Volume 1 of the first authoritative translation of Archimedes' works into English.

This is the second volume of the first fully-fledged English translation of the works of Archimedes - antiquity's greatest scientist and one of the most important scientific figures in history. It covers On Spirals and is based on a reconsideration of the Greek text and diagrams, now made possible through new discoveries from the Archimedes Palimpsest. On Spirals is one of Archimedes' most dazzling geometrical tours de force, suggesting a manner of 'squaring the circle' and, along the way, introducing the attractive geometrical object of the spiral. The form of argument, no less than the results themselves, is striking, and Reviel Netz contributes extensive and insightful comments that focus on Archimedes' scientific style, making this volume indispensable for scholars of classics and the history of science, and of great interest for the scientists and mathematicians of today.

Many of the things you know about science began with Archimedes. What was so unusual about a man who spent almost his whole life on one small island, more than two thousand years ago? Many things about Archimedes were unusual. His mind was never still, but was always searching for something that could be added to the sum of things that were known in the world. No fact was unimportant; no problem was dull. Archimedes worked not only in his mind, but he also performed scientific experiments to gain knowledge and prove his ideas.

Published 1880-1, this three-volume edition of Archimedes' extant works in Greek includes commentaries and parallel Latin translation.

This radical, profoundly scholarly book explores the purposes and nature of proof in a range of historical settings. It overturns the view that the first mathematical proofs were in Greek geometry and rested on the logical insights of Aristotle by showing how much of that view is an artefact of nineteenth-century historical scholarship. It documents the existence of proofs in ancient mathematical writings about numbers and shows that practitioners of mathematics in Mesopotamian, Chinese and Indian cultures knew how to prove the correctness of algorithms, which are much more prominent outside the limited range of surviving classical Greek texts that historians have taken as the paradigm of ancient mathematics. It opens the way to providing the first comprehensive, textually based history of proof.

Making up Numbers: A History of Invention in Mathematics offers a detailed but accessible account of a wide range of mathematical ideas. Starting with elementary concepts, it leads the reader towards aspects of current mathematical research. The book explains how conceptual hurdles in the development of numbers and number systems were overcome in the course of history, from Babylon to Classical Greece, from the Middle Ages to the Renaissance, and so to the nineteenth and twentieth centuries. The narrative moves from the Pythagorean insistence on positive multiples to the gradual acceptance of negative numbers, irrationals and complex numbers as essential tools in quantitative analysis. Within this chronological framework, chapters are organised thematically, covering a variety of topics and contexts: writing and solving equations, geometric construction, coordinates and complex numbers, perceptions of ‘infinity’ and its permissible uses in mathematics, number systems, and evolving views of the role of axioms. Through this approach, the author demonstrates that changes in our understanding of numbers have often relied on the breaking of long-held conventions to make way for new inventions at once providing greater clarity and widening mathematical horizons. Viewed from this historical perspective, mathematical abstraction emerges as neither mysterious nor immutable, but as a contingent, developing human activity. Making up Numbers will be of great interest to undergraduate and A-level students of mathematics, as well as secondary school teachers of the subject. In virtue of its detailed treatment of mathematical ideas, it will be of value to anyone seeking to learn more about the development of the subject.

The Archimedes Palimpsest is the name given to a Byzantine prayer-book which was written over a number of earlier manuscripts. This volume provides colour images and transcriptions of three of the texts recovered from it. Pride of place goes to the treatises of Archimedes, including the only Greek version of Floating Bodies, and the unique copies of Method and Stomachion. This transcription provides many different readings from those made by Heiberg from what he termed Codex C in his edition of the works of Archimedes of 1910-1915. Secondly, fragments of two previously unattested speeches by the Athenian orator Hyperides, which are the only Hyperides texts ever to have been found in a codex. Thirdly, a fragment from an otherwise unknown commentary on Aristotle's Categories. In each case advanced image-processing techniques have been used to create the images, in order to make the text underneath legible.

An antidote to mathematical rigor mortis, teaching how to guess answers without needing a proof or an exact calculation. In problem solving, as in street fighting, rules are for fools: do whatever works—don't just stand there! Yet we often fear an unjustified leap even though it may land us on a correct result. Traditional mathematics teaching is largely about solving exactly stated problems exactly, yet life often hands us partly defined problems needing only moderately accurate solutions. This engaging book is an antidote to the rigor mortis brought on by too much mathematical rigor, teaching us how to guess answers without needing a proof or an exact calculation. In Street-Fighting Mathematics, Sanjoy Mahajan builds, sharpens, and demonstrates tools for educated guessing and down-and-dirty, opportunistic problem solving across diverse fields of knowledge—from mathematics to management. Mahajan describes six tools: dimensional analysis, easy cases, lumping, picture proofs, successive approximation, and reasoning by analogy. Illustrating each tool with numerous examples, he carefully separates the tool—the general principle—from the particular application so that the reader can most easily grasp the tool itself to use on problems of particular interest. Street-Fighting Mathematics grew out of a short course taught by the author at MIT for students ranging from first-year undergraduates to graduate students ready for careers in physics, mathematics, management, electrical engineering, computer science, and biology. They benefited from an approach that avoided rigor and taught them how to use mathematics to solve real problems. Street-Fighting Mathematics will appear in print and online under a Creative Commons Noncommercial Share Alike license.