Mathematics: Making the Invisible Visible

Mathematics: Making the Invisible Visible (Stanford Univ.). This is a series of five two-hour lectures given by Professor Keith Devlin, giving a broad overview of mathematics. Often described as the science of patterns, mathematics is arguably humanity's most penetrating mental framework for uncovering the hidden patterns that lie behind everything we see, feel, and experience. Galileo described mathematics as the language in which the laws of the universe are written. Intended to give a broad overview of the field, these five illustrated lectures look at counting and arithmetic, shape and geometry, motion and calculus, and chance and probability, and end with a mind-stretching trip to infinity.

Lecture 1 - General Overview and the Development of Numbers
Keith Devlin gives an overview of the history of mathematics. He discusses how it has evolved over time and explores many of its practical applications in the world.

Lecture 2 - The Golden Ratio & Fibonacci Numbers: Fact versus Fiction
Professor Keith Devlin dives into the topics of the golden ratio and fibonacci numbers.

Lecture 3 - The Birth of Algebra
Professor Keith Devlin looks at how algebra, one of the most foundational concepts in math, was discovered.

Lecture 4 - Calculus: One of the Most Successful Technologies
Professor Keith Devlin discusses how calculus is truly one of the most useful discoveries of all time.

Lecture 5 - How Did Human Beings Acquire the Ability to do Math?
Keith Devlin concludes the course by discussing the development of mathematical cognition in humans as well as the millennium problems.

The Language of Mathematics - Making the Invisible Visible
By Keith Devlin. Contents. Preface. Prologue What is Mathematics? Chapter 1 Why Numbers Count. Chapter 2 Patterns of the Mind. Chapter 3 Mathematics in Motion. ...