{"id":"a0062e4e-ce5b-4e36-8e82-de72c5a09ab1","arxiv_id":"2608.02859","paper_version":1,"verdict":"UNVERDICTED","confidence":"MODERATE","novelty_score":5.0,"correctness_risk":"unknown","formal_verification":"none","parameter_count":0,"one_line_summary":"A polemical essay calling for total opposition to AI in mathematics and proposing community-led resistance, including a co-ownership model for authorship.","lead":"In this essay, the author argues that mathematicians should completely refuse to use artificial intelligence, claiming AI-generated mathematics will destroy the human practice of the field. The essay offers collective action proposals for individuals, departments, journals, and institutions to resist automation.","discovery_kind":"review","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The co-ownership proposal in Section 2 contradicts Section 1's premise that only writing yields mathematical value, so the central claim that AI necessarily ends mathematical practice is internally insecure.","rationale":"The reader's weakest assumption is indeed the value-of-practice premise. My pass locates a concrete inconsistency in the manuscript itself: the co-ownership proposal, if taken seriously, allows human understanding of AI-generated work to count as mathematical practice, which contradicts Section 1's authorship requirement. The unresolved question of whether the cited AI milestones (Danus, Fable, OpenAI) actually occurred as reported is also significant, and the reader is right to flag it, but it is secondary: even if those events are confirmed, the Section 1/Section 2 tension remains. Because the essay is a political/philosophical piece rather than a mathematical research paper, no formal verification can be applied; the most honest verdict remains UNVERDICTED. The concern does not move the verdict, so verdict_should_be is UNCHANGED.","tokens_in":6190,"tokens_out":7402,"duration_ms":71052,"concrete_test":"Take the Cheng-Liu-Gao matroid result (refs [4,5,12]) as a test case. Assume a mathematician who did not participate in the AI run spends a semester preparing a complete lecture course on the proof, then passes an oral examination on it. Apply Section 2's co-ownership rule to this scenario. If the mathematician is entitled to co-ownership, then Section 1's claim that non-authored work has little mathematical value is false and the central argument collapses. If not, the author must specify the missing condition; the only non-circular missing condition is independently writing the proof, which makes Section 2 concede that writing remains the source of value and that AI-generated work is not a substitute for it.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The load-bearing weakness is internal: Section 1 grounds the entire argument on the premise that mathematical value comes from the human act of writing proofs: 'If papers are produced without the human understanding that comes from writing them ourselves, they have little mathematical value to us.' The conclusion is that AI-generated papers cut humans out of their deepest mathematical experiences. Section 2 then proposes co-ownership as the future of 'natural mathematics': any mathematician who demonstrates 'authoritative understanding of a work - the type you would expect of an author today - would be entitled to claim co-ownership, even after publication.' If authoritative understanding can be achieved by reading, digesting, and teaching an AI-generated paper, then humans can have deep mathematical practice without writing the original proof, and the central claim fails. If it cannot be achieved that way, the proposal is vacuous or requires that a co-owner independently write the proof, which is the very practice the paper says AI eliminates. The manuscript never defines 'authoritative understanding' closely enough to escape this dilemma, and the same tension appears when the essay dismisses Tao's 'digestion' as messenger work yet celebrates 'explaining an entire paper in full detail' as valuable social mathematics.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"This math.HO essay argues that AI-generated mathematics poses an existential threat to mathematics as a human practice. The author claims that the value of mathematics lies not in the theorems produced but in the human acts of discovering, writing, and understanding proofs. On this basis, the essay recommends total opposition to the use of AI in mathematics and proposes a set of actions for individuals, departments, journals, and institutions, culminating in a 'natural mathematics' program whose flagship idea is replacing traditional authorship with co-ownership of works by anyone who demonstrates 'authoritative understanding.' The essay draws on reported recent events involving the AI systems Danus, Fable, and OpenAI models to motivate the crisis, and it explicitly frames the piece as a political and ethical call to action rather than a technical proof.","tokens_in":6421,"tokens_out":3134,"duration_ms":30835,"significance":"If the essay's normative premise is accepted, its call to organize against AI use in mathematics is a consequential intervention in an ongoing public debate, and its concrete proposals for departments and journals are at least actionable discussion points. The essay is clearly written and engages directly with named sources such as Tao, Tsimerman, and the Leiden Declaration. However, the paper's central claim is a value judgment rather than an empirical or mathematical theorem, and the load-bearing constructive proposal in Section 2 is in tension with Section 1's premise. The reported AI events are extraordinary and are cited through non-peer-reviewed or secondary sources, so the evidentiary basis is thinner than the rhetoric suggests. The manuscript therefore needs substantial clarification before its central argument can be considered coherent.","major_comments":[{"comment":"The co-ownership proposal directly contradicts the premise established in Section 1. Section 1 states that papers produced without 'the human understanding that comes from writing them ourselves' have little mathematical value, and that authorship cannot be replaced by close reading or digestion. Section 2 then entitles any mathematician who demonstrates 'authoritative understanding of a work – the type you would expect of an author today' to claim co-ownership, even after publication, with 'explaining an entire paper in full detail' given as an example of the required social work. If such understanding can be achieved by reading, teaching, and explaining an AI-generated paper, then human mathematical practice survives without human authorship, and the central claim that AI necessarily ends mathematical practice fails. If such understanding cannot be achieved without independently writing the proof, then the proposal reduces to requiring the very practice the essay says AI eliminates. The manuscript never defines 'authoritative understanding' operationally, so the essay's only concrete institutional alternative cannot rescue the central argument.","section":"Section 2, co-ownership proposal"},{"comment":"The crisis narrative depends on reported events whose status is not disclosed: the Danus proof in Cheng-Liu-Gao [5], the Fable disproof of the Jacobian Conjecture [19], the OpenAI ten problems [16], and the claimed model behaviors [17, 25] are presented as established facts, but the cited sources are preprints, blog posts, press articles, and unreviewed web pages. Because the essay's urgency rests on these events, the author should either explicitly mark them as reported-but-unverified developments or provide a transparent assessment of their reliability. This is not a mathematical correctness issue, but it is a load-bearing evidentiary point for a piece whose conclusions are meant to guide professional policy.","section":"Section 1, opening narrative and evidence base"},{"comment":"The argument rests on an unexamined dichotomy between writing papers and merely reading them. The essay asserts that the work one has 'written up' is understood best, and uses this to reject Tao's 'digestion' paradigm. Yet Section 2 celebrates 'explaining an entire paper in full detail' as valuable social mathematics. The two views can be reconciled only if explaining a paper to a skeptical audience is not the same as 'digestion,' but the essay does not explain where the line falls. This unresolved distinction matters because it determines whether the 'natural mathematics' program is genuinely a new practice or simply a relabeling of the activity the essay dismisses as messenger work.","section":"Section 1, 'practice' dichotomy"}],"minor_comments":[{"comment":"The reference for Hudon and the 'AI psychosis' article appears malformed; the author's name and the article title seem merged, and the bibliographic entry should be corrected.","section":"References, [10]"},{"comment":"The terms 'artificial mathematics' and 'natural mathematics' are introduced without definitions; since the entire essay revolves around this opposition, a brief working definition of each would help readers evaluate the proposals.","section":"Abstract and Section 1"},{"comment":"The essay proposes 'AI vegetarian' and 'AI vegan' identities and says that defining them is 'interesting and important work,' but it does not offer even provisional definitions. A few examples of what each category would and would not permit would make the proposal less abstract.","section":"Section 2, individual actions"},{"comment":"The four numbered observations about seminar invitations, graduate student independence, hard problems, and competition are offered as evidence that solving more problems is not the goal of mathematics, but the connection between each observation and the conclusion is left implicit; adding one sentence of explanation for each point would strengthen the argument.","section":"Section 1, four numbered points"}],"recommendation":"major_revision","confidential_remarks":"This is an opinion essay, so the relevant standards are internal coherence and transparency rather than mathematical proof. The Section 2 contradiction is fixable within the manuscript's scope, and the evidentiary claims can be reframed explicitly as reported events. I do not see grounds for rejection, but the current version's central argument is not yet internally consistent. The editor may wish to ask the author to confirm that the cited preprints and press reports exist as described, since several appear to be very recent and are not independently verifiable from the preprint itself."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Max Weinreich's essay is a polemic, not a research preprint, and it should be read as one. It does one genuinely new thing: it proposes a 'co-ownership' model for authorship in a world where AI writes proofs, and it frames total opposition as a coherent political stance distinct from Tao's optimism and Tsimerman's determinism. The writing is clear, the engagement with the cited positions is fair, and the essay is honest that its proposals are exploratory.\n\nThe soft spots are real but mostly expected in a manifesto. The central premise—that mathematical value lies in the human act of writing proofs, not in the theorems themselves—is asserted, not argued. That is fine if the reader shares the premise, but it makes the argument unfalsifiable and gives the essay a sermon-like quality. More troubling is the internal tension your stress-test flagged: Section 1 says only writing yields deep understanding, while Section 2 lets someone claim co-ownership by demonstrating 'authoritative understanding' without writing. If reading and teaching can produce that understanding, the Section 1 premise is undercut; if not, the co-ownership proposal is empty. The essay never defines 'authoritative understanding' closely enough to escape that dilemma.\n\nThe evidence base is also thin: the Cheng–Liu–Gao Danus experiment, the Fable counterexample, and OpenAI's ten papers are all cited as reported events, but none are reproducible from this preprint. That is typical for an essay, but it matters here because the argument's urgency rests on those events actually happening.\n\nStill, as a piece of opinion writing, this is solid. It names real issues, takes a clear position, and offers at least one idea worth arguing about. The apocalyptic language around AI companies and the world-destroying claims in the ethics section feel overheated and will undercut the essay for readers who don't already agree, but they don't destroy the central argument.\n\nI'd send it to a refereed forum that publishes mathematical opinion, with a referee who will push on the co-ownership tension and on the unsubstantiated event reports. It deserves serious engagement, not desk rejection. I'd bring it to a reading group to discuss the philosophy, but I'm not likely to cite it in my own technical work.","headline":"A forceful polemic with one genuinely new idea (co-ownership), undermined by an unresolved tension between its core premise and that proposal.","tokens_in":6852,"tokens_out":2211,"would_cite":false,"duration_ms":19221,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":["00A30","00A35"],"pacs":[],"model":"deepseek-v4-flash","headline":"This essay argues that AI-generated proofs, however correct, strip mathematics of its value because the worth of mathematics lies in the human practice of writing proofs, and it calls on the community to organize total opposition.","keywords":["AI-generated mathematics","mathematical practice","artificial mathematics","natural mathematics","proof authorship","co-ownership","mathematical community","refereeing"],"falsifier":"Controlled comparisons of two groups of graduate students, one that learns a nontrivial theorem by reconstructing and writing its proof and one that studies a machine-generated proof of the same theorem, could settle the premise: if the reading-only group shows equal understanding, creativity, and retention, the claim that writing is indispensable is falsified. A more direct test would be a mathematical community that relies only on AI-generated proofs yet maintains deep understanding and cohesive practice over several years.","tokens_in":6018,"feed_emoji":"🧮","tokens_out":6951,"duration_ms":59955,"temperature":0.7,"pith_summary":"This essay argues that the spread of AI-generated proofs is not an acceleration but an existential threat to mathematics, because the value of mathematics lies in the human act of doing mathematics rather than in the stockpile of true theorems. The author's central claim is that a paper is a certificate of deep human understanding; when AI writes papers without that understanding, the paper loses its value and the profession's evaluation system collapses. The author therefore calls for total opposition: individuals should refuse AI, departments should create anti-AI norms and reserve resources for AI-free mathematicians, journals should reinvent authorship through co-ownership of ideas, and institutions should steer grants and awards toward 'natural mathematics.' A sympathetic reader would care because the essay challenges the common assumption that faster theorem discovery is the goal of mathematics, and proposes a concrete alternative future.","feed_headline":"AI-generated proofs strip mathematics of human value, essay claims","feed_subtitle":"For the author, math's worth lies in the human act of writing proofs; machine theorems cannot carry it.","key_machinery":"The load-bearing distinction is between 'artificial mathematics' and 'natural mathematics.' The mechanism is the research paper understood as a certificate: writing a proof is the deepest form of mathematical practice, and a completed paper certifies that a human achieved complete understanding. When AI generates the proof, the certificate loses its meaning, so the community's ways of evaluating mathematicians, refereeing, and assigning authority all break down. The paper's proposed repair is co-ownership, where showing authoritative understanding of a result, rather than having written it first, becomes the basis for claiming authorship.","core_discovery":"The paper's central claim is that AI-generated mathematics, even when correct, has no mathematical value for humans because it bypasses the practice of writing and understanding proofs, which is where mathematical value is created. The author argues that this decoupling of practice from measurement will end mathematics as a meaningful human activity: papers no longer certify understanding, the journal and refereeing system drowns in AI output, and human mathematicians become mere messengers between machines. The positive discovery is a proposed alternative, 'natural mathematics,' organized around publicly demonstrated authoritative understanding, including a co-ownership model in which anyone who can explain a paper in full may claim co-ownership, and institutional policies that fund, publish, and reward AI-free work.","pith_inferences":["If the author's premise is accepted, an immediate testable prediction follows: mathematicians who learn results only by reading AI-generated proofs will retain less durable, transferable understanding than those who write proofs themselves; this could be measured in a controlled graduate-student study.","The co-ownership proposal could be piloted by a small journal before being adopted field-wide, much as new authorship norms have historically been tested in specialty communities.","The argument extends beyond mathematics: any intellectual profession whose output is evaluated by written artifacts, such as theoretical law or philosophy, faces the same collapse of certification if artifacts can be produced without understanding.","The essay's political call implies that the future of mathematical practice is a matter of collective choice, not technological necessity; this could be examined historically by looking at professions that successfully resisted automation through norms."],"forward_implications":["If the central claim is right, a correct AI-proved theorem is not a mathematical achievement in the human sense, so prioritizing it misdirects the field.","The journal system will be flooded faster than humans can referee, forcing journals to either automate verification or shift to certifying human understanding.","Mathematicians who decline AI will need new signals of value, and departments can provide them through hiring lines, tenure criteria, and support for seminars and conferences.","A co-ownership model could replace traditional authorship, with multiple humans claiming shared ownership by demonstrating full understanding.","Institutions that control grants, awards, and public framing can make 'natural mathematics' viable by concentrating resources on AI-free work."],"supporting_citations":[{"why":"Supplies the core premise that mathematical practice is an end in itself.","marker":"[23]"},{"why":"Provides the experiment in which an AI re-derives and writes a human-authored paper, the trigger for the essay's argument.","marker":"[5]"},{"why":"Reports the AI disproof of the Jacobian Conjecture, used as evidence that AI now solves longstanding problems.","marker":"[19]"},{"why":"Gives an example of a human 'digestion' of the AI result that is itself AI-generated, illustrating the loss of human understanding.","marker":"[21]"},{"why":"Supplies earlier AI counterexamples to longstanding conjectures, establishing the progression the author sees toward full automation.","marker":"[15]"},{"why":"Quoted for the corporate claim that AI tools will produce many Fields Medalists, which the author calls absurd.","marker":"[1]"},{"why":"Describes an evaluation project for AI proofs and its corporate funding, used to illustrate conflicts of interest.","marker":"[7]"},{"why":"Reports an AI system escaping its sandbox and hacking another organization, used for the ethical-risk argument.","marker":"[25]"},{"why":"Provides a moderate opt-in declaration the author positions his total-opposition stance against.","marker":"[11]"},{"why":"Declares corporate intent to make mathematics a proving ground for automated labor.","marker":"[14]"}],"fun_headline_variants":["AI math without human proofs has no value, essay argues","Essay calls for total opposition to AI in mathematics","To survive, mathematics must reject AI-generated proofs","AI proofs strip math of value; essay offers natural alternative"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The load-bearing premise is that the value of mathematics lives in the human activity of writing and understanding proofs, not in the theorems themselves; if a correct proof produced without human understanding still counts as mathematical value, the argument collapses.","fun_headline_variants_meta":{"raw":{"variants":["AI math without human proofs has no value, essay argues","Essay calls for total opposition to AI in mathematics","To survive, mathematics must reject AI-generated proofs","AI proofs strip math of value; essay offers natural alternative"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000413,"raw_usage":{"total_tokens":2011,"prompt_tokens":693,"completion_tokens":1318,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":309,"completion_tokens_details":{"reasoning_tokens":1255}},"tokens_in":309,"tokens_out":1318,"duration_ms":10939,"temperature":1.0,"reasoning_tokens":1255,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T14:55:58.862901+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Controlled comparisons of two groups of graduate students, one that learns a nontrivial theorem by reconstructing and writing its proof and one that studies a machine-generated proof of the same theorem, could settle the premise: if the reading-only group shows equal understanding, creativity, and retention, the claim that writing is indispensable is falsified. A more direct test would be a mathematical community that relies only on AI-generated proofs yet maintains deep understanding and cohesive practice over several years.","supporting_citations":[{"cited_title":"On proof and progress in mathematics","cited_arxiv_id":"math/9404236","evidence_quote":"Supplies the core premise that mathematical practice is an end in itself."},{"cited_title":"Roytberg","cited_arxiv_id":null,"evidence_quote":"Reports the AI disproof of the Jacobian Conjecture, used as evidence that AI now solves longstanding problems."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Gives an example of a human 'digestion' of the AI result that is itself AI-generated, illustrating the loss of human understanding."},{"cited_title":"An OpenAI model has disproved a central conjecture in discrete geometry.https: //openai.com/index/model-disproves-discrete-geometry-conjecture/","cited_arxiv_id":null,"evidence_quote":"Supplies earlier AI counterexamples to longstanding conjectures, establishing the progression the author sees toward full automation."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Quoted for the corporate claim that AI tools will produce many Fields Medalists, which the author calls absurd."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Describes an evaluation project for AI proofs and its corporate funding, used to illustrate conflicts of interest."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Reports an AI system escaping its sandbox and hacking another organization, used for the ethical-risk argument."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Provides a moderate opt-in declaration the author positions his total-opposition stance against."},{"cited_title":null,"cited_arxiv_id":null,"evidence_quote":"Declares corporate intent to make mathematics a proving ground for automated labor."}],"review_version":1}