Gödel

Author: Wang Hao
Translator: Kang Chengkui
Country: United States
Publisher:
Publishing Time: 2002-09-01
Features: One person once experienced both great joy and sorrow in mathematics within less than two years, and he was G?del. In the autumn of 1929, G?del proved the completeness of first-order logic in his doctoral dissertation, which was a tremendous encouragement to the formalist school, which attempted to build the foundation of mathematics using the "axiomatization" method. Hilbert, the leader of the formalist school, was confident that his metamathematics and proof theory would successfully establish the consistency and completeness of all mathematics. G?del's completeness theorem seemed to indicate that the dawn of hope was approaching. In the summer of 1930, K?nigsberg, the birthplace of Kant and also the hometown of Hilbert, in his speech at the ceremony to honor him as an "Honorary Citizen," Hilbert firmly declared, the last sentence: "We must know, we shall know (Wirmüssenwissen.Wirwerdenwissen)." But the following year, G?del's other paper opened the "Pandora's Box." This paper titled "On the Undecidability of Propostions of Formal Systems Concerning the Principles of Mathematics" (1931) contained two astonishing conclusions, the most devastating of which for the mathematical community was: any mathematical system that can include the arithmetic of integers cannot have its consistency established through the logical principles adopted by several foundational schools (the logicist school, the formalist school, the axiomatization school of set theory). Hilbert's fantasy was shattered, and the "disaster" of mathematics had arrived! Someone lamented, "God exists because mathematics is undoubtedly consistent; the devil also exists because we cannot prove this consistency." (Weyl) G?del's influence was profound, one recent example is sufficient to illustrate. In the summer of 2002, at the Beijing International Congress of Mathematicians, Stephen Hawking's report was titled "G?del and M Theory." In contemporary international physics research, many scientists have proposed the existence of a theory that can describe all physical phenomena, calling it the superstring theory. Hawking believes that it is highly unlikely to establish a single grand unification theory that describes the universe. Hawking said his speculation was based on G?del's incompleteness theorem in the field of mathematics. However, G?del has always been a legendary figure shrouded in mystery. His life was eccentric and transcendent, his thoughts profound and far-reaching. Many of us may have learned about G?del after reading Douglas Hofstadter's G?del, Escher, Bach: An Eternal Golden Braid (GEB: A Eternal Golden Band is a translated excerpt of the book). In fact, this remarkable book has added an even greater aura of mystery to G?del's legend. Thanks to Mr. Wang Hao, his book Reflections on Kurt G?del (1987, 1991, translated by Kang Hongkui, Shanghai Century Publishing Group, Shanghai Translation Publishing House, first edition September 2002) has allowed us to finally get close to G?del and feel the great and sincere mind beneath his ordinary exterior. G?del's uniqueness is reflected in his thoughts, his concerns, his lifestyle, and his deep spiritual world. Mr. Wang Hao G?del's life from the perspective of his dedication to fundamental theory. It is worth noting that Mr. Wang Hao first focused on three important historical materials closely related to G?del's life and career (G?del's brother's reply to Mr. Wang Hao, the questionnaire specially designed for G?del's life by Granchon, and Mr. Wang Hao's introduction speech when G?del received the honorary degree from Rockefeller University). Based on these many precious historical materials, Mr. Wang Hao has meticulously sketched out the full picture of G?del's lifelong career. It seems like a coincidence in history that after G?del finally reached Princeton from Vienna through many twists and turns, he became a close friend of Einstein, who had been friends for over a decade. Mr. Wang Hao skillfully used Einstein as a "medium" to describe the friendship between the two wise men and their thoughts and insights in physics, logic, philosophy, politics, art, and even religion, thus opening a direct path for readers to understand G?del's spiritual world. G?del's scientific work is astonishing, and this is also the focus that Mr. Wang Hao has painstakingly described. However, according to G?del himself, he spent more time and effort on philosophy than on science in his life. In philosophy, the five virtues that G?del admired— "choose wisely, pursue accuracy, abandon prejudice, be cautious in experimentation, and have courage"—are truly moving. G?del's broad vision and sharp insight are also reflected in his critiques of science, technology, and society. The book reveals that G?del pointed out in 1962 that "humanity will not improve just because we reach the moon. This must be related to the old conflict between 'natural' science and 'spiritual' science. If the progress of history, legal theory and state theory, philosophy, psychology, literature, art, etc., were as great as that of physics, the danger of atomic war would not exist." How can one not feel moved upon reading this! It is indeed true that "G?del's deeds are thought-provoking, his realm transcends academic boundaries, and truly, one needs a historical perspective that spans several centuries to fully grasp it."