Book Description

What makes mathematicians tick? How do their minds process formulas and concepts that, for most of the rest of the world's population, remain mysterious and beyond comprehension? Is there a connection between mathematical creativity and mental illness?

In The Mind of the Mathematician, internationally famous mathematician Ioan James and accomplished psychiatrist Michael Fitzgerald look at the complex world of mathematics and the mind. Together they explore the behavior and personality traits that tend to fit the profile of a mathematician. They discuss mathematics and the arts, savants, gender and mathematical ability, and the impact of autism, personality disorders, and mood disorders.

These topics, together with a succinct analysis of some of the great mathematical personalities of the past three centuries, combine to form an eclectic and fascinating blend of story and scientific inquiry.

Book Description

Contrary to popular belief--and despite the expulsion, emigration, or death of many German mathematicians--substantial mathematics was produced in Germany during 1933-1945. In this landmark social history of the mathematics community in Nazi Germany, Sanford Segal examines how the Nazi years affected the personal and academic lives of those German mathematicians who continued to work in Germany.

The effects of the Nazi regime on the lives of mathematicians ranged from limitations on foreign contact to power struggles that rattled entire institutions, from changed work patterns to military draft, deportation, and death. Based on extensive archival research, Mathematicians under the Nazis shows how these mathematicians, variously motivated, reacted to the period's intense political pressures. It details the consequences of their actions on their colleagues and on the practice and organs of German mathematics, including its curricula, institutions, and journals. Throughout, Segal's focus is on the biographies of individuals, including mathematicians who resisted the injection of ideology into their profession, some who worked in concentration camps, and others (such as Ludwig Bieberbach) who used the "Aryanization" of their profession to further their own agendas. Some of the figures are no longer well known; others still tower over the field. All lived lives complicated by Nazi power.

Presenting a wealth of previously unavailable information, this book is a large contribution to the history of mathematics--as well as a unique view of what it was like to live and work in Nazi Germany.

Book Description
This volume can be divided into two parts: a purely mathematical part with contributions on finance mathematics, interactions between geometry and physics and different areas of mathematics; another part on the popularization of mathematics and the situation of women in mathematics. ... Read more

Book Description

Book Description

Hailed as one of the greatest mathematical results of the twentieth century, the recent proof of Fermat's Last Theorem by Andrew Wiles brought to public attention the enigmatic problem-solver Pierre de Fermat, who centuries ago stated his famous conjecture in a margin of a book, writing that he did not have enough room to show his "truly marvelous demonstration." Along with formulating this proposition--xn+yn=zn has no rational solution for n > 2--Fermat, an inventor of analytic geometry, also laid the foundations of differential and integral calculus, established, together with Pascal, the conceptual guidelines of the theory of probability, and created modern number theory. In one of the first full-length investigations of Fermat's life and work, Michael Sean Mahoney provides rare insight into the mathematical genius of a hobbyist who never sought to publish his work, yet who ranked with his contemporaries Pascal and Descartes in shaping the course of modern mathematics.

Customer Reviews (2)

A fine account of Fermat's work
There is a tremendous mythology surrounding Fermat, and interest in Fermat is high because of Wiles' proof of "Fermat's last theorem."Fermat was undoubtedly a genius, but exactly what he did and didn't do will never be clear, because he wrote so little about his methods and his proofs. Mahoney's book comes as close as I think it's possible to come in figuring out what Fermat's mathematical interests and methods were, what he proved and what he didn't.Only high school math is required to read this book easily; the writing style is clear, and the structure of the book is well organized.

Some readers may be disappointed to learn that Fermat's abilities were only human, and that he made a number of mistakes. But even a genius is entitled to be less than perfect, and the real Fermat is in many ways more interesting than the myth. I recommend this book to anyone curious about Fermat's mathematical abilities and achievements.

Mathematics in transition: Pierre de Fermat
Thanks to the widely publicized proof of Fermat's Last Theorem by Andrew Wiles, there is a growing public interest in the 17th- century mathematician and his famous theorem. However, readers interested in the theorem and its history should look elsewhere as this book is directed towards the history and the transition of mathematics as a science in the 17th century. Studying the evolution of concepts and methods in mathematics, Michael Mahony sets a standard with this excellent work. A student of Thomas Kuhn, Mahony is meticulous in his treatment and interpretation of historical data about Fermat within its historical context. He is very careful in the use of notational systems and at appropriate times he uses the same symbolism as Fermat used in his correspondence with Mersenne and others. These subtleties are important as the evolution in algebraic symbolism has precisely been functional in the foundation of analytic geometry. Further in line with Kuhn's Structure of Scientific Revolutions Mahony first situates Pierre de Fermat within Viète's analytic program and continuously refers to this program of scientific research. He clearly shows where Fermat departs from this program and lays the foundation of something new as with number theory as a discipline on its own.

The career of Pierre de Fermat coincides with an important revolution within mathematics during the 17th century: together with Descartes he fundamentally altered the balance between the visual and the abstract in mathematics. The Greek tradition of visually stating problems about curves, loci and triangles gave way to an abstract characterization in algebraic equations which allowed a more general treatment of these original problems. Where the Greek tradition provided the starting point for Fermat, he moved that far beyond his original sources that by the end of his carreer the original Greek texts became history for mathematicians.

However, the book is even more than an illustration of science in transition: it reveals the mathematician in transition. The author is very convincing in recreating step by step the way Fermat arrived at new ideas and theorems and how, over time, he became the father of new disciplines in mathematics. Mahony does so by reconstructing all the conceptual steps needed in arriving at new ideas. For the method of maxima and minima, the doctrine of tangents and the quadrature, he relies on available historical data, such as Fermat's letters to Mersenne, Descartes and Frenicle. For Fermat's contributions on number theory however, only a few historical documents are available as Fermat was very secretive about his findings and reluctant to publish anything. With some help from Euler and Weil, Mahony shows very convincingly and fits together how theorems and proofs on number theory emerged over time for the man who was Pierre de Fermat.

Everybody who is keen on mathematics and its history should read this book. Being an excellent case study of science in transition, the book will highly appeal to students in the philosophy of science. ... Read more