26, 2026
Jan. 26, 2026 Researchers have demonstrated that quantum entanglement can link atoms across space to improve measurement accuracy. By splitting an entangled group of atoms into separate clouds, they were able to measure electromagnetic fields more precisely than ...
Jan. 25, 2026 A massive new study comparing more than 100,000 people with today’s most advanced AI systems delivers a surprising result: generative AI can now beat the average human on certain creativity tests. Models like GPT-4 showed strong performance on ...
Jan. 23, 2026 Blockchain could make smart devices far more secure, but sluggish data sharing has held it back. Researchers found that messy network connections cause massive slowdowns by flooding systems with duplicate data. Their new “Dual Perigee” method ...
Jan. 21, 2026 Scientists have discovered that the human brain understands spoken language in a way that closely resembles how advanced AI language models work. By tracking brain activity as people listened to a long podcast, researchers found that meaning unfolds ...
Jan. 20, 2026 Quantum computers could revolutionize everything from drug discovery to business analytics—but their incredible power also makes them surprisingly vulnerable. New research from Penn State warns that today’s quantum machines are not just ...
Jan. 19, 2026 Physicists have unveiled a new way to simulate a mysterious form of dark matter that can collide with itself but not with normal matter. This self-interacting dark matter may trigger a dramatic collapse inside dark matter halos, heating and ...
Jan. 17, 2026 Engineers have created a device that generates incredibly tiny, earthquake-like vibrations on a microchip—and it could transform future electronics. Using a new kind of “phonon laser,” the team ...
Jan. 17, 2026 Researchers have turned artificial intelligence into a powerful new lens for understanding why cancer survival rates differ so dramatically around the world. By analyzing cancer data and health system information from 185 countries, the AI model ...
Jan. 16, 2026 Humans pay enormous attention to lips during conversation, and robots have struggled badly to keep up. A new robot developed at Columbia Engineering learned realistic lip movements by watching its own reflection and studying human videos online. ...
Jan. 15, 2026 A new OLED design can stretch dramatically while staying bright, solving a problem that has long limited flexible displays. The breakthrough comes from pairing a highly efficient light-emitting material with tough, transparent MXene-based ...
Jan. 15, 2026 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 ...
Jan. 13, 2026 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 ...
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Jan. 11, 2026 Scientists have unveiled a new way to capture ultra-sharp optical images without lenses or painstaking alignment. The approach uses multiple sensors to collect raw light patterns independently, then ...
Jan. 9, 2026 Stanford researchers have developed an AI that can predict future disease risk using data from just one night of sleep. The system analyzes detailed physiological signals, looking for hidden patterns ...
Jan. 7, 2026 Researchers have built a new platform that produces ultrashort UV-C laser pulses and detects them at room temperature using atom-thin materials. The ...
Jan. 7, 2026 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 ...
Jan. 6, 2026 Scientists are learning to engineer light in rich, multidimensional ways that dramatically increase how much information a single photon can carry. This leap could make quantum communication more ...
Jan. 6, 2026 Researchers have created microscopic robots so small they’re barely visible, yet smart enough to sense, decide, and move completely on their own. Powered by light and equipped with tiny computers, ...
Jan. 6, 2026 A new chip-based quantum memory uses nanoprinted “light cages” to trap light inside atomic vapor, enabling fast, reliable storage of quantum information. The structures can be fabricated with ...
Jan. 4, 2026 New research shows that AI doesn’t need endless training data to start acting more like a human brain. When researchers redesigned AI systems to better resemble biological brains, some models ...
Jan. 3, 2026 Scientists have developed molecular devices that can switch roles, behaving as memory, logic, or learning elements within the same structure. The ...
Dec. 31, 2025 A philosopher at the University of Cambridge says there’s no reliable way to know whether AI is conscious—and that may remain true for the foreseeable future. According to Dr. Tom McClelland, ...