Bundy A. The Nature of Mathematical Proof 2005 torrent

Textbook in PDF format

Preface
Introduction
Mechanized and non-mechanized proofs; formal and rigorous proofs
Cultures of proving
Conflicts over ‘proof’
Disciplines and applications
References
Additional reference
The nature of mathematical proof
Computation versus intuition
Computer science proofs
Logic
Ontology
Computability
Computer mathematics
State of the art: systems
What is needed?
Romantic versus cool mathematics
References
Introduction
Lakatoss discussion of Eulers Theorem
Cauchys ‘proof’ of Eulers Theorem
Schematic proofs
Implementation of the constructive omega-rule
The relative difficulty of proofs
Schematic proofs as a cognitive model
Comparison to type theory
Rigorous proof as Hilbertian proof highlights
References
What can and do we prove about programs?
References
Panelist position statement: reasoning about the design of programs
References
Panelist position statement: logic and models in computer science
References
Highly complex proofs and implications of such proofs
Discussion
Introduction
Questions concerning the predicate calculus
Consistency questions
Set theory, the ultimate frontier
The ultimate pessimism deriving from Skolems views
References
Proofs of novel complexity
Idealized proofs
Incompleteness
Unprovability theory
The fundamental theorems
Complex methods in arithmetic
Isabelle
Texts on unwinding
Examples
Girard unwinding
Kohlenbachs work
Closing remarks
References
The justification of mathematical statements
Appendix A
References
Introduction
What is constructive mathematics?
What significance do the differences have?
Computer-assisted mathematics
References