It turns out that imaginary numbers aren’t really needed for quantum mechanics.

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, ...

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.” ...

Mathematicians were disturbed, centuries ago, to find that calculating the properties of certain curves demanded the seemingly impossible: numbers that, when multiplied by themselves, turn negative.

In the third century BCE, Apollonius of Perga asked how many circles one could draw that would touch three given circles at exactly one point each. It would take 1,800 years to prove the answer: eight ...

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 ...