A standard formula for pi has been Found Hidden in Hydrogen Atoms

For the 1st time, scientists have exposed a classic formula for pi in the world of quantum physics. Pi is the ratio between a circle's perimeter and its diameter, and is incredibly significant in pure mathematics, but now scientists have also establish it "lurking" in the world of physics, when using quantum workings to contrast the energy levels of a hydrogen atom.

Why is that exciting? Well, it reveals an very special and previously unknown link between quantum physics and maths.
"I find it charming that a purely arithmetical formula from the 17th century characterises a physical system that was exposed 300 years later," said one of the guide researchers, Tamar Friedmann, a mathematician at the University of Rochester in the US. Gravely, wow.
The finding was made when Carl Hagen, a particle physicist at the University of Rochester, was education a class on quantum workings and explaining to his student how to use a quantum mechanical technique known as the difference principle' to estimated the energy states of a hydrogen atom.
While comparing these principles to conventional calculations, he noticed an strange trend in the ratios. He ask Friedmann to help him work out this trend, and they fast realised that it was in fact a sign of the Wallis formula for pi – the first time it had even been resulting from physics.
"We weren't look for the Wallis formula for pi. It presently fell into our laps," said Hagen. "It was a complete surprise," additional Friedmann. "I jumped up and downward when we got the Wallis formula out of equations for the hydrogen atom."
Since 1655 there have been abundance of proofs of Wallis's formula, but every one have come from the world of mathematics, and the latest results have people freaking out. The consequences have been published in the Journal of Mathematical Physics.This roughly seems like magic," writes maths contributor Kevin Knudson for Forbes. "That a formula for π is hidden within the quantum mechanics of the hydrogen atom is astonishing and delightful."
"Nature had reserved this secret for the last 80 years," said Friedmann. "I'm glad we exposed it."
We just can't help but speculate what other secret connections are lurk between quantum mechanics and clean mathematics.