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The Invention of Infinity: Mathematics and Art in the Renaissance, by J. V. Field
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As any student of art will tell you, one of the chief accomplishments of the Renaissance was the development of perspective in painting--the introduction of spatial perception that led to the legendary beauty and majesty of works by Giotto, Botticelli, and da Vinci. In The Invention of Infinity, Dr. J. V. Field, a noted historian on math and the arts, tells the remarkable story of how the "practical" mathematics of Renaissance artists actually influenced the development of "proper" mathematics--a true story of life imitating art.
Here is the fascinating history of the emergence of modern mathematics during the Renaissance, and its intimate relationship with the artisan and artistic traditions of the time. The book covers the period from 1300 to 1650, when craftsmen were educated in "practical mathematics," and when the field of mathematics was gradually taking up a more significant place on the intellectual landscape. Field traces the influence of the mathematics of perspective in the arts, and shows how this led to the invention of a new kind of geometry in the 17th century--the new projective geometry of Desargues--which proved to be a highly significant contribution to the development of modern mathematics. Additionally, the author explores the 14th and 15th-century "abacus" schools popular among merchants and craftsmen, and the contrast between these practical, widely used tools and the abstract arithmetic and geometry taught in the universities of the time, and their application in the theory of music and elementary astronomy.
Extensively illustrated with superb color and black and white plates, and including selected extracts from the original mathematical texts, this clear and entertaining account will delight anyone interested in the history of mathematics and art, as well as in the multi-layered social history of the Renaissance.
- Sales Rank: #582839 in Books
- Published on: 1997-05-22
- Original language: English
- Number of items: 1
- Dimensions: 10.00" h x .95" w x 7.75" l, 1.55 pounds
- Binding: Hardcover
- 264 pages
Review
`Compelling book...lavishly illustrated book. Mathematics and arts are clearly equally delightful for Field, and she transmits that enjoyment to the reader.' The Times
`Field's book is indeed a shot of adrenaline in the timid arm of Renaissance art history. Trained as both an art historian and a mathematician, Field plunges right in with a rigorous analysis of the fifteenth-century Italian painter Piero della Francesca's manuscript treatises on mathematics.' Nature
About the Author
About the Author:
Dr. J.V. Field is a Research Fellow in the Department of the History of Art at Birkbeck College, University of London.
Most helpful customer reviews
6 of 6 people found the following review helpful.
Charming art, charming mathematics, unfocused exposition
By Viktor Blasjo
Renaissance artists learned how to draw perspective images. Perhaps the realisation of how to draw checkered floors sparked the development. Then one learned to draw perspective views of cubes and prisms and such. By approximation, these techniques could be of use when drawing more complex bodies and well, but apparently many artists preferred mechanical tricks instead (eye line strings, reference grids, etc.). Indeed, the mathematical sophistication of the Renaissance artists should not be over stated; a detailed 15-page analysis of one of the most celebrated perspective frescos, Masaccio's Holy Trinity, fails to reveal much mathematical depth ("we are dealing with a painting not a theorem"; p. 59). A notable exception is Piero della Francesca, who was a competent mathematician and wrote his time's most sophisticated treatise on perspective, earning him 50 pages here, but even he compromised mathematical precision in some of his paintings. The convergence of mathematics and art was at least as fruitful in the other direction. Desargues saw the importance of the idea of perspectivity in geometry, where it unifies the theory of conics and paves the way for essentially projective theorems such as "Desargues' Theorem".
This is basically a scholarly book, but at times one gets the impression that Field is more interested in showing off pretty pictures and telling amusing side stories rather than explaining the development of ideas on perspective in a clear and structured manner. One of the largest images is a full page reproduction of Titian's portrait of Ranuccio Farnese (p. 153), which has nothing to do with perspective except that the subject once had a book dedicated to him. Why not use the space for more relevant paintings instead? For example, Piero della Francesca's An Ideal Town would go beautifully with the discussion of his perspective treatise. Discussing Taylor's work on perspective, Field remarks that Taylor introduced the term "vanishing point" but then says "Taylor does not quite explain what is supposed to vanish at the vanishing point ... The readers he was addressing were presumably not expected to be so literal minded as to ask that question" (p. 229). I would say that more probably the readers were not expected to be so stupid as to fail to grasp this very simple concept by themselves; but that aside: if Field had wanted to explain ideas rather than to poke fun at people, she could simply have quoted from Taylor's 1719 edition, where, on page 15, he explains: "the further any object is off, upon any line, the smaller is its projection ... and when it comes to this point, its magnitude vanishes, because the original object is at an infinite distance. This is easily conceived by imagining a man to be going from you in a long walk, who appears to be smaller and smaller, the further he goes." (Incidentally, this would also have made clear that, to Taylor at least, a vanishing point is not the same as a centric point, as Field mistakenly implies.)
6 of 8 people found the following review helpful.
Great scholarship!
By Helmer Aslaksen
This is the ideal book for anybody who wants to really understand how painting lead to the birth of projective geometry. It's a sholarly book, and at times it requires some effort on your part, but you will be highly rewarded in the end!
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