Mock theta functions to mock theta conjectures

Abstract

Mathematical genius Srinivasa Ramanujan's second last gift to the mathematicians was his ingeneous discovery of the mock theta functions of order third, fifth and seventh. Earlier it was considered that mock theta functions were last ideas discovered by Ramanujan, but it is recently investigated and established that his last discovery was cranks - not mock theta functions [7:28]. Here, we discuss in brief about developments as well as advancements on mock theta functions during last more than ninety years, and its further extensions to ``mock theta conjectures". The summary of two known proof for the ``mock theta conjectures" given by Hickerson [9] and Folsom [1] respectively, are also discussed.