The Norton History of the Mathematical Sciences (The Norton History of Science) by Ivor Grattan-Guinness (PDF)

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Beginning with the Babylonian and Egyptian mathematicians of antiquity, The Norton History of the Mathematical Sciences charts the growth of mathematics, through its refinement by ancient Greeks and medieval Arabs, to its systematic development by Europeans from the Middle Ages to the early twentieth century.

User’s Reviews

Editorial Reviews: Amazon.com Review From zero to infinity, mathematics has always been more about thoughts than thinkers. Professor Ivor Grattan-Guinness has chosen to focus on concepts, rather than the geniuses who first articulated them, in The Norton History of the Mathematical Sciences, and this new retelling brings a freshness to what had formerly seemed a dry subject. He certainly hasn’t neglected great mathematicians–Pythagoras and Ramanujan each get their due–but his real heroes are number theory, algebra, and their cousins. Grattan-Guinness isn’t afraid of his subject, and he expects the same of his readers; in fact, he knits equations into his narrative rather than setting them apart like most other math books. Much of the History covers the explosive developments of the 19th century, when mathematics matured and diversified beyond Euclid’s wildest dreams, though of course there is also extensive material on mathematics from other times, from the ancient world to the present. Scholarly and well-organized, the book is intended more for research and exploration than straight-through reading, but the author’s lucid prose occasionally makes it difficult to stop reading. Mathematics underlies all of modern science; read The Norton History of the Mathematical Sciences to get a grasp on the deepest infrastructure of our times. –Rob Lightner Review Grattan-Guinness has achieved a synthesis here of remarkable historical and mathematical scope and sensitivity. — Professor Karen Hunger Parshall, editor of Historia Mathematica About the Author Ivor Grattan-Guinness is professor of the history of mathematics and logic at Middlesex University, England. Read more

Reviews from Amazon users which were colected at the time this book was published on the website:

⭐In memoriamIvor Grattan-Guinness23 June 1941–12 December 2014It is always interesting to look backward. This volume offers much of value– in that endeavor– where mathematics is concerned. Reading the dust-jacket: “Grattan-Guinness emphasizes the complex interrelations between applications in both theoretical and practical aspects.“ Ivor Grattan-Guinness has a gift for clarity of prose, he writes: “major changes in historical interpretation are recorded here.“ (preview of the rainbow).(1) Probability, in the Bayesian way… “generated a new approach which has always excited adherence and dissent in large measures.” (page 339).(2) Not only did he pen a now-famous paper predating the black-hole concept (1783), astronomer John Michell did the same with his Bayesian approach to astronomy, writing a paper (1767) on “probable parallax.” (page 341).(3) Of France and education, read: “the need to balance civil and military requirements led to political controversies…” (page 348). Read more of the Ecole Polytechnique in chapter seven.(4) Grattan-Guinness writes: “Gauss’ influence could have been greater, his paper of 1813 on infinite series slept for 20 years.” (page 355).(5) Happily, the web makes available for study many gems of the past, books which were influential in their own day. You can find, and read online, these three textbooks: Traite du calcul differentiel et du integral (Lacroix, 1797), Resume des lecons (Cauchy, 1823) and Traite analytique (Laplace, 1812). These books are referred to on pages 365, 376 and 382 respectively. Even if you do not read the French language, the mathematics is understandable.(6) Disputes about priority: Farkas Bolyai had a son, Janos, who published in the topic of non-Euclidean geometry. Janos and Gauss were at odds regards priority, learn that “Janos was so upset that he never published in mathematics again.” (page 401).(7) Cauchy “avoided geometrical styles which restricted his development of function theory.” (page 407).(8) Complex numbers: “over the centuries, algebraists had heaped opprobrium upon them“ and “our standard words ‘imaginary’ and ‘complex’ carry an aroma of disapproval.” (page 420).(9) About Grassmann: “he spoilt the communication of his innovations by obscure exposition.” (page 424).(10) Allow me to end in 1908, with the publication of a treatise by Burkhardt (in German): Mathematischen Physik. Read “Burkhardt is an unsurpassable 1800-page survey of the pertaining mathematical methods, the transition to the more international scene is especially well-done.” (page 437). You can peruse a copy of that treatise (archive.org).(11) Concluding: There is a 25-page bibliography. There is a 25-five page Index. There is much to keep one entertained in this single-volume history. Many of the primary source-works which Grattan -Guinness references are now available on the web. I have merely scratched the surface, hopefully the prospective reader will dig deeper and discover the works of the masters.Highly recommended.

⭐As America becomes increasingly and ever more disturbingly innumerate, with perhaps no more than 1-2% (if that much) of the population conversant in basic mathematics through trigonometry, one way of creating a portal through which mathphobic individuals might ease into serious study of the queen of the sciences is reading a well written history. Mathematics is the language in which the universe’s laws are written, so it is hardly possible to overstate the subject’s importance. Yet we live in an era when the authors of science books are instructed not to include a single equation because a publishing law has it that every equation reduces sales by 50% (thus 2 equations reduce sales by 75%). Some of the densest, most abstruse physics books I’ve ever read were made nearly incomprehensible by the lack of a single clarifying equation. In a traditionally anti-intellectual society such as America, where reading is frowned upon as geekish and in some quarters of the nation as anti-American, we are at a double disadvantage. This Norton History of the Mathematical Sciences is beautifully written, never sacrificing clarity while confronting some of the most abstract branches of mathematics head-on.Beginning with the nearly invisible origins of the subject in the dim mists of time as a central part of thought itself, we are led into a labyrinth of conjecture emerging into the ancient world and the well documented mathematical innovations of Babylon, Egypt and Greece. The great Arabic contribution, and their transmittance of lost ancient knowledge through Spain during the magnificent Iberian Renaissance, eventually results in the birth of modern mathematics beginning in Renaissance Italy, France, Germany and England. From there, this history begins to focus on the individuals whose names, though sometimes obscure, are known and whose contributions cause an explosive growth in the subject beginning in the 16th Century. New avenues of thought are discovered and old problems solved. The invention of the Calculus by Leibniz and Newton is a prime example of those two paths of intellectual endeavor. The following roll call of names reads like an all-star team of mathematical greatness and innovation: Euler, Bernoulli, Lagrange, Laplace, Gauss, Cauchy, Fourier, Abel, Galois, Riemann, Cayley, Weierstrass, Dirichlet, Lie, Hilbert, Poincare, Hardy. All of them, and many others, are responsible for the magnificent avenues of abstract thought that constitute modern mathematics. Grattan-Guinness does a masterful job in explaining the growth in knowledge, never dumbing down, always clear and succinct, not afraid to include some mathematical terms if the subject demands it.This book is part of what was originally meant as a multi-volume Norton history of science. Previous volumes include a superb history of astronomy and cosmology and one of chemistry. Unfortunately, those two have fallen out of print and are well worth tracking down. The present History of Mathematics may disappear as well, so I suggest that you pounce. It is a fine overview of this glorious subject, worthy of comparison with some of the great histories of the past.Mike Birman

⭐An excellent read, comprehensive in scope. Not a textbook.

⭐This magnificent work covers mathematics from its recorded beginnings to the end of World War I. It provides remarkable insight into the development of the various branches of mathematics, and into the connections between mathematical and scientific ideas. Readers will find a wealth of interesting and useful information, including a superb bibliography. Highly recommended!

⭐This milestone in the history of mathematics-history covers mathematics from its recorded beginnings to the end of World War I. It is a synthesis of remarkable historical and mathematical scope. Professor Grattan-Guinness has established a new paradigm of excellence in the field of mathematics-history.

⭐This much-needed book provides valuable insights into the history of the mathematical sciences. Readers will find a wealth of interesting and useful information, including an excellent bibliography. Highly recommended!

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