Counting in Higher Algebra

Higher algebra is concerned with extending the integers to new domains of counting, specifically the so-called stable homotopy groups of spheres, which encode rich information about algebraic, geometric, and topological objects. Determining these groups proves to be a fundamental and immensely difficult problem in mathematics. In this paper, we describe the chromatic approach to this problem and its connection to arithmetic geometry, which allows for the confirmation of a 50-year-old prediction.