- 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.
- Companion Encyclopedia of the History and Philosophy of the Mathematical Sciences, Volume 1, page 3, 2003
- Non-Newtonian calculi... have considerable potential as alternative approaches to traditional problems.
- "Non-Newtonian Calculus," Middlesex Math Notes (Middlesex University, England), 1977
The Rainbow of Mathematics: A History of the Mathematical Sciences (2000) 
- From the 3rd century onwards, orthodox Christianity, based on a Hebrew story and worshipping the Jew Jesus, also led many campaigns of anti-Semitism.
- p. 127
- 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.
- p. 400
- 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.
- p. 739
- The teaching of axioms should come after conveying the theory in a looser version.
- p. 740
Quotes about Ivor Grattan-Guinness 
- 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.
- From Karen Hunger Parshall's review of The Rainbow of Mathematics (2000)
- Grattan-Guiness's 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.
- From James W. Van Evra's review in Isis of The Search for Mathematical Roots 1870-1940
- Encomium at Mathematical Sciences Foundation.