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 ...

Complex geometry studies spaces that locally resemble complex coordinate systems and examines their intrinsic curvature and topological properties. Central to this field is Kähler geometry, where a ...

The grandest project in mathematics has received a rare gift, in the form of a mammoth 350-page paper posted in February that will change the way researchers around the world investigate some of the ...

To a nonmathematician, having the letter “i” represent a number that does not quite exist and is “imaginary” can be hard to wrap your head around. If you open your mind to this way of thinking, ...

Physicists construct theories to describe nature. Let us explain it through an analogy with something that we can do in our everyday life, like going on a hike in the mountains. To avoid getting lost, ...

Imaginary numbers are necessary to accurately describe reality, two new studies have suggested. Imaginary numbers are what you get when you take the square root of a negative number, and they have ...

Several years ago one of us, Toni, asked another of us, Marco, to come to his office at the Institute of Photonic Sciences, a large research center in Castelldefels near Barcelona. “There is a problem ...

In 1886 the mathematician Leopold Kronecker famously said, “God Himself made the whole numbers — everything else is the work of men.” Indeed, mathematicians have introduced new sets of numbers besides ...