During the 16th and 17th centuries, mathematicians developed a wealth of new ideas but had not carefully employed accurate definitions, proofs, or procedures to document and implement them. However, in the early 19th century, mathematicians began to recognize the need to precisely define their terms, to logically prove even obvious principles, and to use rigorous methods of manipulation. The Foundations of Mathematics presents the lives and accomplishments of 10 mathematicians who lived between CE 1800 and 1900 and contributed to one or more of the four major initiatives that characterized the rapid growth of mathematics during the 19th century: the introduction of rigor, the investigation of the structure of mathematical systems, the development of new branches of mathematics, and the spread of mathematical activity throughout Europe. This readable new volume communicates the importance and impact of the work of the pioneers who redefined this area of study.