"Science and the Modern World (...SMW...) was one of the first products of Whitehead's professional philosophical career... The book was a popular muse upon philosophical and cultural aspects of science, including mathematics... He used historical examples and situations quite regularly, but the historical background was itself popular, based upon his reading of others rather than personal investigation. ...the second chapter, entitled 'Mathematics as an element in the history of thought' ...Whitehead was influenced by the mathematical logic and philosophy of mathematics that he had developed with Bertrand Russell in Principia Mathematica... at the same time of SMW a second editing [of Principia] was being prepared, by Russell alone... When the first edition was finished, Whitehead had written an article on mathematics for the Encyclopedia Britannica... and a popular book Introduction to Mathematics... and they too left some mark on SMW, especially the chapters of the book on variables, periodicity, and trigonometry. In the intervening years he had worked quite notably on mathematics education..."
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Ivor Grattan-Guinness, "Mathematics and Philosophy", La science et le monde moderne d'Alfred North Whitehead? (2006)
https://en.wikiquote.org/wiki/An_Introduction_to_Mathematics
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An Introduction to Mathematics
An Introduction to Mathematics, by Alfred North Whitehead and published in 1911, was intended for a general lay audience. The book touches upon the nature, unity and internal structure of mathematics and its applications toward describing and understanding natural phenamena. It foreshadows some points of Whitehead's later work in philosophy and metaphysics.
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