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 ...

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, ...

A collaboration of a mathematician and a physicist has shown that the modular forms associated with elliptic curves with complex multiplications are expressed in terms of observables in superstring ...

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 ...

A new theory proposes that the universe’s fundamental forces and particle properties may arise from the geometry of hidden extra dimensions. These dimensions could twist and evolve over time, forming ...

Now, on to the subject of complex numbers. We have stayed away from this subject until now simply because we did not want to confuse things. Initially, it is easy to think of signals as “real valued.” ...

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, ...