The recent counterexample to the Jacobian conjecture that was
discovered by Claude AI was discussed more recently
by a different instance of Claude, who remarked that . . .
"It's a strange feeling to admire the cleverness of
something I did and can't remember doing."
The Source
https://claude.ai/share/22abed98-d9af-43c5-9881-b19e009a07b0
https://scrapsfromtheloft.com/movies/disclosure-day-2026-transcript/
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You have the gift but no control. No understanding of your purpose. Not a clue as to what your situation will demand of you beyond today. The only way for you to acquire it is to go back to where it all began. To go home. And when you do, Margaret, you’ll know everything. More than what was ever humanly possible. They gifted each of you. Margaret, what was dormant in you for most of your life was activated only yesterday. And yours, 15 years ago. They gave you fluency in the language in which the book of the universe is written: mathematics. Taught it to you, imbued it so you could understand them. And they imbued you so you could understand us. It’s the two of you. [chuckles] It’s always been just the two of you. [quiet, indistinct chatter] You can direct it or feel where it wants to take you. It can find what you’re looking for. It’ll be an instrument of your will. But you must give yourself over to it. |
I prefer an earlier fantasy on this theme . . .
Many Dimensions, by Charles Williams (1931).
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"L'Internationale", original French version
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International anthem of anarchists, communists, |
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| Also known as | « L'Internationale » |
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| Lyrics | Eugène Pottier, 1871 |
| Music |
Pierre De Geyter, 1888 |
| Audio sample | |
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Instrumental rendition in A major
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Update at 2:08 PM ET on July 20, 2026 . . .
with footnotes screenshot of 9:16 PM ET the same day:
For some news today of interest to mathematicians internationally ,
see Wikipedia on a reported finding by the AI Claude Fable 5
of a counterexample to the Jacobian conjecture.
Update of 9:38 AM ET July 21 —
(Claude Fable 5 appeared recently in this journal . . .
See July 8 — "Affine Generation: Claude Fable 5 Weighs In,"
http://m759.net/wordpress/?p=136411.)
"A Nice Way to See"
Logos
"Me — Thank you very much, Claude, for your perceptive remarks.
(By the way, I had in mind only the affine block actions
that make the conjecture work.) That's all for now.
Claude — Thinking about acknowledging previous mathematical
discussion clarification
Claude — You're welcome — and with the affine block actions,
your conjecture holds exactly as stated: those coset-permuting maps
across all choices of W generate precisely AGL(n,2). It's a nice way
to see the affine group built up from many overlapping S4's.
Glad I could help!"
Background reading . . .
"Binary Coordinate Systems," by Steven H. Cullinane —
http://finitegeometry.org/sc/gen/coord.html .
Quote adapted from a famous young-adult novel . . .
"There is such a thing as affine group generation
by permutation of parallel subspaces."
260413-Falls_ich_Pabst-search-AI_Mode.jpg
Toronto geometer H.S.M. Coxeter, introducing a book by Unitarian minister
Richard J. Trudeau —
"There is a pleasantly discursive treatment of Pontius Pilate’s
unanswered question ‘What is truth?’”
— Coxeter, 1987, introduction to Trudeau’s
The Non-Euclidean Revolution
Another such treatment …
"Of course, it will surprise no one to find low standards
of intellectual honesty on the Tonight Show.
But we find a less trivial example if we enter the
hallowed halls of Harvard University. . . ."
— Neal Koblitz, "Mathematics as Propaganda"
Less pleasantly and less discursively —
"Funny how annoying a little prick can be."
— The late Garry Shandling
University Diaries today has a meditation on
nothingness and the University of North Carolina.
She includes a picture by John Picacio that was done as a
cover illustration for the novel A Canticle for Leibowitz .
Related material:
A June 10 obituary for Msgr. Tim O'Connor, former rector
of Sacred Heart Cathedral in Raleigh, NC.
"To those who knew him, O’Connor’s aesthetic sense
was a defining quality. As rector at Sacred Heart Cathedral—
the seat of the bishop of Raleigh— he led a $500,000
renovation project in the late ’90s that refurbished the floors
and pews and installed art, such as painting the ceiling blue
with 14-karat gold leaf stars."
— Julian Spector — jspector@newsobserver.com
Some context:
Sermon in this journal last Sunday, June 9, which
was the reported date of Msgr. O'Connor's death.
Mary Chapin Carpenter in this journal on July 6, 2008:
Related art:
Ceiling of Raleigh's Sacred Heart Cathedral—
Some context for this art:
From "Spider Robinson: The SF Writer as Empath"
by Ben Bova —
When Analog magazine was housed over at Graybar Building
on Lexington Avenue, our offices were far from plush. In fact,
they were grimy. Years worth of Manhattan soot clung to the
walls. The windows were opaque with grime. (What has this
to do with Spider Robinson? Patience, friend.)
Many times young science fiction fans would come to Manhattan
and phone me from Grand Central Station, which connected
underground with the good old Graybar. "I've just come to New
York and I read every issue of Analog and I'd like to come up and
see what a science fiction magazine office looks like," they would
invariably say.
I'd tell them to come on up, but not to expect too much. My advice
was always ignored. The poor kid would come in and gape at the
piles of manuscripts, the battered old metal desks, and mountains
of magazines and stacks of artwork, the ramshackle filing cabinets
and bookshelves. His eyes would fill with tears. His mouth would
sag open.
He had, of course, expected whirring computers, telephones with
TV attachments, smoothly efficient robots humming away,
ultramodern furniture, and a general appearance reminiscent of a
NASA clean room. (Our present offices, in the spanking new Condé
Nast Building on Madison Avenue, are a little closer to that dream.)
The kid would shamble away, heartsick, the beautiful rainbow-hued
bubble of his imagination burst by the sharp prick of reality.
"Funny how annoying a little prick can be." — Garry Shandling as Senator Stern
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