Can Mathematics Be Proved Consistent?: Goedel's Shorthand Notes & Lectures on Incompleteness

Kurt Gödel's 1931 result, known as the first incompleteness theorem, formalized mathematical proofs and showed that elementary arithmetic statements can be formally provable but not provable. This book presents Gödel's preserved notebooks from 1930, the original version of his incompleteness article, and six contemporary lectures and seminars he gave between 1931 and 1934. The lectures are masterpieces of accessible presentations of deep scientific results.

Format: Paperback / softback
Length: 263 pages
Publication date: 26 July 2021
Publisher: Springer Nature Switzerland AG

Kurt Gödel (1906-1978) made a groundbreaking discovery in 1931 that has since become an iconic symbol of 20th-century science. His research into the quest for rigor in proving mathematical theorems led to the formalization of mathematical proofs, reducing them to a set of mechanical rules. Gödel's most famous result, known as his first incompleteness theorem, revealed that whenever a part of mathematics is formalized, there exist arithmetical statements that should be formally provable but remain unsolved. This remarkable theorem is so named because Gödel also provided an answer to the question, "Can mathematics be proved consistent?" This book presents the first examination of Gödel's preserved notebooks from 1930, written in a long-forgotten German shorthand. It traces his initial ideas, their evolution, and the meticulous composition of his renowned publication, "On Formally Undecidable Propositions." Additionally, the book includes the original version of Gödel's incompleteness article, which was submitted for publication without mentioning the second incompleteness theorem. Furthermore, it presents six contemporary lectures and seminars that Gödel delivered between 1931 and 1934 in Austria, Germany, and the United States. These lectures are remarkable for their accessible presentations of deep scientific results, making them accessible even to individuals without specialized mathematical training. Presented here for the first time, these lectures showcase Gödel's exceptional talent for conveying complex ideas in a clear and concise manner.

Weight: 427g
Dimension: 235 x 155 (mm)
ISBN-13: 9783030508784
Edition number: 1st ed. 2020