Brains, Machines, and Mathematics

Michael A. Arbib
1965

This book is an interdisciplinary exploration of the relationships between neuroscience, computer science, and mathematics, examining how each field contributes to understanding intelligence and cognition.

Arbib begins by introducing the biological basis of intelligence, focusing on how the brain processes information through networks of neurons. He explains key concepts in neurophysiology and how these biological systems inspire computational models. The text then bridges into artificial intelligence, showing how machines can be designed to simulate aspects of human thinking and problem-solving.

A central theme of the book is the use of mathematics as a unifying language. Arbib demonstrates how mathematical models—such as logic, automata theory, and formal systems—are used to describe both brain function and machine computation. He explores topics like finite automata, Turing machines, and algorithms, connecting them to cognitive processes.

The book also addresses questions about the limits of computation and intelligence, including:

• What problems machines can and cannot solve
• How human cognition compares to artificial systems
• The role of formal logic in modeling thought

Throughout, Arbib integrates theory with conceptual examples, making complex ideas accessible while maintaining rigor.