The Mathematics of the Gods and the Algorithms of Men

A Cultural History

Paolo Zellini

• Editorial: Pegasus Books
• Año: 2020
• ISBN:
  9781643134154
• Categoría: Mathematics
• Categoría: History & Philosophy of Mathematics

A masterful cultural history of mathematics from bestselling Italian mathematician and philosopher Paolo Zellini. Is mathematics a discovery or an invention? Have we invented numbers or do they truly exist? What sort of reality should we attribute to them? Mathematics has always been a way of understanding and ordering the world: from sacred ancient texts and pre-Socratic philosophers to twentieth-century logicians such as Russell and Frege and beyond. In this masterful, elegant book, mathematician and philosopher Paolo Zellini offers a brief cultural and intellectual history of mathematics, from ancient Greece to India to our contemporary obsession with algorithms, showing how mathematical thinking is inextricably linked with philosophical, existential and religious questions—and indeed with our cosmic understanding of the world.

Índice

• Cover
• Title Page
• Introduction
• 1. Abstraction, Existence and Reality
• 2. Mathematics of the Gods
• 3. Mathematical and Philosophical Formulas
• 4. Growth and Decrease, Number and Nature
• 5. Katà gnómonos phýsin  : The Nature of the Gnomon
• 6. Dýnamis: The Capacity to Produce
• 7. Intermission: Spiritual Mechanics
• 8. Zeno’s Paradoxes: The Explanation of Movement
• 9. The Paradoxes of Plurality
• 10. The Limited and the Limitless: Incommensurability and Algorithms
• 11. The Reality of Numbers: Cantor’s Fundamental Sequences
• 12. The Reality of Numbers: Dedekind’s Sections
• 13. Mathematics: A Discovery or an Invention?
• 14. From the Continuum to the Digital
• 15. The Growth of Numbers
• 16. The Growth of Matrices
• 17. The Crisis of Fundamentals and the Growth of Complexity: Reality and Efficiency
• 18. Verum et Factum
• 19. Recursion and Invariability
• About the Author
• Notes
• Index
• Copyright