Two vectors close vectorA vector quantity has both direction and magnitude (size). are parallel if they have the same (or opposite) directions. Their magnitude can be different. In the image to the ...

An AI from Google DeepMind can solve some International Mathematical Olympiad (IMO) questions on geometry almost as well as the best human contestants. How does ChatGPT work and do AI-powered chatbots ...

The International Mathematical Olympiad (IMO) is a prestigious competition featuring talented high school students from around the world, in which competitors solve complicated mathematical problems.

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 ...

Vector bundle theory in algebraic geometry examines algebraic families of vector spaces parametrised over the points of algebraic varieties, extending familiar notions such as tangent bundles and line ...