Datacenter disaggregation provides numerous benefits to both the datacenter operator and the application designer. However switching from the server-centric model to a disaggregated model requires developing new programming abstractions that can achieve high performance while benefiting from the greater elasticity. To explore the limits of datacenter disaggregation, we study an application area that near-maximally benefits from current server-centric datacenters: dense linear algebra. We build NumPyWren, a system for linear algebra built on a disaggregated serverless programming model, and LAmbdaPACK, a companion domain-specific language designed for serverless execution of highly parallel linear algebra algorithms. We show that, for a number of linear algebra algorithms such as matrix multiply, singular value decomposition, Cholesky decomposition, and QR decomposition, NumPyWren's performance (completion time) is within a factor of 2 of optimized server-centric MPI implementations, and has up to 15% greater compute efficiency (total CPU-hours), while providing fault tolerance.