We show how to learn low-dimensional representations (embeddings) of a wide range of concepts in medicine, including diseases (e.g., ICD9 codes), medications, procedures, and laboratory tests. We expect that these embeddings will be useful across medical informatics for tasks such as cohort selection and patient summarization. These embeddings are learned using a technique called neural language modeling from the natural language processing community. However, rather than learning the embeddings solely from text, we show how to learn the embeddings from claims data, which is widely available both to providers and to payers. We also show that with a simple algorithmic adjustment, it is possible to learn medical concept embeddings in a privacy preserving manner from co-occurrence counts derived from clinical narratives. Finally, we establish a methodological framework, arising from standard medical ontologies such as UMLS, NDF-RT, and CCS, to further investigate the embeddings and precisely characterize their quantitative properties.