Science Without Numbers caused a stir in 1980, with its bold nominalist approach to the philosophy of mathematics and science. It has been unavailable for twenty years and is now reissued in a revised edition with a substantial new preface presenting the author's current views and responses to the issues raised in subsequent debate.

'The whizz-kid making maths supercool. . . A brilliant book that takes everything we know (and fear) about maths out of the equation - starting with numbers' The Times 'A cheerful, chatty, and charming trip through the world of mathematics. . . Everyone should read this delightful book' Ian Stewart, author of Do Dice Play God? The only numbers in this book are the page numbers. The three main branches of abstract math - topology, analysis, and algebra - turn out to be surprisingly easy to grasp. Or at least, they are when our guide is a math prodigy. With forthright wit and warm charm, Milo Beckman upends the conventional approach to mathematics, inviting us to think creatively about shape and dimension, the infinite and the infinitesimal, symmetries, proofs, and all how all these concepts fit together. Why is there a million dollar prize for counting shapes? Is anything bigger than infinity? And how is the 'truth' of mathematics actually decided? A vivid and wholly original guide to the math that makes the world tick and the planets revolve, Math Without Numbers makes human and understandable the elevated and hypothetical, allowing us to clearly see abstract math for what it is: bizarre, beautiful, and head-scratchingly wonderful.

Engineering professor Barbara Oakley knows firsthand how it feels to struggle with math. In her book, she offers you the tools needed to get a better grasp of that intimidating but inescapable field.

Why collaborations in STEM fields succeed or fail and how to ensure success Once upon a time, it was the lone scientist who achieved brilliant breakthroughs. No longer. Today, science is done in teams of as many as hundreds of researchers who may be scattered across continents. These collaborations can be powerful, but they also demand new ways of thinking. The Strength in Numbers illuminates the nascent science of team science by synthesizing the results of the most far-reaching study to date on collaboration among university scientists. Drawing on a national survey with responses from researchers at more than one hundred universities, archival data, and extensive interviews with scientists and engineers in over a dozen STEM disciplines, Barry Bozeman and Jan Youtie establish a framework for characterizing different collaborations and their outcomes, and lay out what they have found to be the gold-standard approach: consultative collaboration management. The Strength in Numbers is an indispensable guide for scientists interested in maximizing collaborative success.

Science Without Numbers caused a stir in philosophy on its original publication in 1980, with its bold nominalist approach to the ontology of mathematics and science. Hartry Field argues that we can explain the utility of mathematics without assuming it true. Part of the argument is that good mathematics has a special feature ("conservativeness") that allows it to be applied to "nominalistic" claims (roughly, those neutral to the existence of mathematical entities) in a way that generates nominalistic consequences more easily without generating any new ones. Field goes on to argue that we can axiomatize physical theories using nominalistic claims only, and that in fact this has advantages over the usual axiomatizations that are independent of nominalism. There has been much debate about the book since it first appeared. It is now reissued in a revised contains a substantial new preface giving the author's current views on the original book and the issues that were raised in the subsequent discussion of it.

'Science Without Numbers' caused a stir when it was originally published in 1980, with its bold nominalist approach to the philosophy of mathematics and science. It has been unavailable for 20 years and is now reissued in a revised edition with a substantial new preface presenting the author's current views and responses to the issues raised in subsequent debate.

Presents an accessible, in-depth look at the history of numbers and their applications in life and science, from math's surreal presence in the virtual world to the debates about the role of math in science.

According to the doctrine of nominalism, abstract entities--such as numbers, functions, and sets--do not exist. The problem this normally poses for a description of the physical world is as follows: any such description must include a physical theory, physical theories are assumed to require mathematics, and mathematics is replete with references to abstract entities. How, then, can nominalism reasonably be maintained? In answer, Hartry Field shows how abstract entities ultimately are dispensable in describing the physical world and that, indeed, we can "do science without numbers." The author also argues that despite the ultimate dispensability of mathematical entities, mathematics remains useful, and that its usefulness can be explained by the nominalist. The explanation of the utility of mathematics does not presuppose that mathematics is true, but only that it is consistent. The argument that the nominalist can freely use mathematics in certain contexts without assuming it to be true appears early on, and it first seems to license only a quite limited use of mathematics. But when combined with the later argument that abstract entities ultimately are dispensable in physical theories, the conclusion emerges that even the most sophisticated applications of mathematics depend only on the assumption that mathematics is consistent and not on the assumption that it is true. Originally published in 2050. The Princeton Legacy Library uses the latest print-on-demand technology to again make available previously out-of-print books from the distinguished backlist of Princeton University Press. These editions preserve the original texts of these important books while presenting them in durable paperback and hardcover editions. The goal of the Princeton Legacy Library is to vastly increase access to the rich scholarly heritage found in the thousands of books published by Princeton University Press since its founding in 1905.

Geoffrey Hellman presents a detailed interpretation of mathematics as the investigation of structural possibilities, as opposed to absolute, Platonic objects. After dealing with the natural numbers and analysis, he extends his approach to set theory, and shows how to dispense with a fixed universe of sets. Finally, he addresses problems of application to the physical world.