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 ...

Algebraic geometry and the theory of complex manifolds together form a foundational pillar of modern mathematics, interweaving geometric intuition with algebraic precision. Algebraic geometry studies ...

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A forgotten number system invented in the 19th century may provide the simplest explanation for why our universe could have 10 dimensions As children, we all learn about numbers. We start with ...

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.

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 ...

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, ...