Henry Lin, a physicist at Princeton University, gives a technical review of the BFSS conjecture as part of the Institute for Advanced Study's Prospects in Theoretical Physics 2026 program. The BFSS conjecture proposes that a particular matrix quantum mechanics model, in a suitable limit, reproduces M-theory, the eleven-dimensional framework thought to unify the various string theories. Lin walks through the construction of the matrix model, the degrees of freedom it describes, and the evidence accumulated over the past decades for and against the conjecture holding in its strongest form. The talk is aimed at researchers already comfortable with string theory and supersymmetric quantum mechanics, tracing how the conjecture connects to gauge-gravity duality and to ongoing numerical and analytic tests. As the first part of a longer review, it lays out the conceptual groundwork before moving toward more recent developments and open problems in later sessions.