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, ...

The square root of a negative number could easily be regarded as a curious mathematical construction that has little bearing on real life. Indeed, the French polymath René Descartes gave such numbers ...

Scientists have found what they say is a link between complex number theory and string theory. A mathematician and physicist working together found the connection, which they say is part of plotting ...

In standard quantum mechanics, complex numbers are used to describe the wavefunction. Although this has so far proven sufficient to predict experimental results, there is no theoretical reason to ...

Imaginary numbers might seem like unicorns and goblins — interesting but irrelevant to reality. But for describing matter at its roots, imaginary numbers turn out to be essential. They seem to be ...

Using “refreshingly old” tools, mathematicians resolved a 50-year-old conjecture about how to categorize important functions called modular forms, with consequences for number theory and theoretical ...

The University of Colorado Center for Number Theory has interests spanning number theory, from analytic to algebraic. There is a focus on arithmetic geometry, including arithmetic dynamics, elliptic ...

String theory and number theory have common ground in a specific kind of elliptic curve, called a torus. Toruses aren't just for compressing atoms: these curves represent torus cross-sections. The ...