Mathematics

Imaginary Numbers May Be Essential for Describing Reality

Quanta Magazine: 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. All the numbers on the number line, when squared, yield a positive number;…

Mathematicians Set Numbers in Motion to Unlock Their Secrets

Quanta Magazine: Joseph Silverman remembers when he began connecting the dots that would ultimately lead to a new branch of mathematics: April 25, 1992, at a conference at Union College in Schenectady, New York. It happened by accident while he was…

Complex light waves measure hidden objects

Physics World: Researchers in Europe have developed a technique for obtaining accurate laser-based measurements of objects hidden behind complex scattering structures. They say that their mathematical formula, which calculates the optimal waveform needed for the scattering environment, can also be applied…