Language and terminology are so critical to the understanding of modern math- ematics that it is often difficult for even very good mathematicians from different fields to discuss their work in any detail. As a result, common phrases often evolve within each discipline which attempt to capture the avor of some impor- tant idea while avoiding technicality and jargon. For example, when algebraic number theorists are asked why they are so interested in modular forms, it has become common to say with enthusiasm that the coefficients of a modular form "encode arithmetic data". If pressed further, one might go on to say that the modular form gives rise to a Galois representation (in some cases via an elliptic curve).
McMurdy, Ken and Ravindran, Hari, "Do the Coefficients of a Modular Form Really "Encode Arithmetic Data"?" (2008). Mathematical Sciences Technical Reports (MSTR). 31.