In the first full-length biography of John William Dawson (1820-1899), eminent scientist and principal of McGill University, Susan Sheets-Pyenson highlights the extraordinary scope of Dawson's educational and scientific career and his commitment to science, rationality, and the advancement of knowledge.

John Bridge (d.1665), a widower with two sons, emigrated in 1631 from England to Cambridge, Massachusetts. In 1658 he married widow Eliza- beth Saunders, widow of Martin Saunders and earlier widow of Roger Bancroft; they had no children, and she married again after John's death. Descendants and relatives lived in New England, New York, New Jersey, Ohio, Indiana, Michigan, Illinois, Wisconsin, Minnesota and elsewhere. Includes some ancestry and relatives in England.

This monograph considers several well-known mathematical theorems and asks the question, “Why prove it again?” while examining alternative proofs. It explores the different rationales mathematicians may have for pursuing and presenting new proofs of previously established results, as well as how they judge whether two proofs of a given result are different. While a number of books have examined alternative proofs of individual theorems, this is the first that presents comparative case studies of other methods for a variety of different theorems. The author begins by laying out the criteria for distinguishing among proofs and enumerates reasons why new proofs have, for so long, played a prominent role in mathematical practice. He then outlines various purposes that alternative proofs may serve. Each chapter that follows provides a detailed case study of alternative proofs for particular theorems, including the Pythagorean Theorem, the Fundamental Theorem of Arithmetic, Desargues’ Theorem, the Prime Number Theorem, and the proof of the irreducibility of cyclotomic polynomials. Why Prove It Again? will appeal to a broad range of readers, including historians and philosophers of mathematics, students, and practicing mathematicians. Additionally, teachers will find it to be a useful source of alternative methods of presenting material to their students.

The work searches out the societal effects of varying philosophies of and causal relationships between the assumed judicial roles and the achievement of both stability and flexibility within the judicial system.

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