Mind-Bending Math: Riddles and Paradoxes

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24 videos in this collection

Everything in This Lecture Is False
Plunge into the world of paradoxes and puzzles with a "strange loop," a self-contradictory problem from which there is no escape. Two examples: the liar's paradox and the barber's paradox.…
Elementary Math Isn't Elementary
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…
Probability Paradoxes
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…
Strangeness in Statistics
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,…
Zeno's Paradoxes of Motion
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. Then look at the deeper philosophical…
Infinity Is Not a Number
The paradoxes associated with infinity are... infinite! Begin with strategies for fitting ever more visitors into a hotel that has an infinite number of rooms, but where every room is…
More Than One Infinity
Learn how Georg Cantor tamed infinity and astonished the mathematical world by showing that some infinite sets are larger than others. Then use a matching game inspired by dodge ball…
Cantor's Infinity of Infinities
Randomly pick a real number between 0 and 1. What is the probability that the number is a fraction, such as 1/4? Would you believe that the probability is zero?…
Impossible Sets
Delve into Bertrand Russell's profoundly simple paradox that undermined Cantor's theory of sets. Then follow the scramble to fix set theory and all of mathematics with a new set of…
Gödel Proves the Unprovable
Study the discovery that destroyed the dream of an axiomatic system that could prove all mathematical truths - Kurt Godel's demonstration that mathematical consistency is a mirage and that the…
Voting Paradoxes
Learn that determining the will of the voters can require a mathematician. Delve into paradoxical outcomes of elections at national, state, and even club levels. Study Kenneth Arrow's Nobel prize-winning…
Why No Distribution Is Fully Fair
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. Consider the strange results possible with…
Games with Strange Loops
Leap into puzzles and mind-benders that teach you the rudiments of game theory. Divide loot with bloodthirsty pirates, ponder the two-envelope problem, learn about Newcomb's paradox, visit the island where…
Losing to Win, Strategizing to Survive
Continue your exploration of game theory by spotting the hidden strange loop in the unexpected exam paradox. Next, contemplate Parrando's paradox that two losing strategies can combine to make a…
Enigmas of Everyday Objects
Classical mechanics is full of paradoxical phenomena, which Professor Kung demonstrates using springs, a slinky, a spool, and oobleck (a non-Newtonian fluid). Learn some of the physical principles that make…
Surprises of the Small and Speedy
Investigate the paradoxes of near-light-speed travel according to Einstein's special theory of relativity. Separated twins age at different rates, dimensions contract, and other weirdness unfolds. Then venture into the quantum…
Bending Space and Time
Search for the solutions to classic geometric puzzles, including the vanishing leprechaun, in which 15 leprechauns become 14 before your eyes. Next, scratch your head over a missing square, try…
Filling the Gap between Dimensions
Enter another dimension - a fractional dimension! First, hone your understanding of dimensionality by solving the riddle of Gabriel's horn, which has finite volume but infinite surface area. Then venture…
Crazy Kinds of Connectedness
Visit the land of topology, where one shape morphs into another by stretching, pushing, pulling, and deforming - no cutting allowed. Start simply, with figures such as the Mobius strip…
Twisted Topological Universes
Consider the complexities of topological surfaces. For example, a Mobius strip is non-orientable, which means that left and right switch as you move around it. Go deeper into this and…
More with Less, Something for Nothing
Many puzzles are optimization problems in disguise. Discover that nature often reveals shortcuts to the solutions. See how light, bubbles, balloons, and other phenomena provide powerful hints to these conundrums.…
When Measurement Is Impossible
Prove that some sets can't be measured - a result that is crucial to understanding the Banach-Tarski paradox, the strangest theorem in all of mathematics, which is presented in Lecture…
Banach-Tarski's 1 = 1 + 1
The Banach-Tarski paradox shows that you can take a solid ball, split it into five pieces, reassemble three of them into a complete ball the same size as the original,…
The Paradox of Paradoxes
Close the course by asking the big questions about puzzles and paradoxes: Why are we so obsessed with them? Why do we relish the mental dismay that comes from contemplating…

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Close the course by asking the big questions about puzzles and paradoxes: Why are we so obsessed with them? Why do we relish the mental dismay that comes from contemplating a paradox? Why do we expend so much effort trying to solve conundrums and riddles? Professor Kung shows that there's…
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Zeno's Paradoxes of Motion
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. Then look at the deeper philosophical implications, which have gained new relevance through the discoveries of modern physics.
Voting Paradoxes
Learn that determining the will of the voters can require a mathematician. Delve into paradoxical outcomes of elections at national, state, and even club levels. Study Kenneth Arrow's Nobel prize-winning impossibility theorem, and assess the U.S. Electoral College system, which is especially prone to counterintuitive results.
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