Mathematical Enchantments

Adventures in fantastic realms you can build inside your head
Welcome to Mathematical Enchantments (aka "Jim Propp's math blog") !
Blog posts (uploaded on the 17th of each month) are at my wordpress site,

http://mathenchant.wordpress.com,
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
96: Seekers of the One-Stone: text
97: Hamilton's Quaternions, or, The Trouble with Triples: text
98: What is a Matrix?: text
99: The Triumphs of Sisyphus: text
100: Math for Your Ear: text
101: When Five Isn't Prime: text
102: Marvelous Arithmetics of Distance: text
103: Numbers Far Afield: text
104: Vectors from Leibniz to Einstein: text
105: What "a 96 percent chance" doesn't mean: text
106: Plus and Times Set Free: text
107: Nine Years of Blogging About Math: text
108: "Jewish Mathematics"? text
109: Zero-to-the-Zero and the Do-Nothing Machine: text
110: Math's Mutable Rules: text
111: When 1+1 Equals 1: text
112: Math for English Majors and Everybody Else: text
113: Our Fractional Universe: text
114: Industrious Dice: text
115: Can Math Save Your Soul?: text
116: When 1+1+1 Equals 1:
117: The Real Lines versus the Fakes: text
118: Dedekind's Subtle Knife: text
119: How Pi Almost Wasn't: text
120: Is 1 Prime, and Does It Matter?: text
121: Math and the Museum: text
122: Remembering Kelly: text
123: When .999... Isn't 1: text
124: Randomness Made to Order, part 1: text
125: Picturing Mathematics: 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.
Essay #33, "The Genius Box", was expanded and published in the Journal of Humanistic Mathematics; you can read it at https://scholarship.claremont.edu/jhm/vol11/iss2/27/. See also essay #77, "Miracle People: A "Genius Box" Postscript". Compressed versions of several of these essays (#10, #26, #45, #59, #64, #84, #119, and #120) have appeared in Math Horizons.
I have a Twitter feed, under the name @JimPropp, though I'm not as active there as I used to be; nowadays you're more likely to find me at Mastodon (more specifically, mathstodon.xyz), also as @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.
Like this page? Like it on Facebook!
If you want to start a math blog of your own, check out my list of tips for blogging about math in WordPress. Essay #107 may also be of interest; it describes what I learned during my first nine years of blogging.
- Jim Propp, Department of Mathematical Sciences, UMass Lowell