A pair of mathematicians has solved a problem that had tantalized number-theory researchers for more than 8 decades. It is the so-called final problem of the legendary Indian mathematical genius Srinivasa Ramanujan.
In the years before his death in 1920, Ramanujan studied theta functions, which are numerical relationships that show special symmetries. On his deathbed, Ramanujan wrote a letter to his British collaborator G. H. Hardy, in which he listed 17 complicated formulas for new functions. He called them mock theta functions because they had some properties similar to those of theta functions.
The first few pages of Ramanujan's letter were lost, and the surviving portion gives little indication of why Ramanujan grouped these functions. Since that time, the mock theta functions have cropped up in a surprising array of fields, including number theory, probability theory, and statistical mechanics. Yet mathematicians have puzzled over just what the 17 mock theta functi