The objective of the present book of essays is to convey to the intelligent nonmathematician something of the nature, development, and use of mathe matical concepts, particularly those that have found application in current scientific research. The idea of assembling such a volume goes back at least to 1974, when it was discussed by the then-newly-formed Joint Projects Committee for Mathematics (JPCM) of the American Mathematical Soci ety, the Mathematical Association of America, and the Society for Indus trial and Applied Mathematics. Currently, the nine members of the JPCM are Saunders Mac Lane (Chairman) of the University of Chicago, Frederick J. Almgren, Jr. of Princeton University, Richard D. Anderson of Louisiana State University, George E. Carrier of Harvard University, Hirsh G. Cohen ofthe International Business Machines Corporation, Richard C. DiPrima of Rensselaer Polytechnic Institute, Robion C. Kirby of the University of California at Berkeley, William H. Kruskal of the University of Chicago, and George D. Mostow of Yale University. The JPCM decided to make production of this volume its first major proj ect and requested the Conference Board of the Mathematical Sciences (CBMS), of which its three sponsoring societies are all member organiza tions, to approach the National Science Foundation on its behalffor support of the undertaking. A proposal submitted by the C BMS in December 1974 and in revised form in July 1975 was granted by the Foundation in May 1976, and work on assembling the volume got under way.

Leaving aside for once all utilitarian considerations, this book attempts to demonstrate the role and influence of the natural sciences in the development of human thought and in shaping the way in which we perceive the world. This seems to be particularly necessary in the present day and age, in view of the fact that a large section of the public is scarcely aware of the great cultural contribution that the natural sciences make towards moulding our conception of the world and scarcely acknowledges their function in helping us to find our bearings in a world that is becoming increasingly complex.

What can a fingernail tell us about the mysteries of creation? In one sense, a nail is merely a hunk of mute matter, yet in another, it's an information superhighway quite literally at our fingertips. Every moment, streams of molecular signals direct our cells to move, flatten, swell, shrink, divide, or die. Andreas Wagner's ambitious new book explores this hidden web of unimaginably complex interactions in every living being. In the process, he unveils a host of paradoxes underpinning our understanding of modern biology, contradictions he considers gatekeepers at the frontiers of knowledge. Though we tend to think of concepts in such mutually exclusive pairs as mind-matter, self-other, and nature-nurture, Wagner argues that these opposing ideas are not actually separate. Indeed, they are as inextricably connected as the two sides of a coin. Through a tour of modern biological marvels, Wagner illustrates how this paradoxical tension has a profound effect on the way we define the world around us. Paradoxical Life is thus not only a unique account of modern biology. It ultimately serves a radical--and optimistic--outlook for humans and the world we help create.

Mathematics today is approaching a state of cnSIS. As the demands of science and society for mathematical literacy increase, the percentage of American college students intending to major in mathematics plummets and achievement scores of entering college students continue thelt unremit ting decline. As research in core mathematics reaches unprecedented heights of power and sophistication, the growth of diverse applied special ties threatens to fragment mathematics into distinct and frequently hostile mathematical sciences. These crises in mathematics presage difficulties for science and engineer ing, and alarms are beginning to sound in the scientific and even in the political communities. Citing a trend towards "virtual scientific and techno logical illiteracy" and a "shrinking of our national commitment to excel lence . . . in science, mathematics and technology," a recent study con ducted for the President by the U. S. National Science Foundation and Department of Education warns of serious impending shortcomings in public understanding of science. "Today people in a wide range of non scientific . . . professions must have a greater understanding of technology than at any time in our history. Yet our educational system does not now provide such understanding. " The study goes on to conclude that present trends pose great risk of manpower shortages in the mathematical and engineering sciences. "The pool from which our future scientific and engineering personnel can be drawn is . . . in danger of becoming smaller, even as the need for such personnel is increasing. " It is time to take a serious look at mathematics tomorrow.

A comprehensive collection of historical readings in the philosophy of mathematics and a selection of influential contemporary work, this much-needed introduction reveals the rich history of the subject. An Historical Introduction to the Philosophy of Mathematics: A Reader brings together an impressive collection of primary sources from ancient and modern philosophy. Arranged chronologically and featuring introductory overviews explaining technical terms, this accessible reader is easy-to-follow and unrivaled in its historical scope. With selections from key thinkers such as Plato, Aristotle, Descartes, Hume and Kant, it connects the major ideas of the ancients with contemporary thinkers. A selection of recent texts from philosophers including Quine, Putnam, Field and Maddy offering insights into the current state of the discipline clearly illustrates the development of the subject. Presenting historical background essential to understanding contemporary trends and a survey of recent work, An Historical Introduction to the Philosophy of Mathematics: A Reader is required reading for undergraduates and graduate students studying the philosophy of mathematics and an invaluable source book for working researchers.

The traditional debate among philosophers of mathematics is whether there is an external mathematical reality, something out there to be discovered, or whether mathematics is the product of the human mind. This provocative book, now available in a revised and expanded paperback edition, goes beyond foundationalist questions to offer what has been called a "postmodern" assessment of the philosophy of mathematics--one that addresses issues of theoretical importance in terms of mathematical experience. By bringing together essays of leading philosophers, mathematicians, logicians, and computer scientists, Thomas Tymoczko reveals an evolving effort to account for the nature of mathematics in relation to other human activities. These accounts include such topics as the history of mathematics as a field of study, predictions about how computers will influence the future organization of mathematics, and what processes a proof undergoes before it reaches publishable form. This expanded edition now contains essays by Penelope Maddy, Michael D. Resnik, and William P. Thurston that address the nature of mathematical proofs. The editor has provided a new afterword and a supplemental bibliography of recent work.

Mathematics research papers provide a forum for all mathematics enthusiasts to exercise their mathematical experience, expertise and excitement. The research paper process epitomizes the differentiation of instruction, as each student chooses their own topic and extends it as far as their motivation and desire takes them. The features and benefits of the research paper process offer a natural alignment with all eight Common Core State Standards for Mathematical Practice. Writing Math Research Papers serves both as a text for students and as a resource for instructors and administrators. The Writing Math Research Papers program started at North Shore High School in 1991, and it received the 1997 Chevron Best Practices in Education Award as the premier high school math course in the United States. Author Robert Gerver’s articles on high school mathematics research programs were featured in the National Council of Teachers of Mathematics publication Developing Mathematically Promising Students, the NCTM’s 1999 Yearbook, Developing Mathematical Reasoning in Grades K – 12, and in the September 2017 issue of the Mathematics Teacher.