arxiv: 2601.23048 · v3 · submitted 2026-01-30 · 💻 cs.AI

Recognition: no theorem link

From Abstract to Contextual: What LLMs Still Cannot Do in Mathematics

Bowen Cao , Dongdong Zhang , Yixia Li , Junpeng Liu , Shijue Huang , Chufan Shi , Hongyuan Lu , Yaokang Wu

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Guanhua Chen Wai Lam Furu Wei

Authors on Pith no claims yet

Pith reviewed 2026-05-16 09:33 UTC · model grok-4.3

classification 💻 cs.AI

keywords LLMscontextual reasoningmathematical problem formulationbenchmarkserror analysisfine-tuningAIMEMATH

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The pith

LLMs fail to formulate the mathematical core from contextual scenarios even when they solve the abstract versions.

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

The paper argues that progress on abstract math benchmarks has not translated to contextual settings where models must extract the problem from descriptive text. By creating ContextMATH through two transformations that embed problems in scenarios or scale their complexity without changing core reasoning, the authors test 61 models and find consistent performance drops driven by formulation failures. Formulation accuracy falls with increasing problem difficulty, yet larger models handle correct formulations more effectively. Fine-tuning on scenario data yields partial gains, but the dual bottlenecks of formulation and reasoning persist. This positions contextual mathematical reasoning as a key remaining challenge.

Core claim

Formulation of the mathematical problem from a scenario is a prerequisite for successful reasoning, and errors in this step dominate failures in contextual math. While larger models improve at leveraging correct formulations, both formulation and reasoning continue to limit performance, and standard fine-tuning only partially closes the gap.

What carries the argument

ContextMATH benchmark using Scenario Grounding to embed problems in narratives and Complexity Scaling to nest conditions into sub-problems, isolating formulation from reasoning.

If this is right

Incorrect problem formulation accounts for most errors, with accuracy declining as difficulty rises.
Sufficiency of correct formulations increases with model scale.
Fine-tuning on scenario data improves results, but formulation-only training does not.
Substantial performance gaps remain after fine-tuning.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

Advances in contextual reasoning may require new training paradigms beyond standard fine-tuning.
Similar formulation challenges likely affect LLM use in other applied domains like science and engineering.
The benchmark could be extended to measure progress in hybrid LLM-symbolic systems.

Load-bearing premise

The transformations to create contextual problems accurately simulate real-world presentation without altering the underlying reasoning complexity.

What would settle it

A model achieving equivalent accuracy on the contextual benchmark and the original abstract problems would disprove that contextual formulation introduces a significant new bottleneck.

Figures

Figures reproduced from arXiv: 2601.23048 by Bowen Cao, Chufan Shi, Dongdong Zhang, Furu Wei, Guanhua Chen, Hongyuan Lu, Junpeng Liu, Shijue Huang, Wai Lam, Yaokang Wu, Yixia Li.

**Figure 2.** Figure 2: Distribution of error types in failure cases [PITH_FULL_IMAGE:figures/full_fig_p007_2.png] view at source ↗

**Figure 3.** Figure 3: Relationship between reasoning accuracy and formulation metrics. Each point represents a model, with the x-axis showing its average reasoning accuracy across all subsets and the y-axis showing the corresponding values of formulation accuracy (orange), necessity (green), and sufficiency (blue). The fitted lines indicate the overall trends. Results. To present an overview of model behavior, we report aggr… view at source ↗

read the original abstract

Large language models now solve many benchmark math problems at near-expert levels, yet this progress has not fully translated into reliable performance in real-world applications. We study this gap through contextual mathematical reasoning, where the mathematical core must be formulated from descriptive scenarios. We introduce ContextMATH, a benchmark that repurposes AIME and MATH-500 problems into two contextual settings: Scenario Grounding (SG), which embeds abstract problems into realistic narratives without increasing reasoning complexity, and Complexity Scaling (CS), which transforms explicit conditions into sub-problems to capture how constraints often appear in practice. Evaluating 61 proprietary and open-source models, we observe sharp drops: on average, open-source models decline by 13 and 34 points on SG and CS, while proprietary models drop by 13 and 20. Error analysis shows that errors are dominated by incorrect problem formulation, with formulation accuracy declining as original problem difficulty increases. Correct formulation emerges as a prerequisite for success, and its sufficiency improves with model scale, indicating that larger models advance in both understanding and reasoning. Nevertheless, formulation and reasoning remain two complementary bottlenecks that limit contextual mathematical problem solving. Finally, we find that fine-tuning with scenario data improves performance, whereas formulation-only training is ineffective. However, performance gaps are only partially alleviated, highlighting contextual mathematical reasoning as a central unsolved challenge for LLMs.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Desk Editor's Note private letter to a colleague

This paper shows LLMs drop sharply on math problems once they must first extract the equations from descriptive scenarios, with formulation errors as the main culprit across 61 models.

read the letter

The core finding is that abstract benchmark wins do not translate to contextual math. The authors repurpose AIME and MATH-500 problems into ContextMATH using two transformations: Scenario Grounding, which wraps the math in realistic stories, and Complexity Scaling, which turns conditions into sub-problems. On these, open-source models lose 13 and 34 points respectively while proprietary models lose 13 and 20. Error breakdowns show formulation mistakes dominate, and correct formulation is required before reasoning can succeed. Larger models improve on both steps, yet the gaps persist. Fine-tuning on scenario data helps modestly while pure formulation training does not close the difference much.

Referee Report

1 major / 3 minor

Summary. The paper introduces ContextMATH, a benchmark repurposing AIME and MATH-500 problems into contextual settings via Scenario Grounding (SG: embedding into realistic narratives) and Complexity Scaling (CS: transforming conditions into sub-problems). Evaluating 61 LLMs, it reports average performance drops of 13–34 points for open-source models and 13–20 for proprietary ones, with error analysis showing formulation errors as dominant and increasing with original problem difficulty. It concludes that correct formulation is a prerequisite for success (improving with scale), that formulation and reasoning are complementary bottlenecks, and that fine-tuning on scenario data helps while formulation-only training does not.

Significance. If the transformations preserve original reasoning demands, the large-scale evaluation across 61 models with consistent error categorization directly supports formulation accuracy as a prerequisite bottleneck distinct from pure reasoning. The scaling trends and fine-tuning results provide actionable evidence on where progress is occurring and where it stalls. This is a solid empirical contribution identifying contextual mathematical reasoning as an unsolved challenge, with the performance deltas and error breakdowns offering clear, falsifiable observations.

major comments (1)

[Methods (SG/CS transformations)] Methods section (SG and CS definitions): The claim that SG 'embeds abstract problems into realistic narratives without increasing reasoning complexity' is stated without quantitative support such as expert complexity ratings, solution-step counts, or solver-time comparisons between original and transformed problems. This is load-bearing for the central claim that observed drops reflect formulation deficits rather than added intrinsic difficulty; absent such checks, the bottleneck interpretation risks conflating the two.

minor comments (3)

[Results] Table 1 or equivalent results table: clarify whether the reported point drops are absolute accuracy or relative; include per-model variance or confidence intervals to strengthen the scaling claims.
[Error Analysis] Error categorization section: the taxonomy of formulation vs. reasoning errors would benefit from an explicit inter-annotator agreement score or example annotations to ensure reproducibility.
[Fine-tuning Experiments] Fine-tuning experiments: specify the exact data splits and whether the scenario data overlaps with the test set to rule out leakage.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the positive evaluation and constructive feedback. The single major comment is addressed point-by-point below. We will incorporate the suggested validation to strengthen the manuscript.

read point-by-point responses

Referee: Methods section (SG and CS definitions): The claim that SG 'embeds abstract problems into realistic narratives without increasing reasoning complexity' is stated without quantitative support such as expert complexity ratings, solution-step counts, or solver-time comparisons between original and transformed problems. This is load-bearing for the central claim that observed drops reflect formulation deficits rather than added intrinsic difficulty; absent such checks, the bottleneck interpretation risks conflating the two.

Authors: We agree that quantitative validation of preserved reasoning complexity would strengthen the central claim. The SG and CS transformations were constructed by design to avoid introducing new mathematical operations or constraints (SG adds only narrative framing around the original conditions; CS decomposes explicit conditions into sub-problems while retaining the same core deductions). Nevertheless, we acknowledge the absence of explicit metrics in the current version. In the revision we will add (i) solution-step counts for a random sample of 50 problems in both original and transformed forms and (ii) expert complexity ratings (on a 1–5 scale) collected from two independent mathematicians, confirming no systematic increase. These additions will directly support the interpretation that performance drops arise from formulation rather than added difficulty. revision: yes

Circularity Check

0 steps flagged

No circularity: purely empirical benchmark with independent observations

full rationale

The paper presents an empirical study introducing ContextMATH benchmark via descriptive transformations (SG and CS) applied to existing AIME/MATH-500 problems, followed by model evaluations and error analysis. No derivation chain, equations, or first-principles predictions exist that reduce to inputs by construction. Performance drops, formulation accuracy trends, and bottleneck conclusions are direct observations from test results, not fitted parameters renamed as predictions or self-citations that bear the central load. The assumption that SG/CS preserve reasoning complexity is a methodological claim open to external verification (e.g., via step counts or expert ratings) but does not create circularity within the paper's own logic. Self-contained against external benchmarks.

Axiom & Free-Parameter Ledger

0 free parameters · 1 axioms · 0 invented entities

The central claims rest on the assumption that the repurposed problems faithfully represent contextual difficulty without new artifacts; no free parameters or invented entities are introduced.

axioms (1)

domain assumption Repurposed AIME and MATH-500 problems in Scenario Grounding preserve original reasoning complexity.
Invoked in the benchmark construction section to isolate contextual effects.

pith-pipeline@v0.9.0 · 5572 in / 1134 out tokens · 30729 ms · 2026-05-16T09:33:50.670166+00:00 · methodology

discussion (0)

Reference graph

Works this paper leans on

13 extracted references · 13 canonical work pages

[1]

Mathematical Integrity: Does the story perfectly preserve all numbers, relationships (e.g., perpendicularity, equality), and operations from the original problem? Is anything missing or changed?

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[2]

Clarity & Language: Is the story easy to understand? Does it successfully avoid math- ematical jargon and symbols, using clear descriptions instead? Is the final question unam- biguous?

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[3]

After your summary, conclude with the mandatory [Overall Assessment] line

Conciseness: Is the story direct and to the point, without unnecessary details that over- complicate the problem? 15 Published as a conference paper at ICLR 2026 SG Scenario Verification Prompt (continued) Your Output: Please provide your review as a brief summary of your findings. After your summary, conclude with the mandatory [Overall Assessment] line....

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[4]

Original Math Problem{original problem placeholder}

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[5]

Conversion Mappings: 2.1 Concept Mappings:{concept mappings list placeholder} 2.2 Relationship and Attribute Mappings:{relationship mappings list placeholder}

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[6]

Here is the feedback: {feedback placeholder} Output your revised version in plain text in the following format: [Step 1] [Mathematical Element]→[Specific Real-World Analogue]

Real-World Problem:{real world problem text placeholder} A.1.3 SCENARIOGROUNDING: REVISIONPROMPT SG Scenario Revision Prompt Carefully analyze the following feedback to revise your previous response to address all problems. Here is the feedback: {feedback placeholder} Output your revised version in plain text in the following format: [Step 1] [Mathematica...

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[7]

The underlying mathematical problem must remain solvable and equivalent to the original

Maintain Core Alignment Ensure all mathematical quantities, variables, and relationships directly correspond to elements within the real-world context. The underlying mathematical problem must remain solvable and equivalent to the original. — 16 Published as a conference paper at ICLR 2026 CS Scenario Generation Prompt (continued)

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[8]

Embed Conditions through Layered Obfuscation Replace direct mathematical statements and values with more natural, layered, and context- rich descriptions that require deductive reasoning from the solver. * A. Contextualized Numerical Properties (Disguising Specific Values): * This technique involves disguising specific numerical values by describing them ...

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[9]

This increases cognitive load and realism

Introduce Plausible, Irrelevant Information Incorporate details that are contextually relevant to the scenario but mathematically extra- neous to the problem’s solution. This increases cognitive load and realism. Example: For a drone problem, mention its battery capacity, wing span, payload weight, or the color of the packages being delivered, provided th...

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[10]

Avoid redundancy and unnecessary repeti- tion

Language Refinement and Simplicity: Make sure all descriptions are concise and clear. Avoid redundancy and unnecessary repeti- tion. 17 Published as a conference paper at ICLR 2026 CS Scenario Generation Prompt (continued) Avoid using mathematical variables (such as x, k, A, B, etc.) directly in the situation de- scription, but give them specific real-wor...

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[11]

Misassigning which side of the Echo Deck lies along the straight track

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[12]

Misassigning which Echo Deck side forms the chord on the circle

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[13]

Additional logical issue (unjustified ”nice fraction”.) ... How this led to the wrong answer: - By putting 17 along the track instead of 184 and using a 17-length chord for the circle instead of 184, the computed b (the x-position of FLE) shifted incorrectly, producing|107− b| ≈60.5, rather than the correctCE= 104. The mistake is structural (wrong mapping...

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