Cloud computing offers on-demand, scalable computing and storage, and has become an essential resource for the analyses of big biomedical data. The usual approach to cloud computing requires users to reserve and provision virtual servers. An emerging alternative is to have the provider allocate machine resources dynamically. This type of serverless computing has tremendous potential for biomedical research in terms of ease-of-use, instantaneous scalability, and cost effectiveness. In our proof of concept example, we demonstrate how serverless computing provides low cost access to hundreds of CPUs, on demand, with little or no setup. In particular, we illustrate that the all-against-all pairwise comparison among all unique human proteins can be accomplished in approximately 2 minutes, at a cost of less than $1, using Amazon Web Services Lambda. We also demonstrate the feasibility of our approach using Google Functions and show that the same task of pairwise protein sequence comparison can be accomplished in approximately 11.5 minutes. In contrast, running the same task on a typical laptop computer required 8.7 hours.