Sign in

Paul Johnson

@ptwiddle.bsky.social
364 followers 667 following 571 posts

American mathematician in the UK. Mellowing in middle age. He/Him.

PostsRepliesMedia
Paul Johnson @ptwiddle.bsky.social · 13/10/2026
Amused by the disclaimer on Andy Pitman's latest preprint: arxiv.org/abs/2610.10775
Screenshot of the end of a maths paper from the arxiv. The text reads:

10. Tool use

Before they will allow me to post this paper, the moderators of the arXiv have told me to declare any use of “sophisticated tools” in its preparation. I suspect that they do not consider me a “sophisticated tool” for the purposes of this declaration. Despite this, I hope
the following remarks will satisfy them:
• I have understood the technical details of the proofs in this paper for well over a
decade. My 2012 paper [61] depended on Theorem A, and I would not have been
comfortable writing [61] without knowing how to prove Theorem A.
• Every word of this paper was written by me on my iMac using vim in a terminal
window.
• The figures were all drawn by hand using the software Inkscape. I did use an LLM
to convert the labels on the figures from the Inkscape default font to Computer
Modern so they would match the font used in the rest of the paper.
• The references are all papers/books that I already knew about or found using
mathscinet and google. I suppose I might have looked at the AI overview at the top
of a google search.
• I used an LLM to check the grammar and usage of this paper after it was written.
Because of this, it has slightly fewer “the the”s, and also takes more care with trivial
edge cases. For instance, the LLM was very insistent that since M0,3 is a single
point it is wrong to say that Mg,n is not compact and that we need to add points
corresponding to stable curves to compactify it.
• To find references in SGA, I used the LLM generated English translation of SGA that was posted at https://grothendiecksga.com. I would like to thank the anonymous creators of that website.
3100
Paul Johnson @ptwiddle.bsky.social · 03/10/2026
Hmmm. I'm happy with 3 against 4 and 3 against 5 polyrhythms, but I should probably master 4 against 5 before trying to play 3 against 4 against 5 all at once.
Two bars of the piano accompaniment to Gabriel Kahane's Baedeker -- 3/4 time, left hand playing quarter notes, right hand playing five notes against dotted quarter notes, making a 3/4/5 polyrhythm.
140
Paul Johnson @ptwiddle.bsky.social · 18/09/2026
It *feels* like the daily arXiv submission numbers are getting oppressively huge and I just checked arxiv.org/stats/monthl... and yuuuuuuuuup. Also note the pandemic.
Graph showing the number of submissions to the arXiv over time since it started in the mid 90s.  Starts with what looks like linear growth, but the right half of the graph starts to climb rapidly (with, interestingly, a slowdown during the pandemic)
150
Paul Johnson @ptwiddle.bsky.social · 12/09/2026
I'm a simple man; seeing these enharmonic notes back to back amuses me. (@gabrielkahane.bsky.social's Baltimore, for those keeping score at home. Piano party is easy to get through but harder to make sound good. And singing in tune to the harmonies? 😬)
A bar of sheet music. Lyrics "Luke, I guess, got himself into a fight". Piano part has two notes highlighted, played consecutively by right pinky: and F-sharp, and a G-flat.
130
Paul Johnson @ptwiddle.bsky.social · 03/09/2026
Coincidentally, my view when I looked over from reading this:
View out a front window, some terraced houses in the background, foreground has a copy of James C. Scott's "Seeing like a State", and a UCU strike armband
020
Paul Johnson @ptwiddle.bsky.social · 20/08/2026
Satisfying feeling of a proof seeming more complicated than I remembered and worrying it was going to spiral to something messy and unsatisfying (devil of algebra) only to find the cute little picture that makes it easy again (angel of topology/geometry).
A very simple line drawing png make with tikz -- a square representing a torus with a line of slope 2/3 wrapping around it.  A shaded band with slope -1 wraps around, too.
040
Paul Johnson @ptwiddle.bsky.social · 30/07/2026
I remember there being some stuff about "exceptional coffee" in the branding but sadly I didn't capture photographic evidence.
Sandwich board sign advertising "G_2 Coffee at West One"
031
Paul Johnson @ptwiddle.bsky.social · 12/06/2026
Had never noticed this plaque, which leaves out that she moved to Australia a few years later, estranged from her mother Emmeline, and was a founder of the "Australia First" movement, isolationist in World War 2. That famous suffragette-->communist-->fascist pipeline.
Plaque on a pavement, saying "Adela Pankhurst suffragette lived here 1910-1911"
030
Paul Johnson @ptwiddle.bsky.social · 08/06/2026
Perks of being a regular: your barista/shop owner flags you down when he sees you passing across the street to foist leftover pastries on you because they're closed tomorrow.
 Cardamom knot on a plate with a bite out, a few bags in the background with a chocolate croissant visible
090
Paul Johnson @ptwiddle.bsky.social · 20/05/2026
My 9 y.o. made me a set of Borromean Rings. I feel seen.
A hand holding up a set of Borromean rings made from paper
080
Paul Johnson @ptwiddle.bsky.social · 01/05/2026
An 8 by 8 grid of partitions into distinct parts. No explanation given.
340
Paul Johnson @ptwiddle.bsky.social · 23/03/2026
My favorite bit of I94 in North Dakota is the flat as a pancake continental divide. Bismarck is on the Missouri river which flows I to the Mississippi and down to the Gulf of Mexico; Fargo is on the Red River which flows North into Hudson Bay. But it's just great plain between them.
Road side saying there's a continental divide; but it's the middle of a flat green field and not the "expected" mountain.
060
Paul Johnson @ptwiddle.bsky.social · 31/01/2026
Two mutuals in a row doing it with the same bit I was using, so I'll tweak it and do five undergrad courses where we just read a single book: 1. Structure and Interpretation of Computer Programs 2. Tristram Shandy 3. Pale Fire 4. Ulysses 5. Three-Dimensional Geometry and Topology
Two bsky posts from mathematicians, doing the "5 courses you took as an undergrad" meme, with the first four of each being mostly liberal arts courses and the last one being differential geometry.
020
Paul Johnson @ptwiddle.bsky.social · 20/01/2026
The smallest hint of colour.
Grey high rise hospital on a grey day. One window has pink and blue colour frames and yellow and green blocks of colour
030
Paul Johnson @ptwiddle.bsky.social · 18/12/2025
Poster of "The Lovers" Tarot card art with a furby flipping the bird as a priest? And Mr. and Mrs. Blobby as the lovers. Your guess is as good as mine.
100
Paul Johnson @ptwiddle.bsky.social · 16/12/2025
Leaving work *before 4:30* to play dad taxi and it's already basically dark. Bring on the longer days already....
View of an urban sunset. Children's hospital with lots of bright lights in foreground
161
Paul Johnson @ptwiddle.bsky.social · 11/09/2025
Finally getting around to reading @essj.bsky.social's Darryl after seeing I think @jsellenberg.bsky.social talk about it ages ago? Anyway, it's great, Darryl's voice is :chef's kiss:, and *of course* he's a Lebowski guy. It's made me pull Berryman's Dream Songs down off my shelf.
A paragraph from Jackie Ess's Darryl:

Satori is such a perfect woman that she makes a man even out of me. I am a man. But my manhood is like a hothouse flower, not of our climate. Delicate, but real. I feel strong. There's a Bob Dylan song where he says, "Take a woman like your kind to find the man in me.' So is 'your kind' a slightly hippie goth aesthetic in a spiritually realized poly chick? He probably meant a different kinda I think that's why the song works though, it's nothing to do with types. But the song totally inhabits a moment, the guy singing it does t know that yet. I never really liked Bob Dylan, it always felt like he was lecturing me or trying to get me to be a Christian or something, but I heard that song in a movie once, and it made me go back to his stuff.
140
Paul Johnson @ptwiddle.bsky.social · 02/09/2025
Last day of summer vibes.
Squirrel sprawled out on its belly in the sun at the peak of a tiled roof.
091
Paul Johnson @ptwiddle.bsky.social · 05/08/2025
Written out quickly and a bit ugly...
Messy handwritten proof using similar triangles
110
Paul Johnson @ptwiddle.bsky.social · 01/07/2025
Late to the sign meme, but loved this bit of guerilla activism at an intersection close to @sheffielduni.bsky.social that really needs a pedestrian crossing. Just walked by it this morning and the sign has been taken down.
Picture of an official looking sign saying "PEDESTRIANS GOOD LUCK" attached to a lamppost in front of a busy intersection.
2305
Paul Johnson @ptwiddle.bsky.social · 28/06/2025
Thanks! Here's the people who will be streaming by you in an hour or two.
020
Paul Johnson @ptwiddle.bsky.social · 27/06/2025
Just finished session Zero of Slugblaster by @wilkiescandylab.com with @thebadspot.bsky.social , @jenduckie.bsky.social @andrewwormald.bsky.social. Excited for first session, and not just because the endpaper is the 15th and final pentagonal tiling to be found. (And a tiny K-Theory reference...)
Picture of the 15th pentagonal tiling, white lines on black paper)
073
Paul Johnson @ptwiddle.bsky.social · 07/06/2025
First learned about ginger congee when reading The Year of Magical Thinking, and didn't really know what it was but it's comforting powers stuck with me, I made it once, and now it's a go-to. Any food you love that you've learned from a boo/song/ someplace you couldn't see/smell it first?
Bowl of rice porridge with cilantro, pumpkin seeds, and green onion on top, next to some broccoli on a plate.
170
Paul Johnson @ptwiddle.bsky.social · 21/12/2024
Birthday books! "Oh, I follow @antonhur.com on Bluesky!" Scotch and chocolates and socks not pictured.
Two books on a table. Black Paper by Teju Cole, and Toward Eternity by Anton Hur.
240
Paul Johnson @ptwiddle.bsky.social · 19/12/2024
How about some roses? (is a rose is a rose is a rose)
Snipper from Culler and Vogtmann's Moduli of Graphs and Automorphisms of Free Groups. Starting in Section 1.3 Roses, it states the Gertrude Stein Lemma.
131
Paul Johnson @ptwiddle.bsky.social · 16/12/2024
This immediately brought up Thurston's "On Proof and Progress in Mathematics" arxiv.org/abs/math/940...
This question brings to the fore something that is fundamental and pervasive:
that what we are doing is finding ways for people to understand and think about
mathematics.
The rapid advance of computers has helped dramatize this point, because computers and people are very different. For instance, when Appel and Haken completed a proof of the 4-color map theorem using a massive automatic computation,
it evoked much controversy. I interpret the controversy as having little to do with
doubt people had as to the veracity of the theorem or the correctness of the proof.
Rather, it reflected a continuing desire for human understanding of a proof, in
addition to knowledge that the theorem is true.
On a more everyday level, it is common for people first starting to grapple with
computers to make large-scale computations of things they might have done on a
smaller scale by hand. They might print out a table of the first 10,000 primes,
only to find that their printout isn’t something they really wanted after all. They
discover by this kind of experience that what they really want is usually not some
collection of “answers”—what they want is understanding.
030
Paul Johnson @ptwiddle.bsky.social · 08/12/2024
TFW you're exploring on your long run and only vaguely know where you are and stumble across the outdoor market with the good coffee.
Selfie of bearded man (me!) in running gear,  holding a paper espresso cup, in front of small green van with "Motore Cafe" written on it. Nether Edge market, Sheffield.
261
Paul Johnson @ptwiddle.bsky.social · 07/12/2024
I thought everyone had their own copy? (I think mine was around twenty pounds from the massive Sainsbury's).
A hand holding a copy of the Borromean Rings made out of wood: three loops so that are interlocked in such a way that they can't be separated, but if any one loop was removed, the other two could be separated.
071
Paul Johnson @ptwiddle.bsky.social · 03/12/2024
Somebody was thrilled to be watching the Lionesses.
View at a football match. Looking over the shoulder of a young girl as she reads a novel, green of the pitch, bright lights and the crowd in the background.
020
Paul Johnson @ptwiddle.bsky.social · 24/11/2024
Fun on my run!
A stone staircase outside, turned into a waterfall.
010
Paul Johnson @ptwiddle.bsky.social · 19/11/2024
Today's run was more of a sanity jog, stopping to just enjoy the rare snow.
View over a snow covered valley.Snowy forest scene, path along an old mill wall, mill run on the left and the river Rivelin on the right.
020
Paul Johnson @ptwiddle.bsky.social · 18/11/2024
In happier news:
Blurry shot of snow falling in streetlight in front of stone building
020
Paul Johnson @ptwiddle.bsky.social · 18/11/2024
Of course that counts. If you want it not to count switch it to your kid being a bat on Halloween this year (mask handmade by her elder sister).
Not a birb, but a bat -- a child in a narrow brick alley trick or treating in a bat costume.
220
Paul Johnson @ptwiddle.bsky.social · 15/11/2024
One last coffee in the park before the cold snap hits.
Weston Park in Sheffield. Modernist building Arts Tower in the background, teal bandstand, one large tree with just a few leaves hanging on still and a carpet of them spread beneath.
010
Paul Johnson @ptwiddle.bsky.social · 14/11/2024
It's the leave work early to still have a little light on the walk home time of year.
Trees and power lines in silhouette against a grey-blue dusk sky.
010