Lecture Notes: The Story of Maths

Introduction

• Speaker: Marcus de Sotois, a mathematician
• Theme: Exploration of the development of mathematics throughout history
• Objective: To track the growth of mathematics from its origins to the present day
• Method: Use of computer-generated imagery to explore historical mathematical discoveries

Early Beginnings of Mathematics

• Mathematics started as a way to make sense of natural patterns
• Basic concepts of space and quantity are intrinsic to human and animal brains
• Ancient humans began organizing, counting, and ordering their environment

Egyptian Contributions to Mathematics

• Location: River Nile as a cradle of early mathematics
• Historical Context: Societies began settling as early as 6000 BC
• Calendar Development: Egyptians used Nile flooding as a yearly marker
• Measurement: Egyptians used body parts like cubits for measurement
• Decimal System: Hieroglyphs represented numbers but lacked place value
• Rhind Mathematical Papyrus: Contains multiplication and division methods
  • Egyptians used doubling for multiplication
  • Fractions and the Eye of Horus symbolized divisions
• Geometry and Pi: Approximation of a circle's area shows early understanding of geometry

Babylonian Mathematics

• Location: Mesopotamia, modern-day Iraq, Iran, Syria
• Number System: Base 60, suitable for astronomical calculations
• Quadratic Equations: Solved via geometric methods
• Zero: Introduced as a placeholder in numbers
• Plimpton 322 Tablet: Indicates understanding of right-angled triangles
• Babylonian Influence: Games like backgammon used mathematical strategies

Greek Advances in Mathematics

• Greek Empire: Expansion introduced Greek to Babylonian and Egyptian knowledge
• Proof and Deductive System: Systematic approach started with axioms
• Pythagoras: Known for Pythagorean theorem and harmonic series in music
  • Discovered irrational numbers (e.g., square root of 2)
• Plato and Euclid: Emphasized geometry in understanding reality
  • Euclid’s "The Elements" laid foundational geometric theorems

Advanced Greek Mathematics

• Archimedes: Focused on pure mathematics, calculated pi, and volumes of solids
• Roman Empire: Practical use of mathematics for engineering
• Hypatia: Last prominent Greek mathematician in Alexandria, murdered by a Christian mob

Conclusion

• Legacy: Early mathematics from Egypt, Babylon, and Greece forms the foundation of modern knowledge
• Next Journey: Exploration of Asian mathematics, algebra, and numbers
• Further Learning: Resources available at Open University and BBC4

These notes capture the historical journey of mathematics, highlighting key contributions from different civilizations and setting the stage for future mathematical advancements.