Mathematics

An accessible explanation of Kurt Gödel's groundbreaking work in mathematical logic

In 1931 Kurt Gödel published his fundamental paper, "On Formally Undecidable Propositions of Principia Mathematica and Related Systems." This revolutionary paper challenged certain basic assumptions underlying much research in mathematics and logic. Gödel received public recognition of his work in 1951 when he was awarded the first Albert Einstein Award for achievement in the natural sciences—perhaps the highest award of its kind in the United States. The award committee described his work in mathematical logic as "one of the greatest contributions to the sciences in recent times."

However, few mathematicians of the time were equipped to understand the young scholar's complex proof. Ernest Nagel and James Newman provide a readable and accessible explanation to both scholars and non-specialists of the main ideas and broad implications of Gödel's discovery. It offers every educated person with a taste for logic and philosophy the chance to understand a previously difficult and inaccessible subject.

New York University Press is proud to publish this special edition of one of its bestselling books. With a new introduction by Douglas R. Hofstadter, this book will appeal students, scholars, and professionals in the fields of mathematics, computer science, logic and philosophy, and science.

An accessible explanation of Kurt Gödel's groundbreaking work in mathematical logic

In 1931 Kurt Gödel published his fundamental paper, "On Formally Undecidable Propositions of Principia Mathematica and Related Systems." This revolutionary paper challenged certain basic assumptions underlying much research in mathematics and logic. Gödel received public recognition of his work in 1951 when he was awarded the first Albert Einstein Award for achievement in the natural sciences—perhaps the highest award of its kind in the United States. The award committee described his work in mathematical logic as "one of the greatest contributions to the sciences in recent times."

However, few mathematicians of the time were equipped to understand the young scholar's complex proof. Ernest Nagel and James Newman provide a readable and accessible explanation to both scholars and non-specialists of the main ideas and broad implications of Gödel's discovery. It offers every educated person with a taste for logic and philosophy the chance to understand a previously difficult and inaccessible subject.

New York University Press is proud to publish this special edition of one of its bestselling books. With a new introduction by Douglas R. Hofstadter, this book will appeal students, scholars, and professionals in the fields of mathematics, computer science, logic and philosophy, and science.

In the mid-1980s Mikhail Gorbachev's political and economic reforms promised a relaxation of tensions between the U.S.S.R. and the United States without disturbing the basic balance of power in Europe established after the Second World War. Then came the collapse of the Warsaw Pact and the vast democratic revolution that swept the Soviet empire, creating a power vacuum east of Berlin. Could such an upheaval have been a natural and logical extension of the course of reform that Gorbachev began plotting in 1985?
Gorbachev's Revolution argues persuasively that the end of Communism was never the goal of the Soviet leader but rather the unintended result of an intense and many-faceted struggle for power. Anthony D'Agostino demonstrates that the pervasive image of stable in-system reform in fact ignored evidence from history. Succession struggles in the U.S.S.R. were generally wars of ideas in which the victors got their way by challenging their opponents' interpretations of the past.
Through political memoirs, newspaper accounts, and historical documents, Gorbachev's Revolution demonstrates once again that revolutionaries change the world not only according to their own designs but also according to the world's designs on them.