This chapter continues the discussion began in Chapter α. It presents the fourth and final part of author's response to the question, “What is it you do in number theory, anyway?” Here he deals with the Birch–Swinnerton–Dyer (BSD) conjecture. The BSD conjecture was the guiding problem for the first part of his career and has the distinction of being one of the seven Clay Millenium Prize Problems, whose solution carries a million dollar price tag. The BSD conjecture is an attempt to discern order in the apparently unpredictable nature of solutions to elliptic curves, following Hasse's theorem, which places strict limits on the numbers of approximate solutions for varying p.
Iwasawa theory and BSD conjecture