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. Now, using mathematical techniques that emerged well after Ramanujan’s death, two number theorists at the University of Wisconsin-Madison have pieced together an explanatory framework that for the first time illustrates what mock theta functions are, and exactly how to derive them. 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, including physics, chemistry and several branches of mathematics. The findings appear in a series of three papers, the third appearing today in the Proceedings of the National Academy of Sciences. ‘It’s extremely gratifying to be able to say we solved the ‘final problem’ of Ramanujan,’ says co-author Ken Ono, UW-Madison Manasse Professor of Letters and Science, who is widely noted for contributions to number theory. […]