Mind-Bending Math: Riddles and Paradoxes

Course Overview

Course No. 1466

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. In 24 lectures, you’ll explore the ageless riddles that have plagued even our greatest thinkers in history – confounding philosophical, mathematical, and scientific minds.

From ancient Greek philosophers to unusual spaghetti enigmas, you’ll cover amazing (and sometimes history-changing) conundrums about space, time, and topological universes with award-winning professor David Kung.

Video Lectures

01: Everything in This Lecture Is False (33 min)

Explore strange loops through the liar’s paradox, barber’s paradox, and “proving” 1+1=1. Survive the Island of Knights and Knaves through pure logic.

02: Elementary Math Isn’t Elementary (28 min)

Discover why all numbers are interesting, why 0.999… equals 1, why broken spaghetti defies intuition, and how averages can deceive.

03: Probability Paradoxes (31 min)

Tackle the Monty Hall problem and examine how subtle wording changes (“my elder child” vs “one of my children”) alter probability outcomes.

04: Strangeness in Statistics (31 min)

Uncover Simpson’s paradox and other statistical pitfalls that mislead in sports, social science, and even medical research.

05: Zeno’s Paradoxes of Motion (30 min)

Solve ancient Greek paradoxes about motion using calculus while exploring their modern relevance in physics.

06: Infinity Is Not a Number (29 min)

Check infinite guests into a full hotel and examine supertasks – infinite steps completed in finite time.

07: More Than One Infinity (31 min)

Discover how Cantor proved some infinities are larger than others using a dodgeball-inspired matching game.

08: Cantor’s Infinity of Infinities (33 min)

Learn the shocking probability that a random real number is a fraction (zero!) and other infinite set mysteries.

09: Impossible Sets (29 min)

Explore Russell’s paradox that undermined set theory and the axioms developed to restore mathematical consistency.

10: Gödel Proves the Unprovable (30 min)

Understand how Gödel’s incompleteness theorems show mathematical consistency is unattainable.

11: Voting Paradoxes (30 min)

Examine Arrow’s impossibility theorem and why the U.S. Electoral College produces counterintuitive results.

12: Why No Distribution Is Fully Fair (29 min)

Analyze the mathematical struggles behind congressional apportionment and why no perfect system exists.

13: Games with Strange Loops (32 min)

Divide pirate loot, solve the two-envelope problem, explore Newcomb’s paradox and prisoner’s dilemmas.

14: Losing to Win, Strategizing to Survive (29 min)

Discover how two losing strategies can win (Parrondo’s paradox) and use set theory to perform “hat game” miracles.

15: Enigmas of Everyday Objects (30 min)

See springs, slinkies and oobleck demonstrate classical mechanics paradoxes (plus how to float a cruise ship in a gallon).

16: Surprises of the Small and Speedy (33 min)

Experience relativity’s twin paradox and quantum physics’ wave-particle duality and uncertainty principle.

17: Bending Space and Time (30 min)

Solve geometric puzzles including vanishing leprechauns, missing squares, and how to ride square-wheeled bicycles.

18: Filling the Gap between Dimensions (32 min)

Explore fractional dimensions through Gabriel’s horn (finite volume, infinite area) and fractal shapes like the Menger sponge.

19: Crazy Kinds of Connectedness (31 min)

Morph through topological surfaces from Möbius strips to Klein bottles, counting minimum colors needed for each.

20: Twisted Topological Universes (31 min)

Watch Professor Kung play catch in a 3-torus and twist through manifolds in non-orientable spaces.

21: More with Less, Something for Nothing (29 min)

Let nature reveal optimization shortcuts through light, bubbles and the surprising Kakeya needle solution.

22: When Measurement Is Impossible (34 min)

Construct non-measurable sets – the key to understanding Banach-Tarski’s astonishing paradox.

23: Banach-Tarski’s 1 = 1 + 1 (33 min)

Learn how to split one ball into two identical balls through mathematical “magic” with six pieces.

24: The Paradox of Paradoxes (32 min)

Explore why humans obsess over puzzles and paradoxes, and what this reveals about our minds.