Mind-Bending Math: Riddles and Paradoxes

Course Overview

Want to stretch your brain in surprising ways? If you like to think, solve riddles, and exercise your brain, this captivating course examining logic-based brain teasers is for you. Great math riddles and paradoxes have a long and illustrious history, serving as both tests and games for intellectual thinkers across the globe. Examined in the halls of academia and scrutinized by scholars, students, and amateurs alike, these riddles and paradoxes have brought frustration and joy to those seeking intellectual challenges. In addition, it’s well known that brain exercises are as fundamental to staying sharp as body exercises are to staying fit. Stretching your mind to try to solve a good puzzle, even when the answer eludes you, can help improve your ability to focus.

Now, in the 24 lectures of Mind-Bending Math: Riddles and Paradoxes, you’ll explore the ageless riddles that have plagued even our greatest thinkers in history – confounding the philosophical, mathematical, and scientific minds grappling to solve them. You’ll learn how to break down, examine, and solve these famous quandaries. From ancient Greek philosophers to noodling through an unusual enigma involving spaghetti, you’ll cover a wide range of amazing – and in some cases history-changing – conundrums. When it comes to delving into topics such as bending space and time, and topological universes, you need a knowledgeable and captivating instructor, which you get in abundance with award-winning professor of mathematics David Kung. He infuses each lesson with fun tangents, stories, and real-life riddles, making this one of the most intriguing and entertaining math courses available.

Video Lectures

1. Everything in This Lecture Is False – 33 min
   Plunge into the world of paradoxes and puzzles with a “strange loop,” a self-contradictory problem from which there seems no escape. Two examples: the liar’s paradox and the barber’s paradox. Then “prove” that 1+1=1, and visit the Island of Knights and Knaves, where only the logically minded survive!
2. Elementary Math Isn’t Elementary – 28 min
   Discover why all numbers are interesting and why 0.99999… is nothing less than the number 1. Learn that your intuition about breaking spaghetti noodles is probably wrong. Finally, see how averages—from gas mileage to the Dow Jones Industrial Average—can be deceptive.
3. Probability Paradoxes – 31 min
   Investigate a puzzle that defied some of the most brilliant minds in mathematics: the Monty Hall problem, named after the host of Let’s Make a Deal! Hall would let contestants change their guess about the location of a hidden prize after revealing new information about where it was not.
4. Strangeness in Statistics – 31 min
   While some statistics are deliberately misleading, others are the product of confused thinking due to Simpson’s paradox and similar errors of statistical reasoning. See how this problem arises in sports, social science, and especially medicine.
5. Zeno’s Paradoxes of Motion – 30 min
   Tour a series of philosophical problems from 2,400 years ago: Zeno’s paradoxes of motion, space, and time. Explore solutions using calculus and other techniques.
6. Infinity Is Not a Number – 29 min
   The paradoxes associated with infinity are… infinite! Strategies for fitting ever more visitors into a hotel that has an infinite number of rooms, but where every room is already occupied.
7. More Than One Infinity – 31 min
   Learn how Georg Cantor tamed infinity and astonished the mathematical world by showing that some infinite sets are larger than others.
8. Cantor’s Infinity of Infinities – 33 min
   Randomly pick a real number between 0 and 1. What is the probability that the number is a fraction, such as ¼? Would you believe that the probability is zero?
9. Impossible Sets – 29 min
   Delve into Bertrand Russell’s paradox that undermined Cantor’s theory of sets. Follow the scramble to fix set theory and all of mathematics.
10. Godel Proves the Unprovable – 30 min
    Study the discovery that destroyed the dream of an axiomatic system that could prove all mathematical truths.
11. Voting Paradoxes – 30 min
    Learn that determining the will of the voters can require a mathematician. Delve into paradoxical outcomes of elections.
12. Why No Distribution Is Fully Fair – 29 min
    See how the founders of the U.S. struggled with a mathematical problem rife with paradoxes: how to apportion representatives to Congress based on population.
13. Games with Strange Loops – 32 min
    Leap into puzzles and mind-benders that teach you the rudiments of game theory.
14. Losing to Win, Strategizing to Survive – 29 min
    Continue your exploration of game theory by spotting hidden strange loops in unexpected contexts.
15. Enigmas of Everyday Objects – 30 min
    Classical mechanics is full of paradoxical phenomena, demonstrated using common objects.
16. Surprises of the Small and Speedy – 33 min
    Investigate the paradoxes of near-light-speed travel according to Einstein’s theory of relativity.
17. Bending Space and Time – 30 min
    Search for solutions to classic geometric puzzles.
18. Filling the Gap between Dimensions – 32 min
    Understand dimensionality by solving the riddle of Gabriel’s horn.
19. Crazy Kinds of Connectedness – 31 min
    Visit the land of topology, where shapes morph into each other.
20. Twisted Topological Universes – 31 min
    Consider the complexities of topological surfaces.
21. More with Less, Something for Nothing – 29 min
    Discover optimization problems that nature often reveals shortcuts to.
22. When Measurement Is Impossible – 34 min
    Prove that some sets can’t be measured, a result that is crucial to understanding the Banach-Tarski paradox.
23. Banach-Tarski’s 1 = 1 + 1 – 33 min
    The Banach-Tarski paradox shows that you can take a solid ball and split it into pieces and reassemble them in astonishing ways.
24. The Paradox of Paradoxes – 32 min
    Close the course by asking the big questions about puzzles and paradoxes and why they captivate us.