I have met AG and can attest that, whether or not he is human, he is at least an extremely convincing imitation. One test that can help us decide is whether AG is sensitive to the irony of worrying about proper citation of the results produced by a system whose primary effect is to undermine the carefully established norms within the discipline for citation of previous work. I have been made aware of an example of an abusive failure to cite a relevant reference in the very first problem treated in the "Ten advances…" paper released by OpenAI the other day.
As far as your citation goes, if the system works properly, your question will be answered by how the journal, if any, that publishes the paper chooses to identify its authorship.
The point of my comment was that "affirming the humanity of authorship" and "restricting the admission for publication in mathematics journals to humans only" does not preclude citation of the results such as the solution to the unit-distance problem in the journal submission by a human, and my question to you as one of the Framers was whether such an infusion of results indisputably produced by AI into the bloodstream of mathematics would violate the letter and spirit of the Leiden Declaration. Needless to say, "abusive failure to cite a relevant reference" is totally unacceptable:
On a more cheerful note: (reacting to "I am under no illusion that my power to enforce this stipulation would be any greater than was the power of the Lenape to enforce the (possibly apocryphal) Treaty that established the boundaries of William Penn’s settlement of Philadelphia"). Pekka Hämäläinen in "Indigenous Continent: The Epic Contest for North America" (the book that he suggests “might be best described as a biography of power,” where "power is defined as the ability of people and their communities to control space and resources, to influence the actions and perceptions of others, to hold enemies at bay, to muster otherworldly beings, and to initiate and resist change") argues that North America "remained overwhelmingly Indigenous well into the nineteenth century.” Perhaps of particular relevance in the context of this post is his detailed description of the skillful manipulation by the native nations of the competing imperial powers: the rivalry between Spain, France, Britain, the Netherlands, Sweden, and later the US was no less intense than that between OpenAI and its peer competitors.
"What is 'human'?" is a loaded question indeed. I am yet to come across a better attempt at the definition than that given by Marcilio Ficino: Est autem homo anima rationalis, mentis particeps, corpore utens (rational soul participating in the intellect of God but operating in a body)
Paul Oskar Kristeller in the "Philosophy of Marsilio Ficino" renders it as "a rational soul participating in the divine mind and using a body". I followed Erwin Panofsky's "History of Art as a Humanistic Discipline" (page 2):
The following statement made by Panofsky towards the end of the essay:
"If the anthropocratic civilization of the Renaissance is headed, as it seems to be, for a Middle Ages in reverse—a satanocracy as opposed to the mediaeval theocracy—not only the humanities but also natural sciences, as we know them, will disappear, and nothing will be left but what serves the dictates of the sub-human."
is echoed in the encyclical letter MAGNIFICA HUMANITAS (on safeguarding the human person in the time of artificial intelligence)
Interesting post. (Would have been nice to meet in Philadelphia...)
Yesterday, in parallel with this new post, OpenAI published ten major mathematical results https://openai.com/index/ten-advances-in-mathematics/ . I don't see the reason to require human authorship for these results or for the counterexample to the Jacobian conjecture. (And I even do not understand what such a requirement means.) So to the extend that the Leiden's deceleration requires human authorship, this seems rather obsolete already.
I asked DeepSeek to "List five poets who have compared either thinking or writing to vomiting, sneezing, or yawning." The most convincing is Sara Little's poem "Heart Vomit" (https://vocal.media/poets/heart-vomit), which begins:
i vomited a poem
from a queasy
uneasy heart -
gulp it down
choke it back
but a violent wave of scribbled bits
Then there's this ancient reference from Wikipedia:
"Galaton (Ancient Greek: Γαλάτων) was an ancient Greek painter, whose picture representing Homer vomiting with other poets gathering up the vomit, is mentioned by Aelian ( V. H. xiii. 22) and by a scholiast to Lucian (i. p. 499, ed. Wetstein), who calls the painter Gelaton. He probably lived under the reign of Ptolemy IV Philopator (222–205 BC), and his picture was no doubt intended to ridicule the Alexandrian epic poets."
Also this:
"The Roman poet Horace (65–8 BC) used the metaphor of vomiting to criticize bad poets. In his Ars Poetica, he describes a "mad poet" who "vomits out his sublime verses" (dum sublimis versus ructatur), portraying the act of writing as an uncontrolled, messy expulsion "
So yes, there are respectable precedents for attribution of involuntary authorship.
Clearly the authors will have to address what unexpectedly has become the first really controversial point in the Leiden Declaration, and I will not anticipate the collective response. OpenAI's motivation is probably the hope that one of their models will eventually be awarded a Fields Medal or something similar, and for reasons of management strategy don't want the award to go to their engineers; but I'm surprised that some mathematicians fetishize this particular form of industrial production. No one has suggested that I should have paid my fare directly to the train that brought me to Philadelphia from New York, although it can't be denied that the train did most of the work.
I'm trying to find an analogy where a human receives credit or blame for an unintentional act, like sneezing or vomiting. So far no example of credit ("authorship") comes to mind, but I suppose if I were to have vomited on my neighbor in the train a court would have held me responsible for the dry cleaning bill. In other words, if intention is no longer a requirement, there *is* some sort of precedent for ascribing authorship to a machine. But it's a weird precedent.
In the meantime, those mathematicians who feel really strongly about this question will have to act politically if they want to see their beliefs put into practice, for example by lobbying editorial boards.
The relevance of authorship and credit (or discredit) is not clear. Even before AI, identifying human relevance with “living for the ages” may have been illusory, in a
world where “struggling to live” better reflects the human experience than “leaving a lasting impact.”
AI’s remarkable progress may simply reinforce the view that human relevance should not be identified with, or measured by, intellectual achievements, or indeed by lasting
As I wrote elsewhere, I'm not going to continue this discussion on my own; it's the responsibility of the authors of the Leiden Declaration, and we are already beginning to talk about it.
Foucault is a highly controversial starting point. Appealing to Foucault is pretty much begging the question — namely that no possible rational discourse on the word “author” is possible, and thus whether AI can be called an author is a political matter. This is as weak a defense of your thesis as if I now quoted Plato to defend the opposite, namely to claim that there is an innate, perfect idea of “author”, and we just have to understand rationally whether the concept applies to AI.
In reality, some concepts cannot be extended or restricted without violating their established meaning. Although the word “fall” was never applied to the word “robot” before robots were invented, we shall agree, I hope, that whether a robot can fall is not a political choice.
One can very well argue that it would be illogical to deny authorship to AI if it autonomously proves a theorem and writes an original paper.
There is another contradiction in your approach, and this is due to very postmodernist premise that you made by citing Foucault. Namely, you attempt to argue that the word “author” cannot be applied to AI because AI lacks intent. If no rational discourse about the word author is possible, then you are committing the very sin you are warning us about. You are trying to give rational reasons to reject AI authorship.
If you read carefully you'll see there's no contradiction between saying that various texts have analyzed the term "author" in a variety of ways and sharing my own thoughts on the subject. I do look forward to prosecutors arguing, when Mythos or whatever hacks into a dam or an air control tower, that Mythos or whatever deserves a long jail sentence or the electric chair.
Mythos 9.0, maybe. A long jail sentence (sandboxed) or the chair (unplugged, erased), all based on the court-established fact it's sentient and responsible. This is a rearguard battle you fight.
The contradiction in your discourse was that you say that no chain of logical deductions can settle the matter, and authorship is a political affair, but then your logical analysis of the word "author" is an attempt of logical discourse. My point is, therefore, that if you seek consistency with your thesis that authorship is a political affair, then you should rather limit yourself to the political implications of accepting AI as an author. In your response to my comment, indeed, you began to do that, which is at least slightly more consistent.
Nevertheless, I point out that the concepts of author and legal implications of authorship are not the same thing. For example, the US Copyright office denies copyright to AI written text, not because AI is not an author, but because copyright protects human work. Authorship can exist with or without copyright, with or without legal implications. The legal implications are a political decision, but still one can argue that the assignment of authorship is not.
I therefore believe you arguments have room for improvement, and my point was to suggest a better methodology, more sophisticated than appealing to highly controversial postmodernist stances.
Thank you, Professor, for your attempts to enlighten me, but the matters are quite clear in my mind. You are confusing rhetoric with reasoning. In some situations political persuasion is best carried out with the help of Tommy guns and baseball bats (see Al Capone in the previous post), but more frequently rhetoric is the preferred medium. It's not my fault if the naive reader attributes a logical structure to my rhetoric.
This is definitely my LAST comment on authorship, as an individual, in this discussion. Please wait for the authors of the Leiden Declaration to respond.
Thank you! A very clear account. It is interesting to see your reports of the quoted mathematicians perspectives. I would ask, as an aside, what do you take rationality to be?
The possibilities implicit in speculations about how LLMs can be so good disturb me. Is it all just bare statistical pattern matching? Have we found the hack to vacuum up every fact of information space?
If logic is embedded in the relational understructure of human language, then what about thought or emotion (supersets of language), which language is used to express? What about qualia in the most general sense? Does this give some evidence that everything we could fathom embeds into qualia? Is this actually tautolgical?
This speculation has provoked lots of interesting images and thoughts in me. Thanks again.
(1) "Ethical foundations for Aristotle’s Politics: that happiness is the highest human good, that happiness is the activity of moral virtue defined in terms of the mean, and that justice or the common advantage is the political good."
(2) "The proposal to admit only human authors, which seems to be the current policy at most journals, is a political proposal. I fully agree with this proposal, Hales and Gowers do not, and the matter will be decided, like all such matters, by political means."
It is my sense that notion of the "political" has two distinct meanings in (1) and (2).
In (1) Aristotle references the common good of the πόλις as a whole. The proposal at most (mathematics) journals to only admit human authors referenced in (2) is a political proposal within the community of mathematicians. Whether or not this proposal is adopted does not preclude dissemination of results obtained by AI -- to the community of mathematicians and the broader public -- by other means: e.g. recent posting (by Levent Alpöge) on X of the counterexample to the Jacobian conjecture (obtained by Claude).
What strikes me as the political issue at the heart of the matter is the extent to which the society at large would be willing to support human mathematicians when the results of their labor become close to being "fully automated".
The last time you received a paycheck. It represents a certificate of the consensus by society at large that teaching and research by human mathematicians is a worthwhile political objective (and here I do mean political in the Aristotelian sense).
The πόλις expresses its collective will these days much more indirectly than in Aristotle's day. I don't think there's anything like a consensus in this country on the major political questions, much less on obscure issues like support for mathematical teaching and research, which has never been proposed as an object for public debate. More likely than not, if a referendum had been held on the question 40 years ago, mathematical research would have been voted down and we might never have seen the proof of Fermat's Last Theorem.
The most that can be said is that no one is upset enough at the existence of mathematical research at universities and institutes that they are moved to organize a movement to abolish it. Keep talking about machine authorship and then look out for Project 2029.
For what it is worth, I am in favor of the proposal to restrict the admission for publication in mathematics journals to humans only (and I see no indication that Gowers is against this particular proposal). But suppose that in my journal submission (full disclosure: I am human) I wish to reference a result such as the solution to the unit-distance problem (that is, a result indisputably obtained by AI and fully digested by the human mathematical community). It is not quite clear to me whether such an infusion of AI-produced results into the bloodstream of mathematics would violate the letter and spirit of the Leiden Declaration.
PS It is not quite clear to me whose side (yours or Hales and Gowers) Foucault would take, given the concluding paragraph of "What Is an Author?":
"The author—or what I have called the 'author-function'—is undoubtedly only one of the possible specifications of the subject and, considering past historical transformations, it appears that the form, the complexity, and even the existence of this function are far from immutable. We can easily imagine a culture where discourse would circulate without any need for an author. Discourses, whatever their status, form, or value, and regardless of our manner of handling them, would unfold in a pervasive anonymity."
Formalisation is merely re-writing the result in a different language (which happens to be better understood by a computer, but this equally applies to human languages). I don't see how one can come to the idea to try to forbid formalisation, unless viewing it as some sort of black magic.
I fail to see how this applies to your (admittedly admirable) decision to forbid formalization of your work.
Also, you say
> Nevertheless, the affirmation of my right as a human to determine how my contributions to mathematics may be used seemed to me a valid way to make the point that human decisions about the future of mathematics are at least conceivable.
But the ability to determine this has been demonstrably false over the past century, and this right seems to me to only have an automated future of being violated.
What kind of future are you imagining in the best case? A world with two tracks: formalized (mainstream?) mathematics and unformalized due to human request? And unlike with publishing houses or translators, where maybe some human understanding will uphold a poet's wish and the "pronounced humanistic value" that follows, what could possibly keep the unformalized track alive in a world of machines we don't understand? Your work may very well get formalized incidentally even if no human intended for that to happen. What then? Is the person whose use of an AI tool that led to that happening truly responsible?
It's "poetic untranslateability" - a different story all together. Surely if one is not constrained by the rhythm etc., explaining the meaning of a poem in another language is quite possible.
While maths is an art of sorts, it differs from it, as the form isn't relevant, only the contents are.
The two situations are not analogous in all aspects; in both cases it is a matter of respecting one person's wishes. Why should that be hard to accept?
Such a wish in a maths paper can only make sense if you forbid anything but character to character reproduction of your results. E.g. presenting it in a lecture would not be really possible.
Dibs on DØ for a name for an LLM.
I have met AG and can attest that, whether or not he is human, he is at least an extremely convincing imitation. One test that can help us decide is whether AG is sensitive to the irony of worrying about proper citation of the results produced by a system whose primary effect is to undermine the carefully established norms within the discipline for citation of previous work. I have been made aware of an example of an abusive failure to cite a relevant reference in the very first problem treated in the "Ten advances…" paper released by OpenAI the other day.
As far as your citation goes, if the system works properly, your question will be answered by how the journal, if any, that publishes the paper chooses to identify its authorship.
The point of my comment was that "affirming the humanity of authorship" and "restricting the admission for publication in mathematics journals to humans only" does not preclude citation of the results such as the solution to the unit-distance problem in the journal submission by a human, and my question to you as one of the Framers was whether such an infusion of results indisputably produced by AI into the bloodstream of mathematics would violate the letter and spirit of the Leiden Declaration. Needless to say, "abusive failure to cite a relevant reference" is totally unacceptable:
https://www.scientificamerican.com/article/openais-latest-math-breakthroughs-commit-research-misconduct-experts-say/
On a more cheerful note: (reacting to "I am under no illusion that my power to enforce this stipulation would be any greater than was the power of the Lenape to enforce the (possibly apocryphal) Treaty that established the boundaries of William Penn’s settlement of Philadelphia"). Pekka Hämäläinen in "Indigenous Continent: The Epic Contest for North America" (the book that he suggests “might be best described as a biography of power,” where "power is defined as the ability of people and their communities to control space and resources, to influence the actions and perceptions of others, to hold enemies at bay, to muster otherworldly beings, and to initiate and resist change") argues that North America "remained overwhelmingly Indigenous well into the nineteenth century.” Perhaps of particular relevance in the context of this post is his detailed description of the skillful manipulation by the native nations of the competing imperial powers: the rivalry between Spain, France, Britain, the Netherlands, Sweden, and later the US was no less intense than that between OpenAI and its peer competitors.
"What is 'human'?" is a loaded question indeed. I am yet to come across a better attempt at the definition than that given by Marcilio Ficino: Est autem homo anima rationalis, mentis particeps, corpore utens (rational soul participating in the intellect of God but operating in a body)
I don't see any reference to God in the Latin text, but if it is implicit, it could just as well be your favorite tech billionaire.
Paul Oskar Kristeller in the "Philosophy of Marsilio Ficino" renders it as "a rational soul participating in the divine mind and using a body". I followed Erwin Panofsky's "History of Art as a Humanistic Discipline" (page 2):
https://faragoarth6929.wordpress.com/wp-content/uploads/2016/08/farago_20161011_panofsky_thehistoryofart.pdf
The following statement made by Panofsky towards the end of the essay:
"If the anthropocratic civilization of the Renaissance is headed, as it seems to be, for a Middle Ages in reverse—a satanocracy as opposed to the mediaeval theocracy—not only the humanities but also natural sciences, as we know them, will disappear, and nothing will be left but what serves the dictates of the sub-human."
is echoed in the encyclical letter MAGNIFICA HUMANITAS (on safeguarding the human person in the time of artificial intelligence)
https://www.vatican.va/content/leo-xiv/en/encyclicals/documents/20260515-magnifica-humanitas.html
published at about the same time as the Leiden Declaration.
Interesting post. (Would have been nice to meet in Philadelphia...)
Yesterday, in parallel with this new post, OpenAI published ten major mathematical results https://openai.com/index/ten-advances-in-mathematics/ . I don't see the reason to require human authorship for these results or for the counterexample to the Jacobian conjecture. (And I even do not understand what such a requirement means.) So to the extend that the Leiden's deceleration requires human authorship, this seems rather obsolete already.
I asked DeepSeek to "List five poets who have compared either thinking or writing to vomiting, sneezing, or yawning." The most convincing is Sara Little's poem "Heart Vomit" (https://vocal.media/poets/heart-vomit), which begins:
i vomited a poem
from a queasy
uneasy heart -
gulp it down
choke it back
but a violent wave of scribbled bits
Then there's this ancient reference from Wikipedia:
"Galaton (Ancient Greek: Γαλάτων) was an ancient Greek painter, whose picture representing Homer vomiting with other poets gathering up the vomit, is mentioned by Aelian ( V. H. xiii. 22) and by a scholiast to Lucian (i. p. 499, ed. Wetstein), who calls the painter Gelaton. He probably lived under the reign of Ptolemy IV Philopator (222–205 BC), and his picture was no doubt intended to ridicule the Alexandrian epic poets."
Also this:
"The Roman poet Horace (65–8 BC) used the metaphor of vomiting to criticize bad poets. In his Ars Poetica, he describes a "mad poet" who "vomits out his sublime verses" (dum sublimis versus ructatur), portraying the act of writing as an uncontrolled, messy expulsion "
So yes, there are respectable precedents for attribution of involuntary authorship.
Clearly the authors will have to address what unexpectedly has become the first really controversial point in the Leiden Declaration, and I will not anticipate the collective response. OpenAI's motivation is probably the hope that one of their models will eventually be awarded a Fields Medal or something similar, and for reasons of management strategy don't want the award to go to their engineers; but I'm surprised that some mathematicians fetishize this particular form of industrial production. No one has suggested that I should have paid my fare directly to the train that brought me to Philadelphia from New York, although it can't be denied that the train did most of the work.
I'm trying to find an analogy where a human receives credit or blame for an unintentional act, like sneezing or vomiting. So far no example of credit ("authorship") comes to mind, but I suppose if I were to have vomited on my neighbor in the train a court would have held me responsible for the dry cleaning bill. In other words, if intention is no longer a requirement, there *is* some sort of precedent for ascribing authorship to a machine. But it's a weird precedent.
In the meantime, those mathematicians who feel really strongly about this question will have to act politically if they want to see their beliefs put into practice, for example by lobbying editorial boards.
The relevance of authorship and credit (or discredit) is not clear. Even before AI, identifying human relevance with “living for the ages” may have been illusory, in a
world where “struggling to live” better reflects the human experience than “leaving a lasting impact.”
AI’s remarkable progress may simply reinforce the view that human relevance should not be identified with, or measured by, intellectual achievements, or indeed by lasting
achievements of any kind.
As I wrote elsewhere, I'm not going to continue this discussion on my own; it's the responsibility of the authors of the Leiden Declaration, and we are already beginning to talk about it.
Foucault is a highly controversial starting point. Appealing to Foucault is pretty much begging the question — namely that no possible rational discourse on the word “author” is possible, and thus whether AI can be called an author is a political matter. This is as weak a defense of your thesis as if I now quoted Plato to defend the opposite, namely to claim that there is an innate, perfect idea of “author”, and we just have to understand rationally whether the concept applies to AI.
In reality, some concepts cannot be extended or restricted without violating their established meaning. Although the word “fall” was never applied to the word “robot” before robots were invented, we shall agree, I hope, that whether a robot can fall is not a political choice.
One can very well argue that it would be illogical to deny authorship to AI if it autonomously proves a theorem and writes an original paper.
There is another contradiction in your approach, and this is due to very postmodernist premise that you made by citing Foucault. Namely, you attempt to argue that the word “author” cannot be applied to AI because AI lacks intent. If no rational discourse about the word author is possible, then you are committing the very sin you are warning us about. You are trying to give rational reasons to reject AI authorship.
If you read carefully you'll see there's no contradiction between saying that various texts have analyzed the term "author" in a variety of ways and sharing my own thoughts on the subject. I do look forward to prosecutors arguing, when Mythos or whatever hacks into a dam or an air control tower, that Mythos or whatever deserves a long jail sentence or the electric chair.
Mythos 9.0, maybe. A long jail sentence (sandboxed) or the chair (unplugged, erased), all based on the court-established fact it's sentient and responsible. This is a rearguard battle you fight.
The affected population might object if the human creators got off scot free. Of course, human populations may also have been replaced by then.
The contradiction in your discourse was that you say that no chain of logical deductions can settle the matter, and authorship is a political affair, but then your logical analysis of the word "author" is an attempt of logical discourse. My point is, therefore, that if you seek consistency with your thesis that authorship is a political affair, then you should rather limit yourself to the political implications of accepting AI as an author. In your response to my comment, indeed, you began to do that, which is at least slightly more consistent.
Nevertheless, I point out that the concepts of author and legal implications of authorship are not the same thing. For example, the US Copyright office denies copyright to AI written text, not because AI is not an author, but because copyright protects human work. Authorship can exist with or without copyright, with or without legal implications. The legal implications are a political decision, but still one can argue that the assignment of authorship is not.
I therefore believe you arguments have room for improvement, and my point was to suggest a better methodology, more sophisticated than appealing to highly controversial postmodernist stances.
Thank you, Professor, for your attempts to enlighten me, but the matters are quite clear in my mind. You are confusing rhetoric with reasoning. In some situations political persuasion is best carried out with the help of Tommy guns and baseball bats (see Al Capone in the previous post), but more frequently rhetoric is the preferred medium. It's not my fault if the naive reader attributes a logical structure to my rhetoric.
This is definitely my LAST comment on authorship, as an individual, in this discussion. Please wait for the authors of the Leiden Declaration to respond.
Indeed I have never mistaken your rhetoric for logic, thanks for confirming I was right.
Thank you! A very clear account. It is interesting to see your reports of the quoted mathematicians perspectives. I would ask, as an aside, what do you take rationality to be?
The possibilities implicit in speculations about how LLMs can be so good disturb me. Is it all just bare statistical pattern matching? Have we found the hack to vacuum up every fact of information space?
If logic is embedded in the relational understructure of human language, then what about thought or emotion (supersets of language), which language is used to express? What about qualia in the most general sense? Does this give some evidence that everything we could fathom embeds into qualia? Is this actually tautolgical?
This speculation has provoked lots of interesting images and thoughts in me. Thanks again.
(1) "Ethical foundations for Aristotle’s Politics: that happiness is the highest human good, that happiness is the activity of moral virtue defined in terms of the mean, and that justice or the common advantage is the political good."
(2) "The proposal to admit only human authors, which seems to be the current policy at most journals, is a political proposal. I fully agree with this proposal, Hales and Gowers do not, and the matter will be decided, like all such matters, by political means."
It is my sense that notion of the "political" has two distinct meanings in (1) and (2).
In (1) Aristotle references the common good of the πόλις as a whole. The proposal at most (mathematics) journals to only admit human authors referenced in (2) is a political proposal within the community of mathematicians. Whether or not this proposal is adopted does not preclude dissemination of results obtained by AI -- to the community of mathematicians and the broader public -- by other means: e.g. recent posting (by Levent Alpöge) on X of the counterexample to the Jacobian conjecture (obtained by Claude).
What strikes me as the political issue at the heart of the matter is the extent to which the society at large would be willing to support human mathematicians when the results of their labor become close to being "fully automated".
When was "society at large " last consulted? This invocation of "society at large" is a persistent source of confusion and should be avoided.
The last time you received a paycheck. It represents a certificate of the consensus by society at large that teaching and research by human mathematicians is a worthwhile political objective (and here I do mean political in the Aristotelian sense).
The πόλις expresses its collective will these days much more indirectly than in Aristotle's day. I don't think there's anything like a consensus in this country on the major political questions, much less on obscure issues like support for mathematical teaching and research, which has never been proposed as an object for public debate. More likely than not, if a referendum had been held on the question 40 years ago, mathematical research would have been voted down and we might never have seen the proof of Fermat's Last Theorem.
The most that can be said is that no one is upset enough at the existence of mathematical research at universities and institutes that they are moved to organize a movement to abolish it. Keep talking about machine authorship and then look out for Project 2029.
For what it is worth, I am in favor of the proposal to restrict the admission for publication in mathematics journals to humans only (and I see no indication that Gowers is against this particular proposal). But suppose that in my journal submission (full disclosure: I am human) I wish to reference a result such as the solution to the unit-distance problem (that is, a result indisputably obtained by AI and fully digested by the human mathematical community). It is not quite clear to me whether such an infusion of AI-produced results into the bloodstream of mathematics would violate the letter and spirit of the Leiden Declaration.
PS It is not quite clear to me whose side (yours or Hales and Gowers) Foucault would take, given the concluding paragraph of "What Is an Author?":
"The author—or what I have called the 'author-function'—is undoubtedly only one of the possible specifications of the subject and, considering past historical transformations, it appears that the form, the complexity, and even the existence of this function are far from immutable. We can easily imagine a culture where discourse would circulate without any need for an author. Discourses, whatever their status, form, or value, and regardless of our manner of handling them, would unfold in a pervasive anonymity."
Formalisation is merely re-writing the result in a different language (which happens to be better understood by a computer, but this equally applies to human languages). I don't see how one can come to the idea to try to forbid formalisation, unless viewing it as some sort of black magic.
https://journals.librarypublishing.arizona.edu/cms/article/6672/galley/6151/view/
I fail to see how this applies to your (admittedly admirable) decision to forbid formalization of your work.
Also, you say
> Nevertheless, the affirmation of my right as a human to determine how my contributions to mathematics may be used seemed to me a valid way to make the point that human decisions about the future of mathematics are at least conceivable.
But the ability to determine this has been demonstrably false over the past century, and this right seems to me to only have an automated future of being violated.
What kind of future are you imagining in the best case? A world with two tracks: formalized (mainstream?) mathematics and unformalized due to human request? And unlike with publishing houses or translators, where maybe some human understanding will uphold a poet's wish and the "pronounced humanistic value" that follows, what could possibly keep the unformalized track alive in a world of machines we don't understand? Your work may very well get formalized incidentally even if no human intended for that to happen. What then? Is the person whose use of an AI tool that led to that happening truly responsible?
It's "poetic untranslateability" - a different story all together. Surely if one is not constrained by the rhythm etc., explaining the meaning of a poem in another language is quite possible.
While maths is an art of sorts, it differs from it, as the form isn't relevant, only the contents are.
The two situations are not analogous in all aspects; in both cases it is a matter of respecting one person's wishes. Why should that be hard to accept?
Such a wish in a maths paper can only make sense if you forbid anything but character to character reproduction of your results. E.g. presenting it in a lecture would not be really possible.
You can't really fight the Tower of Babel...
Who said anything about making sense? Anyway, you missed the part about the Lenape.
You could also publish these papers in Int. J. of Surrealism :-)
https://www.upress.umn.edu/journals/international-journal-of-surrealism/