Euler’s Constant
Everyone has heard about the number ?, everyone who has taken calculus has heard
about the number e, but there’s a third important number in mathematics that fewer
people have heard about: ? (called gamma, or Euler’s constant). This number, whose
decimal expansion starts out as 0.5772156…, was discovered nearly three centuries
ago when Euler was investigating properties of the harmonic numbers
Hn=1+1/2+1/3+?+1/n. Despite its age, many basic questions about ? remain unsolved.
We will discuss the history of ?, how it can be computed, its connections to
different areas of mathematics, and a long-standing open question about its
(ir)rationality.