There’s a Hidden Connection Between Pi and Quantum Mechanics


Jennifer Ouellette in Gizmodo:

Physicists have uncovered a hidden connection between a famous 350-year-old mathematical formula for pi, everyone’s favorite irrational number, and quantum mechanics. At least one mathematician has pronounced the discovery“a cunning piece of magic.”

The English mathematician John Wallis published his formula for calculating pias the product of an infinite series of ratios in 1655. In a paper published this week in the Journal of Mathematical Physics, University of Rochester physicists announced they had discovered the same formula popping out of their calculations of a hydrogen atom’s energy levels.

Wallis isn’t well known today outside of academic circles, but he rubbed elbows with some of the the greatest names in science in his era. Initially he intended to become a doctor when he started university at the tender age of 13, but he was far more interested in mathematics, and showed a knack for cryptography in particular. It began as just a hobby, but years later, he applied his skills deciphering coded Royalist dispatches on behalf of their political rivals, the Parliamentarians. (The two parties were in the midst of a civil war at the time.) Eventually he became part of the group of scientists who founded the Royal Society of London. There, his love of math blossomed into a bona fide academic pursuit.

Among his peculiar skills: he could perform complicated mental calculations in his head — something he did frequently, given his tendency toward insomnia. One such feat was recorded in the Society’s Philosophical Transactions in 1685: Wallis had calculated the square root of a 53-digits (27 digits in the square root) one sleepless night, and recorded it from memory the next morning.

More here.