Physicists have discovered a jewel-like geometric object that dramatically simplifies calculations of particle interactions and challenges the notion that space and time are fundamental components of ...

Integral geometry and valuation theory form a dynamic field at the intersection of geometric analysis and algebraic topology. This discipline addresses the study of measures – known as valuations – ...

Computer programs can handle all sorts of data, from sums of money in bank accounts to sensor readings from scientific instruments. In many cases, the data are a set of discrete elements, such as ...

Three music professors have devised a new way of analyzing and categorizing music that takes advantage of the deep, complex mathematics they see enmeshed in its very fabric. Writing in Science, they ...

Below left: The figure shows how geometrical music theory represents four-note chord-types -- the collections of notes form a tetrahedron, with the colors indicating the spacing between the individual ...

Arnold’s work was in an area of mathematics that concerns all the different configurations a physical system like bouncing billiard balls or orbiting planets can take. These configurations are encoded ...