The unsolvable Problem

MATH

The Unsolvable Problem

After a years-long intellectual journey, three mathematicians have discovered that a problem of central importance in physics is impossible to solve—and that means other big questions may be undecidable, too

By Toby S. Cubitt, David Pérez-García and Michael Wolf

• Kurt Gödel famously discovered in the 1930s that some statements are impossible to prove true or false—they will always be “undecidable.”
• Mathematicians recently set out to discover whether a certain fundamental problem in quantum physics—the so-called spectral gap question—falls into this category. The spectral gap refers to the energy difference between the lowest energy state a material can occupy and the next state up.
• After three years of blackboard brainstorming, midnight calculating and much theorizing over coffee, the mathematicians produced a 146-page proof that the spectral gap problem is, in fact, undecidable. The result raises the possibility that other important questions may likewise be unanswerable.