Ivor Grattan-Guinness

"Mathematics occupies a peculiar position in cultural life today. Everybody knows that it is one of the most basic, and also ancient, types of knowledge; yet it is not part of normal cultural discourse, and few people know much about its historical development, or even that it has a history."

"The great historian of logic and mathematics Ivor Grattan-Guinness passed away about a month ago, aged 73. ... Ivors work and scholarship spans over an impressive range of topics and areas, and is bound to continue to influence many generations of scholars to come. It is a great loss."

"Mathematics is one of the most basic -- and most ancient -- types of knowledge. Yet the details of its historical development remain obscure to all but a few specialists."

"Operations research has many precursors and allied fields, including Taylorism (after Frederick W. Taylor), scientific management and management science, industrial engineering and systems analysis. As one early textbook explained, the roots of OR "are as old as science and the management function. Its name dates back only to 1940" (Churchman et al. 1957: 3). Certainly its practitioners have expended much energy and ink in search of an acceptable definition of OR. Morse tried unsuccessfully to halt the debate by declaring OR to be the activity carried on by members of the Operations Research Society (Morse 1953: 159) But his colleagues were not so easily dissuaded from debate. Much of the concern with definition focused on the sometimes elusive distinctions between OR and neighbouring fields; the attempt to define, or redefine, OR was also born of the desire to allow the subject to evolve beyond the orthodoxy of wartime experience. Crucial considerations included the balance between model and application, and the complexity of the mathematics involved."

"It [ non-Euclidean geometry ] would be ranked among the most famous achievements of the entire [nineteenth] century, but up to 1860 the interest was rather slight."

"The teaching of axioms should come after conveying the theory in a looser version."

"Non-Newtonian calculi... have considerable potential as alternative approaches to traditional problems."

"In addition, the teaching of theories from axioms, or some close imitation of them such as the basic laws of an algebra, is usually an educational disaster."

"Grattan-Guinness has achieved a synthesis here of remarkable historical and mathematical scope and sensitivity. His book is a must read for historians of science and mathematics, as well as mathematicians."

"Grattan-Guinesss uniformly interesting and valuable account of the interwoven development of logic and related fields of mathematics . . . between 1870 and 1940 presents a significantly revised analysis of the history of the period. . . . [His] book is important because it supplies what has been lacking: a full account of the period from a primary mathematical perspective."