Johannes Rydberg was born in Halmstad, Sweden, and educated at Lund University, where he received a PhD in 1879. The next year he started teaching mathematics there and stayed at Lund for the rest of his life, taking the chair of physics in 1901.

All of Rydberg's work arose from his interest in the periodic classification of the elements introduced by Dmitri Mendeleev. Rydberg's great intuition was that the periodicity was a result of the structure of the atom. His first research was into the relationship between the spectral lines of elements. In 1890 he found a general formula giving the frequency of the lines in the spectral series as a simple difference between two terms. His formula for a series of lines is:

ν = R(1/m ² – 1/n ²)

where n and m are integers. The constant R is now known as the Rydberg constant.

In the early 1900s Rydberg continued to work on the periodic table, reorganizing it, finding new mathematical patterns, and even casting it into spiral form. In the main his theoretical work was confirmed by Henry Moseley's discovery that the positive charge on the nucleus gave a better periodic ordering than the atomic weight.