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.
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From Karen Hunger Parshall's review of The Rainbow of Mathematics (2000)Ivor Grattan-Guinness
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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.
Ivor Grattan-Guinness
Mathematical science is in my opinion an indivisible whole, an organism whose vitality is conditioned upon the connection of its parts. For with all the variety of mathematical knowledge, we are still clearly conscious of the similarity of the logical devices, the relationship of the ideas in mathematics as a whole and the numerous analogies in its different departments. We also notice that, the farther a mathematical theory is developed, the more harmoniously and uniformly does its construction proceed, and unsuspected relations are disclosed between hitherto separate branches of the science. So it happens that, with the extension of mathematics, its organic character is not lost but only manifests itself the more clearly.
David Hilbert
It is with Bernhard Riemann's work that we finally have the mathematical glasses to explore such worlds of the mind. And now my journey through the abstract world of 20th century mathematics has revealed that maths is the true language that the universe is written in. They key to understanding the world around us. Mathematicians aren't motivated by money and material gain, or even by practical applications of their work. For us it's the glory of solving one of the great unsolved problems that have outwitted previous generations of mathematicians. David Hilbert was right; it’s the unsolved problems of mathematics which make it a living subject. Which obsess each new generation of mathematicians. Despite all the things we've discovered over the last 7 millennia, there are still many things we don't understand. And its Hilbert’s call of "We must know, we will know" which drives mathematics.
Marcus du Sautoy
Necessary truth is merely the subject-matter of mathematics, not the reward we get for doing mathematics. The object of mathematics is not, and cannot be, mathematical certainty. It is not even mathematical truth, certain or otherwise. It is, and must be, mathematical explanation.
David Deutsch
He filled his writings with mathematical discoveries, and exhibited on every occasion the remarkable connection between mathematics and philosophy.
Plato
Grattan-Guinness, Ivor
Graves, Robert
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