This volume commemorates the life, work and foundational views of Kurt Gödel by exploring the impact of his work on current research and its future implications not only in the foundations of mathematics and logic, but also in the fields of computer science, artificial intelligence, physics, cosmology, philosophy, theology and the history of science.

Part I. Historical Context - Gödel's Contributions and Accomplishments: 1. The impact of Gödel's incompleteness theorems on mathematics Angus Macintyre; 2. Logical hygiene, foundations, and abstractions: diversity among aspects and options Georg Kreisel; 3. The reception of Gödel's 1931 incompletability theorems by mathematicians, and some logicians, to the early 1960s Ivor Grattan-Guinness; 4. 'Dozent Gödel will not lecture' Karl Sigmund; 5. Gödel's thesis: an appreciation Juliette C. Kennedy; 6. Lieber Herr Bernays!, Lieber Herr Gödel! Gödel on finitism, constructivity, and Hilbert's program Solomon Feferman; 7. Computation and intractability: echoes of Kurt Gödel Christos H. Papadimitriou; 8. From the entscheidungsproblem to the personal computer - and beyond B. Jack Copeland; 9. Gödel, Einstein, Mach, Gamow, and Lanczos: Gödel's remarkable excursion into cosmology Wolfgang Rindler; 10. Physical unknowables Karl Svozil; Part II. A Wider Vision - the Interdisciplinary, Philosophical, and Theological Implications of Gödel's Work: 11. Gödel and physics John D. Barrow; 12. Gödel, Thomas Aquinas, and the unknowability of God Denys A. Turner; 13. Gödel's mathematics of philosophy Piergiorgio Odifreddi; 14. Gödel's ontological proof and its variants Petr Hájek; 15. The Gödel theorem and human nature Hilary Putnam; 16. Gödel, the mind, and the laws of physics Roger Penrose; Part III. New Frontiers - Beyond Gödel's Work in Mathematics and Symbolic Logic: 17. Gödel's functional interpretation and its use in current mathematics Ulrich Kohlenbach; 18. My forty years on his shoulders Harvey M. Friedman; 19. My interaction with Kurt Gödel: the man and his work Paul J. Cohen; 20. The transfinite universe W. Hugh Woodin; 21. The Gödel phenomena in mathematics: a modern view Avi Wigderson.