# Investigating the interaction of linguistic and mathematical reasoning in language models using multilingual number puzzles

arXiv: https://arxiv.org/abs/2506.13886 · HTML: https://mlsanity.com/paper/2506.13886/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 14 of its 29 references that are in the map.
- First posted on arXiv 16 Jun 2025.

## Placed in

- LLM reasoning / [Mathematical reasoning](https://mlsanity.com/lr/mathematical-reasoning/)

## Builds on (most cited first, 14 of 14)

- [GPT-4 Technical Report](https://mlsanity.com/paper/2303.08774/) (2023)
- [Measuring Massive Multitask Language Understanding](https://mlsanity.com/paper/2009.03300/) (2020)
- [DeepSeek-R1: Incentivizing Reasoning Capability in LLMs via Reinforcement Learning](https://mlsanity.com/paper/2501.12948/) (2025)
- [OpenAI o1 System Card](https://mlsanity.com/paper/2412.16720/) (2024)
- [The Illusion of Thinking: Understanding the Strengths and Limitations of Reasoning Models via the Lens of Problem Complexity](https://mlsanity.com/paper/2506.06941/) (2025)
- [Large Language Models for Mathematical Reasoning: Progresses and Challenges](https://mlsanity.com/paper/2402.00157/) (2024)
- [Embers of Autoregression: Understanding Large Language Models Through the Problem They are Trained to Solve](https://mlsanity.com/paper/2309.13638/) (2023)
- [Evaluation of OpenAI o1: Opportunities and Challenges of AGI](https://mlsanity.com/paper/2409.18486/) (2024)
- [Gold-medalist Performance in Solving Olympiad Geometry with AlphaGeometry2](https://mlsanity.com/paper/2502.03544/) (2025)
- [MathOdyssey: Benchmarking Mathematical Problem-Solving Skills in Large Language Models Using Odyssey Math Data](https://mlsanity.com/paper/2406.18321/) (2024)
- [Number Cookbook: Number Understanding of Language Models and How to Improve It](https://mlsanity.com/paper/2411.03766/) (2024)
- [LINGOLY: A Benchmark of Olympiad-Level Linguistic Reasoning Puzzles in Low-Resource and Extinct Languages](https://mlsanity.com/paper/2406.06196/) (2024)
- [Large Linguistic Models: Investigating LLMs' metalinguistic abilities](https://mlsanity.com/paper/2305.00948/) (2023)
- [Linguini: A benchmark for language-agnostic linguistic reasoning](https://mlsanity.com/paper/2409.12126/) (2024)

## Built on by (most cited first, 2 of 2)

- [The Effect of Scripts and Formats on LLM Numeracy](https://mlsanity.com/paper/2601.15251/) (2026)
- [When Tokenization is Secretly Output Supervision](https://mlsanity.com/paper/2609.01386/) (2026)

## Abstract (arXiv)

Across languages, numeral systems vary widely in how they construct and combine numbers. While humans consistently learn to navigate this diversity, large language models (LLMs) struggle with linguistic-mathematical puzzles involving cross-linguistic numeral systems, which humans can learn to solve successfully. We investigate why this task is difficult for LLMs through a series of experiments that untangle the linguistic and mathematical aspects of numbers in language. Our experiments establish that models cannot consistently solve such problems unless the mathematical operations in the problems are explicitly marked using known symbols (+, ×, etc., as in "twenty + three"). In further ablation studies, we probe how individual parameters of numeral construction and combination affect performance. While humans use their linguistic understanding of numbers to make inferences about the implicit compositional structure of numerals, LLMs seem to lack this notion of implicit numeral structure. We conclude that the ability to flexibly infer compositional rules from implicit patterns in human-scale data remains an open challenge for current reasoning models.