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Online Course

Paradox and Infinity

Massachusetts Institute of Technology via edX


In Paradox and Infinity, you will be introduced to highlights from the intersection of philosophy and mathematics.

The class is divided into three modules:

  • Infinity: Learn about how some infinities are bigger than others, and explore the mind-boggling hierarchy of bigger and bigger infinities.
  • Time Travel and Free Will : Learn about whether time travel is logically possible, and whether it is compatible with free will.
  • Computability and Gödel's Theorem : Learn about how some mathematical functions are so complex, that no computer could possibly compute them. Use this result to prove Gödel's famous Incompleteness Theorem.

Paradox and Infinity is a math-heavy class, which presupposes that you feel comfortable with college-level mathematics and that you are familiar with mathematical proofs.

Learners who display exceptional performance in the class are eligible to win the MITx Philosophy Award. High School students are eligible for that award and, in addition, the MITx High School Philosophy award. Please see the FAQ section below for additional information.

Note: learners who do well in Paradox will have typically taken at least a couple of college-level classes in mathematics or computer science. On the other hand, Paradox does not presuppose familiarity with any particular branch of mathematics or computer science. You just need to feel comfortable in a mathematical setting.


Module 1: INFINITY

Week 1 Infinite Cardinalities

Week 2 The Higher Infinite

Week 3 Omega-Sequence Paradoxes


Week 4 Time Travel

Week 5 Newcomb's Problem

Week 6 Probability

Week 7 Non-Measurable Sets

Week 8 The Banach-Tarski Theorem


Week 9 Computability

Week 10 Gödel's Theorem

Taught by

Agustin Rayo

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4.2 rating, based on 5 reviews

Start your review of Paradox and Infinity

  • Charles Durbin

    Charles Durbin completed this course, spending 4 hours a week on it and found the course difficulty to be medium.

    This course was excellent. The instructor was solid, but the content of the course is what makes this such a unique experience. If you have a penchant for abstract thinking and contemplating the complexities and puzzles of life - whether or not you enjoy mathematics - this course has a world of pleasures to offer. If you really hate math, then I would suggest skipping a couple of the weeks - but there's so many other stimulating things to learn that it's still worth it.

    Would have loved to hear more on how mathematicians and physicists struggle to find common ground with the concept of infinity...
  • Profile image for Monica Guimaraes
    Monica Guimaraes

    Monica Guimaraes is taking this course right now, spending 20 hours a week on it and found the course difficulty to be very hard.

    There are not enough exercises to thoroughly learn the material. The exams are extremely tricky and more difficult than the exercises provided.
  • Jacob Regan completed this course.

  • Steven Xu completed this course.

  • Yue Yun completed this course.

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