Welcome to Mathematical Enchantments (aka "Jim Propp's math blog") !

Blog posts (uploaded on the 17th of each month) are at my wordpress site,

and links to all posts and to audio files (in .wav or .mp3 format) are for the time being available right here:

- 0: Why this blog? : text and audio
- 1: The lessons of a square-wheeled trike : text and audio
- 2: The life of games : text
- 3: The one about .999... : text
- 4: Polya's urn : text
- 5: Erdos for epsilons: "The Boy Who Loved Math" : text
- 6: "Really Big Numbers" : text
- 7: How to be wrong : text
- 8: When not to expect what you're expecting : text
- 9: Believe it, then don't: toward a pedagogy of discomfort : text
- 10: The paintball party problem and the habit of symmetry : text (this essay was published in abridged form in 2017 in Math Horizons and received the 2018 Trevor Evans Award)
- 11: Fermat's Last Theorem: the curious incident of the boasting Frenchman : text
- 12: Sri Ramanujan and the secrets of Lakshmi: text
- 13: "The Man Who Knew Infinity": what the film will teach you (and what it won't) : text
- 14: Bertrand's Ballot Problem : text
- 15: Going Negative, part 1 : text
- 16: Going Negative, part 2 : text
- 17: Breaking logic with self-referential sentences : text
- 18: Will '17 be the Year of the Pig? : text
- 19: Avoiding chazakah with the Prouhet-Thue-Morse sequence : text
- 20: Three-point-one cheers for pi! : text
- 21: Band saw blades, bedbug zappers, rubber bands and me : text
- 22: More about .999... : text
- 23: Minus infinity : text
- 24: Reading, writing, and rigor : text
- 25: Swine in a Line : text
- 26: Prof. Engel's Marvelously Improbable Machines : text (this essay was published in abridged form in 2018 in Math Horizons and was republished in Princeton University Press, Best Writing on Mathematics 2019)
- 27: How Do You Write One Hundred in Base 3/2? : text
- 28: The global roots of Exploding Dots : text
- 29: Impaled on a Fencepost : text
- 30: The Roots of Unity : text
- 31: On Size, Death, and Dinosaurs : text
- 32: Roasting a Dodo and Biking on Mars : The Magic of Dimensional Analysis: text
- 33: The Genius Box : text
- 34: Who Knows Two? : text
- 35: Time and Tesseracts : text
- 36: Why does Exploding Dots work? : text
- 37: A pair of shorts ("The Mystery of the Vanishing Rope Trick" and "Cantor's Paradise Meets Skolem's Paradox") : text
- 38: Knots and Narnias : text
- 39: A New Game with Infinity : text
- 40: ChipChip : A new sort of sorting: text
- 41: Between the World and the Mind : text
- 42: Stance and Distance in Popular Writing about Math : text
- 43: Introducing "Thirdsday" : text
- 44: The Magic of Nine : text
- 45: Who Mourns the Tenth Heegner Number? : text (this essay was published in abridged form in 2019 in Math Horizons and was reprinted in Best Writing on Mathematics 2020)
- 46: Flip Your Students, Flip Yourself : text
- 47: Mazes, Puzzles, and Proofs : text
- 48: A Mathematician in the Jury Box, or, "But how should we define 'intoxicated'?" : text and audio.
- 49: Carnival of Mathematics #170 : text
- 50: Mathematical FlimFlam : text and audio
- 51: My Favorite Theorem : text and audio
- 52: Calculus is Deeply Irrational : text
- 53: Sphere-Packing : text
- 54: Guess Again: The Ehrenfeucht-Mycielski Sequence : text
- 55: Let Us Define Our Terms : text
- 56: The Null Salad : text
- 57: What Proof Is Best? : text
- 58: Chess with the Devil : text
- 59: The Square Root of Pi : text (this essay was published in abridged form in 2021 in Math Horizons)
- 60: Air from Archimedes : text
- 61: Confessions of a Conway Groupie : text
- 62: The Mathematics of Irony : text
- 63: Math, Games, and Ronald Graham : text
- 64: The Muffin Curse : text (this essay was published in abridged form in 2022 in Math Horizons)
- 65: How Can Math Be Wrong? : text
- 66: When 1+1 Equals 0 : text
- 67: The Positive Side of Impossible : text
- 68: Children of the Labyrinth : text
- 69: My Life with Aztec Diamonds : text
- 70: Thoughts from the Outfield : text
- 71: Dividing by Zero : text
- 72: Who Needs Zero? : text
- 73: Going Negative, part 3 : text
- 74: Going Negative, part 4 : text
- 75: In Praise of Pedantry : text
- 76: Reckoning and Reasoning : text
- 77: Miracle People: A "Genius Box" Postscript : text
- 78: Here There Be Dragons : text
- 79: Why Names Matter: text
- 80: Numbers from Games: text
- 81: Bad Soup: text
- 82: The Clatter of the Primes: text
- 83: Breaking Pi: text
- 84: Tricks of the Trade: text
- 85: Good Shurik Grothendieck: text
- 86: The Remarriage of Math and Physics: text
- 87: Twisty Numbers for a Screwy Universe: text
- 88: Let x Equal x: text
- 89: What Lovelace Did: From Bombelli to Bernoulli to Babbage: text
- 90: Teaching with Magic Paper: text
- 91: The Infinite Stairway: text
- 92: Beneath (and Beyond): text
- 93: Denominators and Doppelgängers: text
- 94: Things, Names, and Numbers: text
- 95: Unlimited Powers: text

Two of these essays have appeared in the Princeton University Press series
*Best Writing on Mathematics*.
Specifically, essay #26, "Professor Engel's Marvelously Improbable Machines",
was reprinted in Best Writing on Mathematics 2019,
and essay #45, "Who Mourns the Tenth Heegner Number?",
was reprinted in Best Writing on Mathematics 2020.

I also have a Twitter feed, under the name @JimPropp.

Other mathematical writings of mine for a general audience are: Chinook (a report on the 1994 Man-Machine World Checkers Championship); my review of "The Cat in Numberland"; and my review of "The Art of Mathematics: Coffee Time in Memphis". (See the bottom of my list of publications for information on where they were published.)

I did a half-hour radio interview in 2007, in which I talked about mathematical proof.

In 2012 and 2013, I gave two talks (or the same talk twice) called "Wild Beauty: Postcards from Mathematical Worlds". The first has better sound-quality, but the second has better slides.

Here's a video of a talk I gave at the University of Connecticut back in April of 2014. It covers many of the themes that I'll be treating in my blog.

In 2016, I gave two talks at the 11th Gathering for Gardner: The Programmable Galton Board: A Shameless Shill and Conway's Impact on the Theory of Random Tilings.

In April of 2017, I gave a talk at the Festival of Bad Ad Hoc Hypotheses ("BAHFest"), and won first prize for my talk on why the dinosaurs really went extinct (and what humankind needs to do to make sure that we don't meet the same fate). Hint: It's about gravity. I've also posted a Q-and-A I did after the event, telling the story of how I came to give the talk.

In 2018, I gave a talk at the 13th Gathering for Gardner: You Can't Count to Thirteen (in Base Two-and-Three).

The logo that appears at the top of the page was designed by me and implemented by Sandi Gubin. Want to know what it is and why I chose it? See essays 41 and 58.

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If you want to start a math blog of your own, check out my list of tips for blogging about math in WordPress.

- Jim Propp, Department of Mathematical Sciences, UMass Lowell