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REVIEW 3 major objections 6 minor 2 cited by

MMATH: A Multilingual Benchmark for Mathematical Reasoning

T0 review · 3 major / 6 minor · reviewed 2026-08-07 · deepseek-v4-flash

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Pith's one-line read Reasoning in English while answering in the target language simultaneously improves accuracy and preserves language consistency, as shown on MMATH, a new 10-language mathematical reasoning benchmark.

desk verdict Useful benchmark, real off-target phenomenon, but the EN-Think training claim is confounded by machine-translation quality and needs a proper control before it can support the paper's central conclusion. read the letter →

arxiv 2505.19126 v1 pith:22IVXYKZ submitted 2025-05-25 cs.CL

Wenyang Luo , Wayne Xin Zhao , Jing Sha , Shijin Wang , Ji-Rong Wen This is my paper
classification cs.CL
keywords MMATHmultilingualmathematicalreasoningoff-targetgenerationlanguageconsistencyratiocross-lingualchain-of-thoughtEnglish-centricfine-tuningLLMsbenchmarkconstruction
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

The reading

This paper introduces MMATH, a multilingual benchmark of 374 competition-level math problems translated into ten languages, and uses it to study how large reasoning models behave outside English. The central claim is that having a model reason internally in English while producing its final answer in the user's language is a better recipe than either fully English or fully native reasoning: it improves accuracy and preserves language consistency at the same time. The authors show this by fine-tuning Qwen2.5-32B-Instruct on English reasoning traces with target-language answers (EN-Think), which reaches an average MMATH score of 66.72 and an answering language-consistency ratio of 97.61, beating both fully English fine-tuning (62.38) and fully native-language reasoning (61.46). The benchmark also exposes a pervasive off-target problem where reasoning models answer low-resource-language questions in English or Chinese, and the paper offers prompting, thinking interventions, and training strategies to mitigate it.

What carries the argument

The load-bearing objects are MMATH itself and the EN-Think training configuration. MMATH is a set of 374 math problems from AIME, CNMO, and MATH-500 translated into Chinese, Arabic, Spanish, French, Japanese, Korean, Portuguese, Thai, and Vietnamese through a three-stage pipeline: LLM translation, cross-model iterative revision, and human verification. EN-Think is supervised fine-tuning on 3,000 examples where the question and final answer are in the target language but the chain-of-thought is in English. The language consistency ratio (LCR), computed with fastText language identification, is the metric that lets the paper quantify the off-target problem and verify that EN-Think preserves the answer language while switching the thinking language.

What would settle it

Have independent native-speaking mathematicians re-translate a random sample of MMATH problems from English and compare the two versions' difficulty; if the low-resource language versions such as Thai or Arabic come out systematically harder or more ambiguous than the English or Chinese versions, the per-language score gaps and the EN-Think advantage could be translation artifacts rather than reasoning effects.

Watch

Extended reading notes

Core claim

The paper's core discovery is that the language a model thinks in and the language it answers in can be decoupled to the benefit of both. On the MMATH benchmark, models that reason in English and answer in the target language outperform models that reason natively (66.72 vs 61.46 average) and models trained entirely in English (62.38), while achieving near-perfect answer-language consistency (97.61 LCR). The authors further observe that off-target thinking—thinking in a language other than the question's—is often more accurate than target-language thinking, especially for low-resource languages like Arabic and Thai, suggesting that English-centric internal reasoning is a strength to exploit rather than a failure to suppress.

Load-bearing premise

The benchmark translations preserve the exact mathematical semantics and difficulty of the original English problems, so cross-language score differences reflect model reasoning ability rather than translation artifacts.

Editorial extensions

If this is right

  • Models trained or prompted to think in English and answer natively can serve monolingual users without an accuracy penalty; the paper shows that 3K training examples suffice for a 32B chat model to rival a dedicated reasoning model (66.72 vs 67.01).
  • The off-target problem is measurable and can be mitigated by moderate thinking interventions such as discourse-initiated or question-restatement prompting, which raise answering LCR from below 60% to above 96%.
  • Accuracy alone overstates a model's multilingual capability in low-resource languages, so evaluations should report answer-language consistency alongside answer correctness.
  • Fine-tuning on English-only data (EN-SFT) actually worsens answer-language consistency (59.20 LCR), meaning the standard recipe for improving reasoning can actively hurt monolingual usability.
  • Benchmark conclusions about multilingual readiness should separate thinking-language from answer-language, since even advanced models like DeepSeek-R1 show large per-language disparities on MMATH.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • If translation artifacts are controlled, the decoupling advantage may generalize to non-math reasoning, implying that English-centric internal scaffolding is a general property of these models rather than a math-specific trick.
  • The EN-Think gain could partly reflect that English chain-of-thought traces distilled from DeepSeek-R1 are higher-quality than any currently available native-language traces; a testable extension would train Native-Think with equally strong native-language reasoning data.
  • A natural next benchmark would add languages with more distant scripts, such as Hindi, Swahili, or Greek, to test whether the EN-Think recipe scales beyond the ten languages and whether answer-language consistency degrades with script distance.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 6 minor

Summary. The paper introduces MMATH, a multilingual mathematical reasoning benchmark built from AIME 2024 (30 problems), AIME 2025 (15), CNMO (18), and a filtered subset of MATH-500 (311), translated into 10 languages (English, Chinese, Arabic, Spanish, French, Japanese, Korean, Portuguese, Thai, Vietnamese) via a three-stage pipeline (LLM translation, iterative LLM revision by three models, and human revision by certified native speakers). The authors evaluate chat and reasoning LLMs, introduce a language consistency ratio (LCR), document an off-target problem where models think or answer in unintended languages, and explore prompting (ATP, DIT, QRT) and three SFT strategies (EN-SFT, Native-Think, EN-Think). They report that EN-Think (English reasoning with native-language answers) achieves the best average accuracy (66.72) with high answering LCR (97.61), supporting the claim that reasoning in English while answering in the target language improves both performance and consistency.

Significance. If the central comparison is taken at face value, MMATH is a valuable community resource: it extends multilingual math evaluation from grade-school (MGSM) to competition-level problems, with a carefully documented translation and validation pipeline and public code and data. The empirical finding that EN-Think outperforms Native-Think is practically relevant for multilingual deployment. The paper also ships reproducible evaluation code, a transparent LCR metric validated by a 100-sample human check, and an honest limitations section. However, the load-bearing EN-Think versus Native-Think comparison is confounded by machine-translation quality of the training CoT, so the headline conclusion requires additional controlled experiments before it can be accepted as stated.

major comments (3)
  1. [Section 3.3.3 (Datasets Creation; Tables 7 and 8)] The claim that reasoning in English rather than in the native language drives the 5.26-point improvement is confounded by translation quality. All Light-R1 3K examples are originally in English; for Native-Think the entire example, including the long CoT, is machine-translated with GPT-4o-mini and never human-verified, whereas EN-Think uses the untranslated English CoT. Thus Native-Think may simply be trained on degraded targets. The paper validates benchmark translations (Section 2, with only 3% human edits) but reports no analogous quality check for the training-data translations. Please add a condition that holds CoT quality fixed across languages (e.g., human-validate the translated CoT, or back-translate the English CoT through the same pipeline as a control), or temper the causal claim.
  2. [Section 3.3.1 (Table 4 and subsection title)] The subsection title 'Off-target Thinking Increases Accuracy' makes a causal claim from observational data. The comparison conditions on the language the model happened to choose, which may correlate with problem difficulty, model confidence, or other latent factors. The DIT and QRT interventions in Section 3.3.2 alter more than just thinking language (they insert discourse markers or question restatements), so they do not isolate the effect of language. Please either reframe this as an associational observation or provide a controlled manipulation that varies only thinking language while holding reasoning content fixed.
  3. [Section 3.1 and all result tables] All results are point estimates averaged over 4 generations with no variance or significance testing. On small subsets such as AIME 2025 (15 problems, Table 13), a single-run difference of about 6.7 points is within sampling noise, so several per-language or small-gap comparisons (e.g., the 1-point ATP gains in Table 5, or per-language EN-Think versus EN-SFT gaps in Table 7) may not be robust. Please report per-run results, standard deviations, confidence intervals, or significance tests for the headline comparisons.
minor comments (6)
  1. [Throughout tables] The header 'A VG' should read 'AVG' in Tables 2, 5, 7, 13, and 14.
  2. [Abstract and Section 5] 'temporary reasoning models' should be 'contemporary reasoning models' in both places.
  3. [Figure 7] 'Buneo' is a typo for 'Bueno' (Spanish).
  4. [Table 11] 'Universidade NOV A de Lisboa' should be 'Universidade NOVA de Lisboa'.
  5. [Section 3.3.1] 'it may has already lost' should be 'it may have already lost'.
  6. [Section 3.3.2] The phrase 'more truthful multilingual ability' is vague; consider specifying what 'truthful' means operationally.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the benchmark is independent of the training data, and the EN-Think result is evaluated on held-out MMATH items.

full rationale

The paper's claims are empirical rather than derivational, and no equation-level or definition-level reduction of a result back to its own inputs can be exhibited. The MMATH benchmark is constructed independently of the fine-tuning experiments (Section 2): 374 English problems are translated through a three-stage GPT-4/Claude/Grok/human pipeline, and the models in Section 3 are then evaluated on this fixed benchmark using a held-out protocol (temperature 0.6, four repeated samples, macro-average). The training data in Section 3.3.3 come from Light-R1 3K, which is separate from MMATH; accuracy and LCR are measured on MMATH, not on the training distribution, so the EN-Think result (66.72, 97.61 answering LCR) is not an artifact of fitting to the test set. The high answering LCR of EN-Think is expected because the training examples explicitly contain native-language answers, but evaluating generalization on held-out native-language questions is a legitimate empirical test rather than a circular prediction. Similarly, DIT and QRT are simple prompt manipulations motivated by observed discourse patterns; they involve no fitted numeric parameters or test-score optimization, and their measured accuracy drops are empirical outcomes. The strongest potential concern, that Native-Think versus EN-Think confounds reasoning language with machine-translation quality of the CoT, is a real external-validity threat, and the Limitations section itself acknowledges that "synthesizing multilingual reasoning data remains a challenging problem" and that the "translation-based approach represents a preliminary attempt." But a confound is not circularity: the 5.26-point gap is not forced by construction, and no passage of the paper identifies the conclusion with an input or with a fitted parameter. There is no load-bearing self-citation chain; the only overlapping-author citation (Huang et al., 2023) is background related work, not the basis for the central claim. Therefore no circular step meets the evidentiary bar, and the honest finding is no significant circularity.

Assumptions & free parameters 0 free parameters · 5 assumptions · 0 invented entities

The paper makes no parametric fits. Its dependencies are on translation fidelity, language identification accuracy, answer extraction correctness, and the representativeness of the small benchmark. These are domain assumptions rather than invented entities.

assumptions (5)
  • domain assumption Translated MMATH questions preserve the mathematical semantics and difficulty of the English originals.
    The entire benchmark's validity rests on translation fidelity; Section 2's pipeline uses LLM translation plus human revision, but only 3% of translations were changed in human review, and no independent equivalence metric is reported.
  • domain assumption fastText language identification correctly classifies thinking and answer languages.
    LCR is computed via fastText; the authors validate on 100 samples (95% accuracy), but math-heavy outputs with LaTeX may be misclassified.
  • domain assumption Answer extraction via OpenCompass's math extraction and math_verify is accurate.
    Accuracy scores rely on extracting boxed answers; fallback to final numerical values when no boxed output exists may introduce errors.
  • domain assumption The 374-problem benchmark, including only 15 AIME 2025 problems, is representative enough for reliable cross-language comparisons.
    Subset sizes are small; with 4 repeats, AIME 2025 averages are based on 60 samples per language, making differences of a few points noisy.
  • domain assumption The Light-R1 3K subset is a suitable training distribution for multilingual complex reasoning after translation.
    EN-Think training uses this dataset translated into 10 languages; its quality and coverage of complex reasoning are not independently verified.

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Cite this review

Pith. "Pith review of MMATH: A Multilingual Benchmark for Mathematical Reasoning." pith.science (2026). https://pith.science/paper/22IVXYKZ

@misc{pith2026250519126,
  author       = {Pith},
  title        = {Pith review of: MMATH: A Multilingual Benchmark for Mathematical Reasoning},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/22IVXYKZ}},
  note         = {Machine review of arXiv:2505.19126}
}
read the original abstract

The advent of large reasoning models, such as OpenAI o1 and DeepSeek R1, has significantly advanced complex reasoning tasks. However, their capabilities in multilingual complex reasoning remain underexplored, with existing efforts largely focused on simpler tasks like MGSM. To address this gap, we introduce MMATH, a benchmark for multilingual complex reasoning spanning 374 high-quality math problems across 10 typologically diverse languages. Using MMATH, we observe that even advanced models like DeepSeek R1 exhibit substantial performance disparities across languages and suffer from a critical off-target issue-generating responses in unintended languages. To address this, we explore strategies including prompting and training, demonstrating that reasoning in English and answering in target languages can simultaneously enhance performance and preserve target-language consistency. Our findings offer new insights and practical strategies for advancing the multilingual reasoning capabilities of large language models. Our code and data could be found at https://github.com/RUCAIBox/MMATH.

Figures

Figures reproduced from arXiv: 2505.19126 by the authors.

Figure 1
Figure 1. A demonstration of off-target generation. The [PITH_FULL_IMAGE:figures/full_fig_p001_1.png] view at source ↗
Figure 2
Figure 2. The percentage to think in each language. [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. The percentage to answer in each language. [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (7 more)
Figure 4
Figure 4. Figure 4: The demonstration of our benchmark con￾struction process. D Case study E Other Results [PITH_FULL_IMAGE:figures/full_fig_p011_4.png]
Figure 5
Figure 5. Figure 5: Multilingual native language prompts for different languages. [PITH_FULL_IMAGE:figures/full_fig_p012_5.png]
Figure 6
Figure 6. Figure 6: Our ATP prompts, used to ask LLMs to explicitly answer in the target language. [PITH_FULL_IMAGE:figures/full_fig_p012_6.png]
Figure 7
Figure 7. Figure 7: Multilingual discourse marks used in our DIT thinking intervention method. These are collected from our [PITH_FULL_IMAGE:figures/full_fig_p014_7.png]
Figure 8
Figure 8. Figure 8: The percentage to answer in each language when prompted with ATP (Figure [PITH_FULL_IMAGE:figures/full_fig_p014_8.png]
Figure 9
Figure 9. Figure 9: Our QRT thinking intervention, which imitates LLMs’ behavior about repeating questions before actually [PITH_FULL_IMAGE:figures/full_fig_p015_9.png]
Figure 10
Figure 10. Figure 10: The percentage to think and answer in each language for our training methods: EN-SFT (fully English [PITH_FULL_IMAGE:figures/full_fig_p016_10.png]

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Forward citations

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Reviewed August 7, 2026 · model on record in the stance chip above.