Dave Richeson
@divbyzero.bsky.social
Mathematician. John J. & Ann Curley Chair in Liberal Arts at Dickinson College. Author of Tales of Impossibility and Euler's Gem. Coffee drinker. [Everything in the timeline before October 2024 was imported from my Twitter/X feed 2008-24.]
Pinned
Dave Richeson
@divbyzero.bsky.social
· Oct 21
Since I'm new here, I'll introduce myself. I'm a math prof at Dickinson College. I'm author of Euler's Gem and Tales of Impossibility. I was editor of Math Horizons. I am interested in topology, dynamical systems, geometry, history of math, recreational math, math & art, and expository math writing.
Reposted by Dave Richeson
For what it's worth, I tangled with the same year-of-publication question until I came across this (fascinating!) footnote in Copeland's book "The Essential Turing", and it sounded authoritative enough for me to take it as gospel.
![A footnote from Copeland's book "The Essential Turing". It reads:
"Proceedings of the London Mathematical Society, 42 (1936–7), 230–65. The publication date of ‘On Computable Numbers’ is sometimes cited, incorrectly, as 1937. The article was published in two parts, both parts appearing in 1936. The break between the two parts occurred, rather inelegantly, in the middle of Section 5, at the bottom of p. 240 (p. 67 in the present volume). Pages 230–40 appeared in part 3 of volume 42, issued on 30 Nov. 1936, and the remainder of the article appeared in part 4, issued on 23 Dec. 1936. This information is given on the title pages of parts 3 and 4 of volume 42, which show the contents of each part and their dates of issue. (I am grateful to Robert Soare for sending me these pages. See R. I. Soare, ‘Computability and Recursion’, Bulletin of Symbolic Logic, 2 (1996), 284–321.)
The article was published bearing the information ‘Received 28 May, 1936.—Read 12 November, 1936.’ However, Turing was in the United States on 12 November, having left England in September 1936 for what was to be a stay of almost two years (see the introductions to Chapters 3 and 4). Although papers were read at the meetings of the London Mathematical Society, many of those published in the Proceedings were ‘taken as read’, the author not necessarily being present at the meeting in question. Mysteriously, the minutes of the meeting held on 18 June 1936 list ‘On Computable Numbers, with an Application to the Entscheidungs- problem’ as one of 22 papers taken as read at that meeting. The minutes of an Annual General Meeting held [...]"](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:f6tvcgb4p6fmvinz23kus77k/bafkreicnvavdeuakfijlzm5z5t3pv7p6ppou3lohgligl7jumyvi3czwh4@jpeg)
![The continuation of a footnote from Copeland's book "The Essential Turing". It reads:
"[...] on 12 Nov. 1936 contain no reference to the paper. (I am grateful to Janet Foster, Archives Consultant to the London Mathematical Society, for information.)"](https://cdn.bsky.app/img/feed_thumbnail/plain/did:plc:f6tvcgb4p6fmvinz23kus77k/bafkreicbeixwjoo5ceveokhzdu3tw7zqmdmg77l2deuhgqxtkfibr4snda@jpeg)
January 5, 2026 at 11:10 PM
For what it's worth, I tangled with the same year-of-publication question until I came across this (fascinating!) footnote in Copeland's book "The Essential Turing", and it sounded authoritative enough for me to take it as gospel.
Years ago (15?) I must have written my name and email address somewhere, and someone typed it as "Dale" instead of "Dave." It is interesting to observe the waves of Dale-email I get when some spammer buys that list of addresses. I hadn't for a while until a week or so ago, and now I'm flooded again.
January 5, 2026 at 5:09 PM
Years ago (15?) I must have written my name and email address somewhere, and someone typed it as "Dale" instead of "Dave." It is interesting to observe the waves of Dale-email I get when some spammer buys that list of addresses. I hadn't for a while until a week or so ago, and now I'm flooded again.
Here's an old blog post I wrote about a footnote in Turing's 1937 article "On computable numbers with an application to the Entscheidungsproblem," in which he gave a topological argument that any alphabet must be finite. divisbyzero.com/2010/05/27/t...
Turing’s topological proof that every written alphabet is finite
Recently one of my colleagues was reading Alan Turing’s groundbreaking 1936 article “On Computable Numbers with an Application to the Entscheidungsproblem.” This is the article in…
divisbyzero.com
January 5, 2026 at 4:48 PM
Here's an old blog post I wrote about a footnote in Turing's 1937 article "On computable numbers with an application to the Entscheidungsproblem," in which he gave a topological argument that any alphabet must be finite. divisbyzero.com/2010/05/27/t...
Reposted by Dave Richeson
Super-ambitious project by Jonatan Nielavitzky: a 3D printed Babbage Difference Engine! He says it's a work-in-progress but it looks pretty polished to me.
Show him some appreciation on youtube if you have a moment! (I'm trying to encourage him to keep going)
www.youtube.com/watch?v=NvOR...
Show him some appreciation on youtube if you have a moment! (I'm trying to encourage him to keep going)
www.youtube.com/watch?v=NvOR...
3D Printed Difference Engine
YouTube video by Jonatan Nielavitzky
www.youtube.com
January 5, 2026 at 2:26 PM
Super-ambitious project by Jonatan Nielavitzky: a 3D printed Babbage Difference Engine! He says it's a work-in-progress but it looks pretty polished to me.
Show him some appreciation on youtube if you have a moment! (I'm trying to encourage him to keep going)
www.youtube.com/watch?v=NvOR...
Show him some appreciation on youtube if you have a moment! (I'm trying to encourage him to keep going)
www.youtube.com/watch?v=NvOR...
My year in books: Goodreads said I read 49 books in 2025. However, six were DNFs (a record for me in one year?). As in previous years, I gravitated toward novels, but it is the nonfiction books that really stuck with me. Here are my favorite reads of the year, in no particular order.
January 2, 2026 at 8:07 PM
My year in books: Goodreads said I read 49 books in 2025. However, six were DNFs (a record for me in one year?). As in previous years, I gravitated toward novels, but it is the nonfiction books that really stuck with me. Here are my favorite reads of the year, in no particular order.
My son was **very** pleased with this gift he bought me: a Klein bottle opener! 🤣🤣🤣
January 1, 2026 at 10:36 PM
My son was **very** pleased with this gift he bought me: a Klein bottle opener! 🤣🤣🤣
I saw my college friend Josh Hudak last week. He makes stunning orreries (mechanical models of the solar system), including the glass planets, all the gears, etc. (His entry point was via glass blowing.) Check out his work here www.instagram.com/planetarymac.... He had some questions for me related
December 30, 2025 at 1:43 PM
I saw my college friend Josh Hudak last week. He makes stunning orreries (mechanical models of the solar system), including the glass planets, all the gears, etc. (His entry point was via glass blowing.) Check out his work here www.instagram.com/planetarymac.... He had some questions for me related
I was listening to an interview with Johnny Marr. He shared this quote by Pablo Picasso, which I think is great:
“Inspiration exists, but it has to find you working.”
“Inspiration exists, but it has to find you working.”
December 28, 2025 at 11:32 PM
I was listening to an interview with Johnny Marr. He shared this quote by Pablo Picasso, which I think is great:
“Inspiration exists, but it has to find you working.”
“Inspiration exists, but it has to find you working.”
Another winter season, another example of four and eight pointed snowflakes.
December 28, 2025 at 5:54 PM
Another winter season, another example of four and eight pointed snowflakes.
Computer scientists probably know this, but TIL that the Python programming language was named after Monty Python.
December 26, 2025 at 4:20 PM
Computer scientists probably know this, but TIL that the Python programming language was named after Monty Python.
We got a bird feeder with a camera in it for my parents for Christmas. I had an idea for how it could be the basis of a New Yorker comic. Here’s what I came up with (artwork by ChatGPT).
December 26, 2025 at 3:00 AM
We got a bird feeder with a camera in it for my parents for Christmas. I had an idea for how it could be the basis of a New Yorker comic. Here’s what I came up with (artwork by ChatGPT).
Went for a post-meal walk today and saw a vehicle had driven through paint. My phone measured the distance between the marks as 8 ft. 8 in. = 104 in. So, the diameter of the tires were 104/π=33 in. It must have been a large-wheeled vehicle like a truck or jeep.
December 26, 2025 at 2:55 AM
Went for a post-meal walk today and saw a vehicle had driven through paint. My phone measured the distance between the marks as 8 ft. 8 in. = 104 in. So, the diameter of the tires were 104/π=33 in. It must have been a large-wheeled vehicle like a truck or jeep.
My son was telling me about how, when you copy something, several versions are saved for pasting. This website allows you to see what's on the pasteboard. evercoder.github.io/clipboard-in... I copied some Excel cells, and it saved the cells as HTML, plaintext, and an image of the grid. Who knew?
December 23, 2025 at 2:09 PM
My son was telling me about how, when you copy something, several versions are saved for pasting. This website allows you to see what's on the pasteboard. evercoder.github.io/clipboard-in... I copied some Excel cells, and it saved the cells as HTML, plaintext, and an image of the grid. Who knew?
Reposted by Dave Richeson
It’s always a highlight of the year.
The 2025 Headline of the Year Nominees
🧵
🧵
December 23, 2025 at 1:02 AM
It’s always a highlight of the year.
I'm rereading Cliff Stoll's 1989 book _The Cuckoo's Egg._ It's the true story of a 1986 incident in which Stoll, an astronomer working at Lawrence Berkeley National Laboratory, tracks down a hacker who gained access to their computer network.
In it, he discusses the logical implications of
In it, he discusses the logical implications of
Louis Armstrong - Everybody Loves My Baby
YouTube video by Okmusix
www.youtube.com
December 22, 2025 at 12:32 AM
I'm rereading Cliff Stoll's 1989 book _The Cuckoo's Egg._ It's the true story of a 1986 incident in which Stoll, an astronomer working at Lawrence Berkeley National Laboratory, tracks down a hacker who gained access to their computer network.
In it, he discusses the logical implications of
In it, he discusses the logical implications of
One of my least favorite words to see in a proof: "where." It can mean either "for all" or "for some." An example:
Suppose f(n)=0, where n∊A.
Suppose f(n)=0 for all n∊A.
Suppose f(n)=0 for some n∊A.
Similarly, just using the word "for":
Suppose f(n)=0 for n∊A.
Suppose f(n)=0, where n∊A.
Suppose f(n)=0 for all n∊A.
Suppose f(n)=0 for some n∊A.
Similarly, just using the word "for":
Suppose f(n)=0 for n∊A.
December 19, 2025 at 4:36 PM
One of my least favorite words to see in a proof: "where." It can mean either "for all" or "for some." An example:
Suppose f(n)=0, where n∊A.
Suppose f(n)=0 for all n∊A.
Suppose f(n)=0 for some n∊A.
Similarly, just using the word "for":
Suppose f(n)=0 for n∊A.
Suppose f(n)=0, where n∊A.
Suppose f(n)=0 for all n∊A.
Suppose f(n)=0 for some n∊A.
Similarly, just using the word "for":
Suppose f(n)=0 for n∊A.
I made a Spotify playlist of 50 songs from 2025 that I enjoyed (with my favorites at the top). One song per artist. It was a GOOD YEAR for music! (I know Spotify isn't a great company, but I'm locked in to a family plan with my kids and wife.)
open.spotify.com/playlist/7d3...
open.spotify.com/playlist/7d3...
50 Songs from 2025
open.spotify.com
December 17, 2025 at 6:10 PM
I made a Spotify playlist of 50 songs from 2025 that I enjoyed (with my favorites at the top). One song per artist. It was a GOOD YEAR for music! (I know Spotify isn't a great company, but I'm locked in to a family plan with my kids and wife.)
open.spotify.com/playlist/7d3...
open.spotify.com/playlist/7d3...
Ben Sparks made this wonderful GeoGebra app that lets you create a twisted band (Möbius strip, etc.) and cut it in half or into thirds. As someone who uses GeoGebra quite a bit: Wow! www.geogebra.org/m/v5z33vth
December 17, 2025 at 4:15 PM
Ben Sparks made this wonderful GeoGebra app that lets you create a twisted band (Möbius strip, etc.) and cut it in half or into thirds. As someone who uses GeoGebra quite a bit: Wow! www.geogebra.org/m/v5z33vth
My colleague shared this with me: Regexle (a daily RegEx hexagonal crossword puzzle). regexle.com
December 14, 2025 at 12:02 AM
My colleague shared this with me: Regexle (a daily RegEx hexagonal crossword puzzle). regexle.com
I saw Gwenifer Raymond's album _Last Night I Heard the Dog Star Bark_ on a "best of 2025" list. I'm loving it! But I also wonder whether she studied set theory and whether her song "Banjo Players Of Aleph One" is about the cardinality of the real numbers. gweniferraymond.bandcamp.com/track/banjo-...
Banjo Players of Aleph One, by Gwenifer Raymond
from the album Last Night I Heard The Dog Star Bark
gweniferraymond.bandcamp.com
December 12, 2025 at 3:25 PM
I saw Gwenifer Raymond's album _Last Night I Heard the Dog Star Bark_ on a "best of 2025" list. I'm loving it! But I also wonder whether she studied set theory and whether her song "Banjo Players Of Aleph One" is about the cardinality of the real numbers. gweniferraymond.bandcamp.com/track/banjo-...
Here are a couple of neat theorems due to John Conway and Cameron Gordon (1983):
Any embedding of K_6 in 3D has two linked triangles (red and blue below).
Any embedding of K_7 in 3D has a knotted Hamiltonian circuit (red below).
Article: people.reed.edu/~ormsbyk/138...
Any embedding of K_6 in 3D has two linked triangles (red and blue below).
Any embedding of K_7 in 3D has a knotted Hamiltonian circuit (red below).
Article: people.reed.edu/~ormsbyk/138...
December 11, 2025 at 8:16 PM
Here are a couple of neat theorems due to John Conway and Cameron Gordon (1983):
Any embedding of K_6 in 3D has two linked triangles (red and blue below).
Any embedding of K_7 in 3D has a knotted Hamiltonian circuit (red below).
Article: people.reed.edu/~ormsbyk/138...
Any embedding of K_6 in 3D has two linked triangles (red and blue below).
Any embedding of K_7 in 3D has a knotted Hamiltonian circuit (red below).
Article: people.reed.edu/~ormsbyk/138...
Today's the last day of my intro-to-proofs class. I decided to tell them about several ways to show that a set is countably infinite. Here's an ancient blog post with a few nonstandard methods. divisbyzero.com/2009/09/11/c...
Cardinality of infinite sets, part 1: four nonstandard proofs of countability
The study of cardinalities of infinite sets is one of the most intriguing areas of mathematics that an undergraduate mathematics major will encounter. It never fails to bring crooked smiles of joy,…
divisbyzero.com
December 11, 2025 at 3:22 PM
Today's the last day of my intro-to-proofs class. I decided to tell them about several ways to show that a set is countably infinite. Here's an ancient blog post with a few nonstandard methods. divisbyzero.com/2009/09/11/c...
One of my independent study students in knot theory made me this crocheted Möbius band (using Shiying Dong's video tutorial)!
December 10, 2025 at 8:08 PM
One of my independent study students in knot theory made me this crocheted Möbius band (using Shiying Dong's video tutorial)!