The Joy of Mathematics

Professor Benjamin introduces the ABCs of math appreciation; the field's applications, its beauty and structure, and its certainty; mathematics is a source of endless delight through creative play with numbers.

How to add all the numbers from 1 to 100 instantly; what makes a square number square and a triangular number triangular; why the rules of arithmetic really work; how one calculates in bases other than 10.

A number is prime if it is evenly divisible by only itself and the number one; Professor Benjamin proves that there are an infinite number of primes; how primes are the building blocks of the number system.

Combinatorics is the study of counting questions, such as how many outfits are possible if one owns eight shirts, five pairs of pants and 10 ties; combinatorics can also be used to analyze numbering systems and games of chance.

The Fibonacci numbers follow a simple pattern in which each number is the sum of the two preceding numbers; Fibonacci numbers have many beautiful and unexpected properties; Fibonacci numbers in nature, art and poetry.

Arguably the most important area of mathematics, algebra introduces the idea of using an abstract variable to represent an unknown quantity; discovering algebra's golden rule, which is to do unto one side of an equation as one does unto the other.