Eigenvectors and invariant subspaces are also of interest beyond just mathematics—to take one example, it has been said that Google owes its success to " the $25 billion eigenvector." Discover the ...

When Lisa Piccirillo solved a decades-old mystery about the “Conway knot,” she had to overcome the knot’s uncanny ability to hoodwink some of the most powerful tools mathematicians have devised. Known ...

Informally, a dynamic system is any physical system that evolves with time (e.g., a pendulum, a planet orbiting the sun, the weather, etc). From a more mathematically precise perspective, one can ...

Two weeks ago, a modest-looking paper was uploaded to the arXiv preprint server with the unassuming title “On the invariant subspace problem in Hilbert spaces”. The paper is just 13 pages long and its ...

Knot theory investigates the embeddings of closed curves in three-dimensional space and employs algebraic structures to capture their essential features. At its core, the knot group, together with ...

A combination of transformations can sometimes be described using a single transformation, eg when a shape is transformed by two consecutive translations, the result can be expressed as a single ...