REVIEW 4 major objections 6 minor 2 cited by
SOLIDGEO: Measuring Multimodal Spatial Math Reasoning in Solid Geometry
T0 review · 4 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash
Pith's one-line read The paper introduces SOLIDGEO, a 3,113-question benchmark for solid-geometry reasoning, and reports that the best evaluated model reaches 49.5 percent accuracy against 77.5 percent for humans.
desk verdict SolidGeo is a genuinely needed benchmark with a plausible headline gap, but the correctness of answer keys and LLM-based grading are not yet pinned down. read the letter →
The pith
A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.
The reading
What carries the argument
The load-bearing object is the benchmark itself, constructed by combining keyword-filtered problems from six existing benchmarks with 10,932 candidate problems gathered from K-12 educational sources and then running a four-stage filter: keeping only multimodal samples with answers and diagrams, removing blurry or low-resolution images, using large-model semantic classification to confirm solid-geometry relevance, and applying n-gram similarity checks to remove cross-set duplicates. The annotation scheme is an eight-part taxonomy, covering composite solid structures, spatial metric relations, solid shape identification, planar unfolding and configuration, measurement of solid geometric forms, solid geometry modeling, multi-view projection, and 3D coordinate and vector reasoning, plus three difficulty levels assigned by majority voting of three multimodal models and reviewed by human experts. What carries the argument is the combination of a broad, fine-grained testbed and a human baseline, which lets the paper attribute low accuracies to spatial reasoning rather than to problem format or data noise.
What would settle it
A direct test would be to take the 1,376 newly collected problems, keep their answers secret, and have a panel of independent geometry experts re-solve and re-score them; if a large share of labels are wrong, the reported accuracies would shift. Alternatively, evaluate models on a future version of SOLIDGEO from which the 1,737 existing-benchmark items have been removed; if accuracy drops sharply, the original result reflected memorization rather than spatial reasoning.
Extended reading notes
Core claim
The core discovery is a quantified capability gap in multimodal spatial mathematical reasoning, established through a new dedicated benchmark. SOLIDGEO gathers 3,113 solid-geometry problems from six existing datasets plus 1,376 newly curated items, filters them through a four-stage pipeline, and annotates each with one or more of eight subject categories and a difficulty level from 1 to 3. On this testbed, all evaluated models fall short of the 77.5 percent human score, with the best model at 49.5 percent; the strongest open-source fast single-pass model reaches about 29.6 percent and the strongest open-source long chain-of-thought model about 26.6 percent. The paper concludes that 3D spatial reasoning, including projection, unfolding, spatial measurement, and vector reasoning, remains a distinct bottleneck for current multimodal models even when they perform well on plane geometry.
Load-bearing premise
The benchmark's validity rests on the assumption that the 1,376 newly collected problems have correct ground-truth answers and that the 1,737 problems drawn from public benchmarks are not already memorized by the evaluated models, and the paper does not analyze either source of error.
Editorial extensions
If this is right
- Solid-geometry ability should be treated as a separate evaluation axis from plane-geometry ability when benchmarking multimodal models.
- The 49.5 percent versus 77.5 percent gap gives a concrete target: a model that reaches human level on SOLIDGEO would demonstrate spatial reasoning well beyond current systems.
- The eight-category taxonomy lets future work identify which spatial skill, such as planar unfolding or multi-view projection, is weakest and target it directly.
- The finding that longer chain-of-thought output does not consistently improve accuracy implies that scaling reasoning length alone will not close the spatial-reasoning gap.
- Future model releases can be compared against the reported results and the human baseline on the same benchmark without re-running the full evaluation.
Reading between the lines
- Editorial extension: because 1,737 of the problems come from public benchmarks, the reported accuracies could be inflated by training-data contamination; the paper does not test this, so a held-out version using only the 1,376 newly collected problems would be a useful robustness check.
- Editorial extension: the benchmark could also serve as a training resource if the answer keys are correct, but its value for that purpose depends on independent verification of the newly collected labels.
- Editorial extension: the error pattern suggests that spatial reasoning may not improve with language-only reasoning scaling, so progress may require models that can manipulate three-dimensional structure internally rather than merely produce longer text.
Editorial analysis
A structured set of objections, weighed in public.
Referee Report
Summary. The paper introduces SOLIDGEO, a multimodal benchmark of 3,113 solid-geometry problems with associated images, sourced partly from six existing benchmarks (1,737 problems) and partly newly collected from K-12 educational material (1,376 problems). Each problem is annotated with one of eight fine-grained subject categories and a difficulty level from 1 to 3. The authors evaluate 27 LLMs and MLLMs under zero-shot, chain-of-thought, and two-shot settings, reporting accuracy by category, difficulty, and question type, along with token-efficiency analyses and an error taxonomy for two representative models. The headline results are that OpenAI-o1 reaches 49.5% accuracy versus 77.5% for human high-school students, and the paper concludes that current models fall significantly short of human-level solid-geometry reasoning.
Significance. If the benchmark's labels, ground-truth answers, and grading are reliable, SOLIDGEO fills a genuine gap: existing multimodal math benchmarks contain very few solid-geometry items, and those items are mostly simple counting or basic volume tasks. The paper's assets are substantial: a fine-grained eight-category taxonomy, difficulty annotations, real-world K-12 and competition sourcing, an evaluation spanning 27 open- and closed-source models, token-efficiency analysis, and a falsifiable headline claim—a 28-point gap between the best model and human performance—that the community can track. However, the benchmark's validity as a measurement instrument rests on three load-bearing assumptions: that the 1,737 public-benchmark items are not substantially memorized by the evaluated models, that the 1,376 newly collected items have correct ground-truth answers, and that the LLM-based answer grader is accurate. The manuscript currently provides insufficient evidence for each of these assumptions, so the central quantitative comparison is not yet fully pinned down.
major comments (4)
- [§3.2, §3.3, Appendix D.3] The statement in Section 3.3 that 'each problem ... has been manually verified for correctness' is not supported by the annotation protocol. Section 3.2 and Appendix D.3 describe human review only for subject and difficulty labels, explicitly saying that annotators 'verified both the subjects and difficulty labels'; nowhere is there a protocol for checking answer keys. For the 1,376 newly collected problems, answers come from Mathpix OCR of Zujuan PDFs, and OCR errors in fractions, radicals, multi-part free responses, or diagrams would directly flip correctness scores for both models and the human baseline. Please either report the answer-verification protocol (who checked the answer keys, how disagreements were resolved, and how many answers were corrected) or revise the claim in Section 3.3 to refer only to label verification.
- [Appendix G.2] All model scores and the human baseline are graded by the DeepSeek API with no reported validation of the grader. Since 2,144 of 3,113 problems are open-ended and many answers contain mathematical expressions (e.g., '-1-2√2' in Figure 34), grader errors can systematically shift every accuracy reported in Table 3 and Table 4. Please provide a validation set with human-graded responses, report grader agreement (for example, on 200–300 sampled responses per question type), and consider releasing the graded model outputs so that readers can independently audit the scoring.
- [§3.2, Appendix A.4, Table 3] The paper does not address train/test contamination from the six existing public benchmarks that contribute 1,737 of the 3,113 problems (OlympiadBench 24.93%, MathVerse 11.47%, MathVision 7.84%, DynaMath 4.49%, CMMaTH 4.66%, GeoEval 2.41%). These benchmarks predate the evaluated models, and the models may have seen the exact items during pretraining. Because the paper reports only aggregate accuracy, it is impossible to tell whether the 49.5% figure for OpenAI-o1 is inflated by memorization of public-benchmark items. Please report accuracy separately for the 1,376 newly collected and 1,737 existing problems, and include a contamination analysis (for example, exact or near-duplicate retrieval against training corpora, or memorization probes), or explain explicitly why contamination is unlikely to affect the headline human-model gap.
- [Appendix F, Table 4] The human baseline protocol is not sufficiently detailed to support the precision of the 77.5% figure. Appendix F states that 60 high-school students were recruited and that 'each student assigned their own section of the questions,' which appears to mean that each question was answered by a single student; no redundancy, inter-rater statistics, or standard errors are reported. A single student's mistake on one item changes the human accuracy by roughly 0.03 percentage points, and the reported category-level human scores (for example, 90.2% on Solid Shape Identification) should be accompanied by confidence intervals or a description of how many students answered each item. Additionally, the anomalous difficulty trend in Table 4—Gemini-2.5-pro at 22.1% on Level 1 but 80.7% on Level 3, and OpenAI-o1 improving from 46.6% to 57.4%—deserves a concrete explanation rather than the current speculation, because it suggests that the difficulty labels may not behave as intended for these models.
minor comments (6)
- [Table 3 vs. Table 4] The reported overall accuracy for OpenAI-o1 differs between Table 3 (49.5%) and Table 4 (49.6%); please reconcile these numbers.
- [§4.2] The sentence 'The results presented in Table 2 highlight the inherent difficulty of SOLIDGEO' appears to refer to Table 3, since Table 2 is a comparison of benchmarks; please fix the cross-reference.
- [General] The dataset is said to be 'released at SOLIDGEO,' but no URL is given; please provide a working link or repository identifier.
- [§3.2, Appendix D.3] The annotation pipeline uses GPT-4o, Claude-3.7-Sonnet, and Qwen-VL-Max to assign difficulty and category labels before human review; please report inter-annotator agreement or the number of cases resolved by experts, so readers can assess label reliability.
- [Table 4] The per-difficulty and per-question-type breakdowns are reported without sample sizes or confidence intervals; adding these would help assess whether category-level differences (for example, the 3DCV human score of 69.2% versus Gemini-2.5-pro's 72.9%) are meaningful.
- [Appendix E] The token-distribution figures are qualitative; please add summary statistics (median, mean, and interquartile range) for the generated-token distributions in the main text or appendix.
Circularity Check
No significant circularity; SOLIDGEO is a measurement benchmark, and its headline numbers are external evaluations rather than derived predictions.
full rationale
SOLIDGEO is a benchmark paper: its central claims are measured accuracies (OpenAI-o1 at 49.5%, human at 77.5%) and dataset statistics, not quantities derived from an underlying model or theorem. Tracing the construction pipeline (Section 3.2 and Appendix D), the steps are: OCR from Zujuan PDFs, structural and image-quality filtering, DeepSeek-based topic classification, n-gram deduplication, and majority-vote labeling of subject and difficulty by GPT-4o, Claude-3.7-Sonnet, and Qwen-VL-Max with human review. None of these steps defines the evaluated quantity (problem-solving accuracy) in terms of the labels: evaluation compares model outputs against ground-truth answers via the DeepSeek API, and the accuracy numbers are not derived from or fitted to the labeling pipeline. Overlap between the models used for labeling/judging and the models evaluated (e.g., DeepSeek used both as a semantic filter/judge and as one evaluated model; GPT-4o and Claude used as label voters and later evaluated) is a potential bias or contamination concern, but it is not circular: no equation or construction forces the reported accuracies to equal a fitted parameter or a self-citation. Self-citations (GeoEval [5], MV-MATH [40], CMMaTH [79], the System-1/System-2 survey [76]) are background or minor data sources; CMMaTH supplies only 4.66% of items, so the 'first large-scale SOLIDGEO benchmark' claim does not stand or fall on that source. Separately, the Section 3.3 assertion that each problem 'has been manually verified for correctness' is not backed by the Appendix D.3 protocol, which verifies subject and difficulty labels only; this is an answer-key validity risk, not circularity. Under the review rules, a missing-support validity issue does not raise the circularity score, so the finding is no significant circularity.
Assumptions & free parameters
assumptions (4)
- domain assumption The DeepSeek API and three MLLMs (GPT-4o, Claude-3.7-Sonnet, Qwen-VL-Max) correctly filter and annotate solid geometry problems.
- domain assumption The 1,737 problems from existing benchmarks have correct ground truth answers and are genuinely solid geometry problems.
- domain assumption Human performance measured on 60 high school students is a representative baseline for human-level solid geometry reasoning.
- domain assumption Answer grading via the DeepSeek API with the prompts in Table 10 correctly determines whether model responses match ground truth.
Cite this review
Pith. "Pith review of SOLIDGEO: Measuring Multimodal Spatial Math Reasoning in Solid Geometry." pith.science (2026). https://pith.science/paper/VVPU6LWI
@misc{pith2026250521177,
author = {Pith},
title = {Pith review of: SOLIDGEO: Measuring Multimodal Spatial Math Reasoning in Solid Geometry},
year = {2026},
howpublished = {\url{https://pith.science/paper/VVPU6LWI}},
note = {Machine review of arXiv:2505.21177}
}
read the original abstract
Geometry is a fundamental branch of mathematics and plays a crucial role in evaluating the reasoning capabilities of multimodal large language models (MLLMs). However, existing multimodal mathematics benchmarks mainly focus on plane geometry and largely ignore solid geometry, which requires spatial reasoning and is more challenging than plane geometry. To address this critical gap, we introduce SolidGeo, the first large-scale benchmark specifically designed to evaluate the performance of MLLMs on mathematical reasoning tasks in solid geometry. SolidGeo consists of 3,113 real-world K-12 and competition-level problems, each paired with visual context and annotated with difficulty levels and fine-grained solid geometry categories. Our benchmark covers a wide range of 3D reasoning subjects such as projection, unfolding, spatial measurement, and spatial vector, offering a rigorous testbed for assessing solid geometry. Through extensive experiments, we observe that MLLMs encounter substantial challenges in solid geometry math tasks, with a considerable performance gap relative to human capabilities on SolidGeo. Moreover, we analyze the performance, inference efficiency and error patterns of various models, offering insights into the solid geometric mathematical reasoning capabilities of MLLMs. We hope SolidGeo serves as a catalyst for advancing MLLMs toward deeper geometric reasoning and spatial intelligence.
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