Prime Numbers and the Riemann Hypothesis by Barry Mazur and William Stein

摘要

What makes a math problem “great”? Antiquity, difficulty, and partial progress over time toward a resolution are certainly attributes that come to mind. A great conjecture should stimulate new ideas in mathematics. It should have many corollaries. It should possess some kind of intrinsic naturality and have connections to one or more basic mathematical objects. When the solution to a great problem is finally found, it contains revolutionary ideas and breeds new questions, reveals new vistas for mathematics, and suggests new approaches in old areas. The problem and its solution inevitably have many generalizations.