The Infinite Quest

The Institute of Art and Ideas


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Infinity has inspired wonder and terror throughout the history of mathematics. As the cutting edge of cosmology grapples with the question of whether the infinite exists in nature, mathematicians are continue build on work where there can be infinitely many infinities. In this course Professor Peter Cameron shows how an idea until recently considered unworkable is in fact central to modern scientific and mathematical thought.

By the end of the course, you will have learned:

why mathematics cannot work without infinity
why infinity may not exist in nature
how infinity and the curvature of space are entangled
why information may be the basis of reality
the smallest infinity possible
how to prove that infinities can have different sizes
the continuum hypothesis of infinite sets
why there is always a larger infinity.

As part of the course there are in-video quiz questions to consolidate your learning, suggested further readings to stimulate a deeper exploration of the topic, discussion boards to have your say and an end-of-course assessment set by Professor Cameron.

IAI Academy courses are designed to be challenging but accessible to the interested student. No specialist knowledge is required.

The end-of-course assessment is available for authentication by our online proctoring partners Software Secure. Lean how you can earn a verified certificate.

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Where and when

Starts Location

What you'll learn on the course

Larger infinity
History of infinity
Cantor’s Paradise

Course programme

Course Syllabus
  • Part One: From the Greeks to the GeeksNot just a mathematical curiosity, the history of infinity is rife with madness, power and paradox
  • Part Two: Is the Universe Infinite?Could the universe not contain any real infinities? Cameron challenges leading cosmologists.
  • Part Three: Cantor’s ParadiseDid Georg Cantor solve the puzzle of infinity with set theory, and if not, can we do so at all?

Suggested Further Readings

A selection of further readings has been suggested by Professor Cameron as part of this course.

Explore Further

Our editors have brought together a range of content from across which further explores the ideas in this course.

About the Instructor
  • Peter Cameron

    Multiple award-winning Professor of Mathematics Peter Cameron frequently engages the public in how to think like a mathematician. He has an Erdös number of 1.