The cosmos may have something in common with a doughnut. In addition to their fried, sugary goodness, doughnuts are known for their shape, or in mathematical terms, their topology. In a universe with ...

The field of complex geometry, intertwined with Lie theory, represents a vibrant area where algebraic and differential techniques converge to unravel the structure of complex manifolds and their ...

Complex geometry and algebraic geometry are intertwined disciplines that investigate spaces defined by complex analytic structures and polynomial equations. Complex geometry focuses on complex ...

Whether it’s a 3D printed robot chassis or a stained glass window, looking at a completed object and trying to understand how it was designed and put together can be intimidating. But upon closer ...

Its performance matches the smartest high school mathematicians and is much stronger than the previous state-of-the-art system. Google DeepMind has created an AI system that can solve complex geometry ...

There are theories about the structure of the universe, such as 'an open universe that continues to expand,' 'a closed universe that continues to contract,' and 'a flat universe that neither expands ...

DeepMind said its AlphaGeometry AI model was able to solve complex geometry problems at a level comparable to an Olympiad gold-medalist, showcasing the ability of AI models to use reasoning skills ...

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Reducing redundant information to find simplifying patterns in data sets and complex networks is a scientific challenge in many knowledge fields. Moreover, detecting the dimensionality of the data is ...