Welcome to the Quanta Audio Edition.

In each of these bi-weekly episodes, we bring you a story direct from the Quanta website about developments in basic science and mathematics.

I'm Susan Vallett.

For decades, mathematicians have struggled to understand matrices that reflect both order

and randomness, like those that model semiconductors.

A new method could change that.

That's next.

Quantum Magazine is an editorially independent online publication supported by the

Simon's Foundation to enhance public understanding of science.

The mystery was this.

In the 1950s, a physicist at Bell Labs named George Fahare was injecting silicon with tiny quantities of other elements, such as phosphorus or arsenic.

When he put a little in, the electrons would move freely through the resulting material.

But as he added more, the material's internal

structure became more random, impeding the electrons' motion. Rather than happening gradually,

as one might expect, this obstruction occurred suddenly when the concentration passed a particular

point, trapping the electrons. Then their movement stopped entirely.

Jan Fiatorov, a physicist at King's College, London, says the material would be conducting and then

suddenly no longer conduct. The sharp change in behavior was reminiscent of phase transitions,

like the sudden freezing of water

at zero degrees Celsius. That was intriguing. Fiatorov says physicists love transitions. Soon,

Philip W. Anderson, another Bell Labs physicist, developed a model to describe the puzzling behavior.

He hoped to rigorously prove that his model behaved just as Feher's experiments had.

...