The Rise of Hellenistic Alexandria
The rise of Alexandrian mathematics in Hellenistic culture, marked by specialization, technical expertise, and significant contributions from mathematicians like Archimedes and Apollonius.
Mathematics
The Reception and Revival of Euclid's Geometry
A comprehensive treatise on geometry that has had a profound impact on mathematics and science for centuries.
Theoretical Pursuits: A Historical Examination
A historical examination of the development of theoretical pursuits in mathematics, exploring how abstract concepts found significance in various fields.
The Foundations of Geometry: Euclid's Elements
Euclid's Elements, written around 300 B.C., presents a comprehensive treatise on geometry that has had a profound impact on mathematics, science, and philosophy.
A Mathematical Exploration: The Method of Exhaustion and its Limitations
A mathematical technique used to find areas and perimeters by inscribing and circumscribing polygons with increasing sides, developed by ancient Greeks like Archimedes.
The Development of Irrational Numbers: A Philosophical Exploration
A philosophical exploration of the development of irrational numbers, from ancient Greek mathematicians to their impact on mathematics and reality.
The Intersection of Mathematics and Greek Philosophy
Exploring how the Greeks' emphasis on mathematics influenced their philosophical thought, and its lasting impact on Western philosophy.
The Limits of the Syllogism
The limits of deductive reasoning, exploring the relationship between logic, mathematics, and philosophical tradition, questioning the preeminence of the syllogism.
The Concept of Unity in Mathematics and Metaphysics
Exploring the concept of unity in mathematics and metaphysics, examining its relationships with key terms and figures.
The Philosophical Significance of Mathematics
Mathematics has a profound impact on philosophical thought, shaping ideas about truth, time, and reality through mathematical concepts like exact truth, ideal vs. sensible objects, eternalism, rationalism, and God's thoughts.
The Discovery of Incommensurables: A Challenge to Pythagoras' Philosophy
A challenge to Pythagoras' philosophy on incommensurables, their discovery and impact on Euclidean geometry.
The Emergence of Western Civilization: The Intellectual Achievements of Ancient Greece
The Emergence of Western Civilization: The Intellectual Achievements of Ancient Greece