Mystery of Infinity (02:12)

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Host Dan Rockmore notes that for centuries, the mathematic study of infinity was taboo. He tells the story of Achilles' race with the tortoise.

Pythagoras Observes Music (01:46)

Pythagoras and his followers believe that whole number ratios are the backbone of goodness and harmony in the world. This is challenged in the diagonal of a square.

Mystery of the Infinite (03:46)

Take a deeper look into a square's diagonal. Learn what it means for the square root of 2 to be irrational. Pythagorean assumptions are directly contradicted by Theodorus.

Actual Infinite (01:33)

John Wallis is first to use the "lazy 8" as a symbol for infinity. Georg Cantor forces infinity into mathematics.

What is a Number? (04:43)

Rockmore interviews Jim Tanton to talk about Cantor and infinity. Tanton uses pictures of cats and dogs to explain set theory. They discuss cardinality aleph zero.

Impossible Infinity (02:47)

Cantor argues that it's impossible to make a list of all the real numbers between zero and one. Counting numbers and real numbers are two different types of infinity.

Infinite Sets (02:29)

Tanton uses three friends to discuss a finite case. Cantor discovers that subsets will always be a bigger infinity than original sets.

Cantor's Aleph (01:18)

Georg Cantor helps turn infinity into a graspable concept for mathematicians. Rockmore describes multiple theories on why Cantor chose the Hebrew letter.

Infinite Beauty (05:30)

Ivars Peters believes that math gives artists a new way to express themselves. He describes the work of M.C. Escher and Helaman Ferguson.