number theory puzzle

Mathematicians have finally laid to rest the legendary mystery surrounding an elusive group of numerical expressions known as the "mock theta functions." Number theorists have struggled to understand the functions ever since the great Indian mathematician Srinivasa Ramanujan first alluded to them in a letter written on his deathbed, in 1920. Their new theory is proving invaluable in the resolution of long-standing open questions in number theory. In addition, the UW-Madison advance will for the first time enable researchers to apply mock theta functions to problems in a variety of fields.Working from Ramanujan's letter, number theorists believed that mock theta functions are related to a well-understood class of mathematical expressions-the 'theta' functions-that have been in use for centuries. Theta functions constitute a certain sequence of numbers that has proved useful in various problems of mathematical analysis. Mock theta functions similarly constitute an infinite series of numbers. But what has been completely baffling is what it is about mock theta series that make them so rich and powerful