Explore the Katz-Grothendieck conjecture in this expository seminar from the Geometry, Arithmetic and Differential Equations of Periods (GADEPs) series. Delve into the modulo primes criterion for detecting linear differential equations with only algebraic solutions. Gain historical context through Kronecker's criterion for rationality of algebraic numbers and Schwarz's list of algebraic Gauss hypergeometric functions. Examine the main evidence supporting the conjecture, understanding its "P then Q" structure and the relative ease of proving "Q then P". Aimed at master's and Ph.D. students with basic knowledge of number theory and algebra, this talk provides valuable insights into an important mathematical conjecture.