{"id":"87b6a6ea-419b-4c98-b9f3-2caba4294a2f","arxiv_id":"2505.08744","paper_version":1,"verdict":"CONDITIONAL","confidence":"MODERATE","novelty_score":7.0,"correctness_risk":"medium","formal_verification":"none","parameter_count":0,"one_line_summary":"DeepMath-Creative is a new 179-problem benchmark measuring LLM mathematical creativity through constructive proof and counterexample tasks; the best model, O3 Mini, reaches only about 70% accuracy on basic undergraduate items.","lead":"This paper introduces DeepMath-Creative, a 179-problem benchmark that asks language models to prove statements or construct counterexamples across algebra, topology, and analysis. In tests, the best model, O3 Mini, scored around 70% on the easiest undergraduate-level tasks, and performance collapsed on harder and open problems.","discovery_kind":"new_method","skeptic_critique":{"model":"deepseek-v4-flash","headline":"The 'memorized patterns, not creativity' conclusion is unsupported: no evidence distinguishes memorized retrieval from constructive transfer, and the reported 70% accuracy does not match Table 2.","rationale":"Good faith: the paper collects 179 constructive problems, proposes a reasonable three-level rubric, and documents qualitative failure modes. The dataset itself is a potentially useful resource, and the CONDITIONAL verdict seems appropriate. My stress-test does not find a mathematical error in individual problems; it targets the causal interpretation. The abstract and Section 5 assert that success is 'likely' due to memorized patterns, but the benchmark was not designed to test this. A moderate accuracy score measures ability, not mechanism. To attribute success to memorization one needs either a contamination check showing problems are in training data, or a control showing performance collapses when the same mathematics is presented in an unseen form. Neither is present. The numeric mismatch between the abstract's 70% and Table 2's 74.3% is not fatal by itself, but it undermines precision and could indicate an error in the accuracy computation or dataset count. These issues are addressable, so they do not warrant rejection; they justify the conditional stance and a request for the dataset and checks before accepting the interpretive claim.","tokens_in":9081,"tokens_out":5984,"duration_ms":65038,"concrete_test":"Release the full benchmark and run two checks. (1) Contamination: compute exact and near-duplicate overlap (e.g., min-hash 13-grams) between all 179 problem statements and publicly available pretraining corpora (Common Crawl, arXiv, GitHub, Math StackExchange); flag any item with overlap above a pre-specified threshold. (2) Held-out variants: create 40 isomorphic rewrites of representative problems (same construction, new wording, notation, and parameters) that cannot be in any training corpus, test the same five models under the same rubric, and compare pass rates. If held-out pass rates are statistically equivalent to the original, the memorization explanation is not supported; if they drop sharply, it is. This also permits correcting the accuracy figure to reconcile the abstract with Table 2.","verdict_should_be":"UNCHANGED","load_bearing_attack":"The paper's strongest claim has two parts: O3 Mini scores about 70% on DeepMath-Creative, and this performance is 'likely attributable to the recombination of memorized patterns rather than authentic creative insight' (Abstract; Section 5). For the second part to hold, the authors would need to show that correct answers are better explained by retrieval of near-identical training content than by constructive generalization. They do not. Section 3.1 asserts that problems are 'previously unseen', but no contamination check is reported: no exact-match search, no near-duplicate analysis, and no evidence about model training corpora. More importantly, even a perfectly uncontaminated benchmark cannot establish the causal attribution, because the scoring rubric (Table 1) only checks the mathematical validity of the final construction. A correct construction could arise from recombining memorized lemmas and templates or from genuine synthesis; the rubric cannot distinguish these. The observed pattern of high scores on undergraduate-level items and low scores on difficult items (Section 4.1.2) is consistent with both a lack of creative ability and a failure to recognize the required construction. A concrete inconsistency also weakens the measurement: Section 3.2 fixes N=179, but Table 2 reports 133 '1 score' responses for GPT, which is 74.3%, not 70%; none of the five rows yields exactly 70%. Since the headline number supports the 'merely' judgment, this discrepancy matters.","agreement_with_reader":"partial"},"referee_report":{"model":"deepseek-v4-flash","summary":"The paper introduces DeepMath-Creative, a benchmark of 179 expert-designed constructive mathematics problems in algebra, topology, geometry, and analysis, framed in a bidirectional 'prove or provide a counterexample' format. It proposes a 0/0.5/1 scoring rubric distinguishing direction accuracy from process accuracy, evaluates five LLMs (GPT o3-mini, Claude 3.7 Sonnet, Gemini 2.0 Flash, DeepSeek R1, Qwen QwQ-32B) under manual expert grading, and reports that the best model, O3 Mini, achieves about 70% accuracy, mostly on undergraduate-level items, with sharp declines on harder and open problems. The authors conclude that this performance likely reflects recombination of memorized patterns rather than genuine mathematical creativity.","tokens_in":9369,"tokens_out":4903,"duration_ms":48386,"significance":"If the benchmark is released and the scoring is validated, DeepMath-Creative would fill a genuine gap: existing math benchmarks emphasize multi-step computation and proof, while constructive proof and counterexample generation are underrepresented. The expert curation, the unified problem format, and the qualitative failure analysis are useful contributions. However, the central claims are currently weakened by an internal inconsistency between the reported 70% accuracy and Table 2, by the absence of inter-rater reliability evidence, and by the unsupported causal attribution to memorization rather than creativity. The benchmark has clear potential, but the paper as written does not yet establish the strength of its headline conclusion.","major_comments":[{"comment":"The abstract and Section 4.1.2 state that O3 Mini achieves 'merely 70% accuracy,' but Table 2 reports 133 one-score responses out of 179, which is 74.3%, and no model row in Table 2 yields 70%. Since this numeric claim directly supports the 'merely' judgment and the interpretation of limited creativity, the inconsistency must be resolved and the reported figure corrected.","section":"Abstract; Section 4.1.2; Table 2"},{"comment":"The conclusion that performance is 'likely attributable to the recombination of memorized patterns rather than authentic creative insight' (Abstract; Section 4.1.2; Section 5) is not supported by the reported evidence. Section 3.1 asserts that problems are 'previously unseen,' but no contamination check (exact-match or near-duplicate search) is described, and the scoring rubric in Table 1 only evaluates whether the final construction is valid, not whether it is novel or independent of memorized templates. A correct construction assembled from known lemmas and a genuinely novel construction receive the same score. The authors should either reframe this statement as a speculative hypothesis or provide analyses that directly test the memorization explanation.","section":"Section 3.1; Section 3.3; Section 5"},{"comment":"Manual expert grading is the sole scoring mechanism, but the paper reports no inter-annotator agreement (e.g., Cohen's kappa or percentage agreement), and it is not stated whether each response was independently graded by more than one expert. Given the coarse 0/0.5/1 rubric and the qualitative distinctions required (e.g., between 'significant flaws' and 'minor errors'), the reliability of the headline scores is undemonstrated.","section":"Section 3.3"},{"comment":"The evaluation procedure reports no sampling temperature, no number of independent runs, and no variance measure; the text reads as though each model was queried once per problem. The inter-model differences in Table 2 (e.g., GPT at 74.3% versus DeepSeek at 71.5%) are small relative to the sampling noise expected from single stochastic generations. Please report decoding settings and repeat the evaluation multiple times, or at least provide confidence intervals.","section":"Section 3.3; Section 4"},{"comment":"The paper states that roughly 60% of the problems are undergraduate-level and 40% are master's-level, and it claims that O3 Mini's performance was 'primarily attained on undergraduate-level problems,' but no difficulty-stratified results are presented. Table 2 only gives aggregate counts. Without a breakdown by difficulty and domain, the claim that the models succeed mainly on basic undergraduate tasks is not verifiable from the reported data.","section":"Section 3.2; Section 4.1.2"}],"minor_comments":[{"comment":"The dataset composition is given only as approximate percentages ('approximately 50% in algebra, 15% in topology, and 35% in analysis'; 'around 60%' undergraduate and 'approximately 40%' master's). Please provide exact counts and make the full distribution available in the repository.","section":"Section 3.2"},{"comment":"Model names are used inconsistently: 'O3 Mini' versus 'GPT o3-mini.' Please standardize the naming throughout, including version identifiers.","section":"Abstract; Section 4.1.1"},{"comment":"The quoted Qwen response contains apparent OCR artifacts such as 'aolocalpproperty' and 'ospreadparound.' If these are verbatim model outputs, state that; if they are transcription errors, correct them.","section":"Figure 4"},{"comment":"The paper states that all benchmark problems have standard answers but does not provide an answer key or solution file. To make the benchmark reproducible, please release the full dataset, scoring rubrics, and example solutions at the cited GitHub repository.","section":"Section 5; Data Release"}],"recommendation":"major_revision","confidential_remarks":"The benchmark is potentially useful, but the present version has a headline-number inconsistency and several methodological gaps that must be addressed before it can be recommended for publication. I would encourage the editor to request a revision rather than reject, since the core dataset and evaluation idea are sound and the issues appear fixable with additional analyses and careful rewriting. One additional concern for the editor: the paper promises an open-source initiative and a dedicated model, but the current version does not include a working dataset link or evaluation code, which limits the reproducibility of the claims."},"author_rebuttal":null,"desk_editor":{"model":"deepseek-v4-flash","letter":"Colleague,\n\nRead DeepMath-Creative. The contribution is the dataset itself, and that part holds up better than the authors' own summary. A set of 179 expert-authored constructive problems in algebra, topology, and analysis, all in a prove-or-counterexample format, is genuinely new against GSM8K, MATH, AIME, MMLU-Math, and FrontierMath. The scoring rubric is coarse but sensible: full credit for a correct construction, half credit for the right direction with flaws, zero for committing to the wrong direction. That fills a real gap in LLM math evaluation, and the multi-round expert review is a reasonable quality-control story.\n\nThe soft spots are real but mostly fixable. First, the headline: the abstract and Section 5 say 'merely 70%,' but Table 2 gives 133/179 = 74.3% for O3 Mini, and none of the five rows lands on exactly 70%. That matters for the 'merely' judgment. Second, the paper claims the problems are previously unseen but gives no contamination check, no near-duplicate search, no analysis of training corpora. That is a common shortfall in benchmark work, but here it is load-bearing for the stronger conclusion. Third, the manual grading reports no inter-annotator agreement. With a 0/0.5/1 scale and qualitative rubric, that is a serious omission. Fourth, each model is sampled once with no temperature or variance reporting, so the cross-model differences are anecdotal.\n\nThe deeper problem is attribution. The rubric can tell you whether a model produced a valid construction, but it cannot tell you whether that construction came from recombining memorized patterns or from genuine synthesis. The authors assert the former, and the stress-test note lands: the data don't support that causal story. A correct answer to an undergraduate problem just shows the model can solve that problem; it is not evidence about mechanism. The paper is best read as saying current models struggle on constructive tasks, more so as difficulty rises. That is defensible and useful. The creativity-versus-memorization conclusion should be softened or backed with controlled experiments (e.g., held-out novel constructions, perturbation tests, or process-level analysis).\n\nWho is this for? People building or evaluating math-capable LLMs. The benchmark is a concrete resource and the format could transfer to other domains. I'd send it to peer review with the expectation of revision: fix the counts, add contamination analysis, report sampling and agreement, and rein in the conclusion. The dataset deserves referee time; the interpretation doesn't survive as written.","headline":"The benchmark is a real contribution; the 70% memorization conclusion is not supported by the paper's own data.","tokens_in":9996,"tokens_out":3836,"would_cite":true,"duration_ms":31941,"reading_group":"maybe","serious_thinker":"yes","would_accept_peer_review":true},"rs_alignment":null,"lean_confirmation":null,"pith_extraction":{"msc":[],"pacs":[],"model":"deepseek-v4-flash","headline":"A new creative-math benchmark tops out at 70 percent for the best AI model, suggesting that LLMs recombine memorized patterns rather than create.","keywords":["mathematical creativity","LLM evaluation","benchmark","counterexample construction","constructive problems","mathematical reasoning","open problems"],"falsifier":"Run a contamination audit: search the training corpora of the five models for the 179 benchmark problems, their paraphrases, or their solutions, then compare scores on demonstrably novel items with scores on items having near-duplicates in training data. If models score about the same on both groups, the memorization-based explanation loses force; if they score higher on near-duplicates, the paper's conclusion is supported.","tokens_in":8926,"feed_emoji":"🧮","tokens_out":6865,"duration_ms":65758,"temperature":0.7,"pith_summary":"DeepMath-Creative is a benchmark of 179 expert-written problems in algebra, topology, and analysis, each phrased as a proposition the model must either prove or refute by constructing a concrete example or counterexample. The paper defines mathematical creativity through constructiveness: the ability to build mathematical objects, functions, or structures that satisfy given properties. Under lenient scoring that ignores minor logical gaps, the best tested model, O3 Mini, reaches only about 70 percent accuracy, mostly on familiar undergraduate-level constructions. Accuracy drops sharply on harder problems, and no model offers substantive strategies for open problems. The paper concludes that this pattern is more consistent with recombination of memorized patterns than with genuine creative synthesis.","feed_headline":"Best AI model scores just 70% on a creative-math benchmark","feed_subtitle":"A 179-problem prove-or-refute benchmark suggests LLMs reuse memorized patterns, not new ideas.","key_machinery":"The carrier of the argument is the benchmark itself: a unified 'prove it or provide a counterexample' format applied to 179 expert-designed problems, together with a three-level scoring rubric that separates direction accuracy from process accuracy and relies on manual grading by mathematicians. This format operationalizes creativity as constructiveness, which the paper identifies as one of three dimensions of mathematical creativity, alongside inventing new concepts and new methods. The constructed examples are concrete and verifiable, so the benchmark turns the abstract idea of creativity into a measurable score on a defined task.","core_discovery":"The paper's central empirical claim is that current LLMs show partial constructive proficiency, enough to solve a majority of basic constructive problems, but that this proficiency is brittle and directionally fragile. Each answer is scored 0 for choosing the wrong direction, 0.5 for a reasonable but flawed construction, and 1 for a complete, correct proof or counterexample. Under this lenient rubric, the best model scores about 70 percent, while other tested models score lower, and the dominant failure modes are wrong direction, spurious proofs that reach a correct conclusion through invalid steps, and verbose nonconvergent reasoning. Because the problems were designed to be previously unseen and to require construction rather than recall, the paper attributes the partial success to recombination of memorized patterns rather than to authentic creativity.","pith_inferences":["If the memorization-recombination reading is right, a contamination audit should find that model accuracy on benchmark items is predictable from textual proximity to training data; scoring near-duplicate and truly novel items separately would test this directly.","Because the benchmark restricts creativity to construction of examples, it likely under-samples other creative acts named in the paper, such as inventing new concepts or methods; a model could plausibly score low here yet show other forms of generative originality.","A natural next experiment is to train models on the benchmark and test transfer to a held-out set of newly written constructive problems; flat transfer would support pattern memorization, while positive transfer would suggest the benchmark can drive genuine creative skill."],"forward_implications":["Mainstream mathematical benchmarks that reward reasoning on known problem types overstate model ability; a creativity-oriented evaluation reveals a lower ceiling on genuine problem-solving.","At master's-level and open problems, current models do not produce usable research strategies, so they are not yet reliable assistants for frontier mathematical research.","The sharp drop from undergraduate to harder problems implies that gains from pretraining and reasoning fine-tuning have not generalized to novel constructions.","The 70 percent figure is an upper bound on constructive ability, since it was awarded under lenient criteria; stricter demands for full rigor would place the best model lower."],"supporting_citations":[{"why":"Supplies an exemplar real-analysis problem about weak convergence and convergence in measure used to illustrate the benchmark's constructive format.","marker":"[1]"},{"why":"Provides the GSM8K dataset as a contrast case of basic arithmetic word problems that reward multi-step reasoning rather than creative construction.","marker":"[2]"},{"why":"FrontierMath serves as the advanced-reasoning benchmark against which DeepMath-Creative positions its call for more open, constructive problems.","marker":"[3]"},{"why":"DeepSeek-R1 is one of the five evaluated models and represents the current class of reasoning-focused LLMs.","marker":"[4]"},{"why":"MMLU's mathematics subset is cited as a multiple-choice benchmark with traditional formats that do not test constructiveness.","marker":"[5]"},{"why":"The MATH dataset provides the competition-style reasoning baseline that the paper says has reached near-saturation for leading models.","marker":"[6]"},{"why":"AIME 2024 is cited as a benchmark of deductive school-level problem solving that lacks creative construction tasks.","marker":"[7]"},{"why":"Poincaré's description of mathematical creation as discerning useful combinations supplies the paper's conceptual definition of creativity.","marker":"[11]"}],"fun_headline_variants":["AI math 'creativity' is just pattern recall, benchmark suggests","Lenient scoring: best LLM still only 70% on creative math","Benchmark: LLMs can solve creative math but only by rote","LLMs 'recombine memorized patterns' not creative in math benchmark","Creative math benchmark: AI tops out at 70% with no real insight"],"cache_read_input_tokens":3200,"weakest_assumption_plain":"The conclusion rests on the benchmark problems being genuinely unseen by the tested models, yet the paper provides no contamination check to rule out that models memorized these problems or near-analogues during pretraining.","fun_headline_variants_meta":{"raw":{"variants":["AI math 'creativity' is just pattern recall, benchmark suggests","Lenient scoring: best LLM still only 70% on creative math","Benchmark: LLMs can solve creative math but only by rote","LLMs 'recombine memorized patterns' not creative in math benchmark","Creative math benchmark: AI tops out at 70% with no real insight"]},"model":"deepseek-v4-flash","effort":"low","cost_usd":0.000785,"raw_usage":{"total_tokens":3468,"prompt_tokens":950,"completion_tokens":2518,"prompt_tokens_details":{"cached_tokens":384},"prompt_cache_hit_tokens":384,"prompt_cache_miss_tokens":566,"completion_tokens_details":{"reasoning_tokens":2420}},"tokens_in":566,"tokens_out":2518,"duration_ms":18671,"temperature":1.0,"reasoning_tokens":2420,"cache_read_input_tokens":384,"cache_creation_input_tokens":0},"cache_creation_input_tokens":0},"created_at":"2026-08-15T21:46:46.100956+00:00","model_set":{"reader":"deepseek-v4-flash"},"falsifier":"Run a contamination audit: search the training corpora of the five models for the 179 benchmark problems, their paraphrases, or their solutions, then compare scores on demonstrably novel items with scores on items having near-duplicates in training data. If models score about the same on both groups, the memorization-based explanation loses force; if they score higher on near-duplicates, the paper's conclusion is supported.","supporting_citations":[{"cited_title":"Counterexamples in Real Analysis","cited_arxiv_id":null,"evidence_quote":"Supplies an exemplar real-analysis problem about weak convergence and convergence in measure used to illustrate the benchmark's constructive format."},{"cited_title":"The V alue of Science","cited_arxiv_id":null,"evidence_quote":"Poincaré's description of mathematical creation as discerning useful combinations supplies the paper's conceptual definition of creativity."}],"review_version":1}