Daily quote by Langlands program

• At the heart of Langlands' program is the general notion of an "automorphic representation" π and its L-function L(s, π ) ... both defined via group theory and the theory of harmonic analysis on so-called adele groups ... The conjectures of Langlands ... amount (roughly) to the assertion that the other zeta-functions arising in number theory are but special realizations of these L(s, π ).
  Herein lies the agony as well as the ecstasy of Langlands' program. To merely state the conjectures correctly requires much of the machinery of class field theory, the structure theory of algebraic groups, the representation theory of real and p-adic groups, and (at least) the language of algebraic geometry. In other words, though the promised rewards are great, the initiation process is forbidding.
  • Stephen Gelbart, (1984) . "An elementary introduction to the Langlands program". Bull. Amer. Math. Soc. 10 (2): 177-219. DOI:10.1090/S0273-0979-1984-15237-6. (quote from p. 178)