Fenner Tanswell

@fennert.bsky.social

471 Followers 390 Following

Philosopher of Mathematics and Logic working at TU Berlin. Also into epistemology, science, Xphi and the philosophy of extinction. Flightfree and carfree. fennertanswell.com

Quote from the OpenAI prompt: "Use adversarial agents throughout: every candidate proof must be checked for exact-two
multiplicity, repeated-edge closed trails masquerading as cycles, parallel-edge 2-cycles,
disconnected graphs, cutvertices, bridges introduced by reductions, and circular use of an
equivalent CDC statement."

Quote from The Guardian's Politics live blog: "The Lib Dems may not be standing in Clacton, but Count Binface (see 5.19am) says he is up for it.

(Quote Binface) Labour, Tories, Lib Dems and Greens: I demand you stand down in Clacton.

I will be a unity candidate and pledge to build at least one affordable house.

Nigel Farage says he wants The People versus the Establishment.

So be it. Leave him to me.

Table showing the frequencies of the term "important".

Table from the paper listing the frequency codes for the uses of the term "interesting".

Quote from Terence Tao: "In any case, I would indeed say that this is a situation in which the AI-generated paper inadvertently highlighted a tighter connection between two areas of mathematics (in this case, the anatomy of integers and the theory of Markov processes) than had previously been made explicit in the literature (though there were hints and precursors scattered therein which one can see in retrospect). That would be a meaningful contribution to the anatomy of integers that goes well beyond the solution of this particular Erdos problem."

Quote from the Quanta article reading "When Ryu asked ChatGPT, “it kept giving me incorrect proofs,” he said. “But the lead-up to the inevitable error had interesting steps, correct partial results that seemed potentially useful.” As the LLM made incremental progress, he would check its answers, keep the correct parts, and feed them back into the model with a new prompt. “I had to play the role of the verifier,” Ryu said. “With ChatGPT, I felt like I was covering a lot of ground very rapidly, much more quickly than I could do on my own. That’s what kept me going.”"

Quote from Mochizuki: "By contrast, the mathematical content of
Stages 4 and 5, as well as (to a lesser extent) Stage 3, are understood by a much larger class of mathematicians and have never
been a source of confusion/debate, hence should be regarded as
long-term goals that seem much more amenable to LeanForm by
research groups not so closely connected to my research group
at RIMS, e.g., (perhaps) via machine-based autoformalization."

Another quote from Mochizuki with crazytown bananapants underlinings and italics, reading "In particular, it follows that the LeanForm of species/mutations becomes essentially immediate once one has a LeanForm
of ZFC as a first order theory. In the fall of 2025, I discovered,
on the one hand, that such a LeanForm had in fact already recently been achieved by a young Japanese researcher named Shogo Saito, but, on the other hand, (was quite surprised to learn!)
that such a LeanForm does not yet exist in MathLib (the standard library for refereed Lean code). Here, we observe that the
technical significance of formalizing ZFC as a first order theory
lies in the fact that this is necessary in order to be able to work
with “some indeterminate set-theoretic formula φ” (i.e., as opposed to specific set-theoretic formulas “a ∈ A”, “B ⊆ C ∩ D”,
etc., which are “natively” available in Lean)."

A Mochizuki quote from the new paper, with wackidoodle underlinings and italics, reading: "The significance of LeanForm: verification vs. communication:
Classically, the significance of LeanForm is typically regarded as
lying in the verification of the logical correctness of a mathematical theory. In the case of IUT, however, although this verification aspect of LeanForm is welcome, in fact the logical structure
of the theory is rather simple, so this verif. aspect of LeanForm
is not a central focal point of interest from the point of view of
researchers in IUT. Rather, in the case of IUT, the significance
of LeanForm lies in producing a precise record of the logical str.
of IUT that is immune to false misinterpretations and hence
can be used, in a pivotal way, to communicate this simplicity
in a maximally efficient/precise way to other mathematicians."

Tao: These problems are like distant locations that you would hike to. And in the past, you would have to go on a journey. You can lay down trail markers that other people could follow, and you could make maps.

AI tools are like taking a helicopter to drop you off at the site. You miss all the benefits of the journey itself. You just get right to the destination, which actually was only just a part of the value of solving these problems.

“[…] in many cases, the solution the chatbots provide is
very long, detailed, and written in a “professional” way,
but it still may be completely wrong, or make no sense
at all when examined more carefully. This may fool a
human to think that such a detailed and long solution
would be correct, so extra caution is needed when we use
such tools for solving similar exercises.” (Emphasis ours.
Plevris et al. 2023, p. 18)

A reverse centaur with a massive horse head and puny human legs. Cannot run fast or think good.

A man with prominent buttocks feels the heat from a campfire using a cable of nerves that snakes up his leg, past said buttocks, along his back and into his brain covered in fuzzy hair. The man's expression is of stoned glee.

Fenner holding a copy of his book "Mathematical Rigour and Informal Proof" in a bookshop.

A quote from wikipedia reading: ""Chesterton's fence" is the principle that reforms should not be made until the reasoning behind the existing state of affairs is understood. The quotation is from Chesterton's 1929 book, The Thing: Why I Am a Catholic, in the chapter, "The Drift from Domesticity":

In the matter of reforming things, as distinct from deforming them, there is one plain and simple principle; a principle which will probably be called a paradox. There exists in such a case a certain institution or law; let us say, for the sake of simplicity, a fence or gate erected across a road. The more modern type of reformer goes gaily up to it and says, "I don't see the use of this; let us clear it away." To which the more intelligent type of reformer will do well to answer: "If you don't see the use of it, I certainly won't let you clear it away. Go away and think. Then, when you can come back and tell me that you do see the use of it, I may allow you to destroy it.""

A graph displaying the weighted rankings for the three studies.

An example of the binary decision prompting for our study. The question reads "A sign says "No Vehicles in the Park". Which example would be the worst violation?". The two options are "Ambulance" and "Helicopter".