# Math Takes Two: A test for emergent mathematical reasoning in communication

arXiv: https://arxiv.org/abs/2604.21935 · HTML: https://mlsanity.com/paper/2604.21935/

## Key facts

- No citing papers in the map yet (data through 14 Oct 2026).
- Placed in Mathematical reasoning, one of 17 directions in LLM reasoning.
- Builds on 17 of its 34 references that are in the map.
- First posted on arXiv 30 Mar 2026.

## Placed in

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

## Builds on (most cited first, 17 of 17)

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- [Solving Quantitative Reasoning Problems with Language Models](https://mlsanity.com/paper/2206.14858/) (2022)
- [The Concrete Distribution: A Continuous Relaxation of Discrete Random Variables](https://mlsanity.com/paper/1611.00712/) (2016)
- [Measuring and Narrowing the Compositionality Gap in Language Models](https://mlsanity.com/paper/2210.03350/) (2022)
- [Object-Centric Learning with Slot Attention](https://mlsanity.com/paper/2006.15055/) (2020)
- [Mathematical Capabilities of ChatGPT](https://mlsanity.com/paper/2301.13867/) (2023)
- [Multi-Agent Cooperation and the Emergence of (Natural) Language](https://mlsanity.com/paper/1612.07182/) (2016)
- [DreamCoder: Growing generalizable, interpretable knowledge with wake-sleep Bayesian program learning](https://mlsanity.com/paper/2006.08381/) (2020)
- [Emergence of Language with Multi-agent Games: Learning to Communicate with Sequences of Symbols](https://mlsanity.com/paper/1705.11192/) (2017)
- [Proof or Bluff? Evaluating LLMs on 2025 USA Math Olympiad](https://mlsanity.com/paper/2503.21934/) (2025)
- [Compositional Generalization from First Principles](https://mlsanity.com/paper/2307.05596/) (2023)
- [Compositional generalization in a deep seq2seq model by separating syntax and semantics](https://mlsanity.com/paper/1904.09708/) (2019)
- [COLA: A Benchmark for Compositional Text-to-image Retrieval](https://mlsanity.com/paper/2305.03689/) (2023)
- [The Emergence of Compositional Languages for Numeric Concepts Through Iterated Learning in Neural Agents](https://mlsanity.com/paper/1910.05291/) (2019)
- [Machine learning and information theory concepts towards an AI Mathematician](https://mlsanity.com/paper/2403.04571/) (2024)
- [Forgotten Polygons: Multimodal Large Language Models are Shape-Blind](https://mlsanity.com/paper/2502.15969/) (2025)

## Abstract (arXiv)

Although language models demonstrate remarkable proficiency on mathematical benchmarks, it remains unclear whether this reflects true mathematical reasoning or statistical pattern matching over learning formal syntax. Most existing evaluations rely on symbolic problems grounded in established mathematical conventions, limiting insight into the models' ability to construct abstract concepts from first principles. In this work, we propose Math Takes Two, a new benchmark designed to assess the emergence of mathematical reasoning through communication. Motivated by the hypothesis that mathematical cognition in humans co-evolved with the need for precise communication, our benchmark tests whether two agents, without prior mathematical knowledge, can develop a shared symbolic protocol to solve a visually grounded task where the use of a numerical system facilitates extrapolation. Unlike many current datasets, our benchmark eschews predefined mathematical language, instead requiring agents to discover latent structure and representations from scratch. Math Takes Two thus provides a novel lens through which to develop and evaluate models with emergent numerical reasoning capabilities.