How Well Can LLMs Verbalize Mathematical Formulas? A Multi-Domain Evaluation
Organizations: IU International University of Applied Sciences Germany
Abstract
Large Language Models (LLMs) have shown strong capabilities across natural language tasks. But their ability to generate accurate written verbalizations of mathematical formulas has not been systematically evaluated. Such verbalization is important for text-to-speech systems supporting audio-based learning and visually impaired users. We evaluated five state-of-the-art LLMs across six scientific domains and constructed Read-Aloud Math, a balanced multi-domain corpus with LaTeX formulas, manually validated simple and extended transcriptions, multiple variants, textual context, domain labels, and formula complexity levels. Using multi-reference BLEU, GPT-5.2 achieved the highest score for simple transcriptions (75.9% without context, 64.9% with context), although without context it did not significantly outperform Grok 4.1 Fast or Claude Sonnet 4.5. Claude Sonnet 4.5 achieved the highest score for extended transcriptions without context (36.5%), and Grok 4.1 Fast with context (48.8%). For extended transcriptions, Statistics and Mathematics scored highest across the two context settings, while Physics scored lowest. Formula length was significantly negatively associated with BLEU for simple transcriptions without context, but not with context, whereas BLEU increased significantly with formula length for extended transcriptions in both settings. Grouping symbols were most frequently involved in transcription differences, while variable names, capitalization, and Greek letters were associated with lower BLEU scores. Overall, LLM-based formula verbalization is promising but remains sensitive to transcription type, textual context, and formula characteristics.
Figures & tables
| Domain | ØSimple vars. | ØExtended vars. | ØContext chars. |
| Mathematics | 3.1 | 4.9 | 9,065.7 |
| Statistics | 3.6 | 4.7 | 9,787.4 |
| Physics | 3.7 | 4.8 | 16,481.8 |
| Chemistry | 4.2 | 5.0 | 15,306.2 |
| Economics | 3.8 | 5.0 | 9,000.9 |
| Computer Science | 3.8 | 5.0 | 11,635.6 |
| Simple transcription | Extended transcription | |||||||||||||||||||||||
| Without textual context | With textual context | Without textual context | With textual context | |||||||||||||||||||||
| Domain | Gem | Deep | GPT | Clau | Gr | Avg. | Gem | Deep | GPT | Clau | Gr | Avg. | Gem | Deep | GPT | Clau | Gr | Avg. | Gem | Deep | GPT | Clau | Gr | Avg. |
| Mathematics | 59.9 | 63.0 | 68.7 | 67.4 | 76.3 | 67.0 | 43.9 | 60.2 | 57.5 | 55.3 | 60.6 | 55.5 | 30.6 | 23.4 | 20.3 | 38.2 | 39.4 | 30.4 | 36.7 | 41.4 | 45.1 | 50.1 | 54.4 | 45.6 |
| Statistics | 75.7 | 68.3 | 74.8 | 80.2 | 81.3 | 76.0 | 55.8 | 69.2 | 66.8 | 71.0 | 73.8 | 67.3 | 38.0 | 23.2 | 23.2 | 37.4 | 43.5 | 33.0 | 34.1 | 37.7 | 45.1 | 47.6 | 59.2 | 44.8 |
| Physics | 60.7 | 54.3 | 80.8 | 63.8 | 61.0 | 64.1 | 37.1 | 46.8 | 64.8 | 52.3 | 52.3 | 50.7 | 22.3 | 19.5 | 19.1 | 31.3 | 33.1 | 25.1 | 25.7 | 26.7 | 37.9 | 44.8 | 39.6 | 34.9 |
| Chemistry | 60.3 | 54.3 | 77.5 | 63.0 | 75.5 | 66.1 | 42.1 | 48.6 | 63.8 | 53.1 | 45.3 | 50.6 | 25.5 | 24.8 | 21.9 | 36.7 | 38.3 | 29.4 | 28.8 | 29.1 | 45.8 | 40.1 | 43.2 | 37.4 |
| Simple transcription | Extended transcription | |||||||||||||||||||||||
| Without textual context | With textual context | Without textual context | With textual context | |||||||||||||||||||||
| #symbols | Gem | Deep | GPT | Clau | Gr | Avg. | Gem | Deep | GPT | Clau | Gr | Avg. | Gem | Deep | GPT | Clau | Gr | Avg. | Gem | Deep | GPT | Clau | Gr | Avg. |
| 1-10 | 76.4 | 74.9 | 84.0 | 80.4 | 85.2 | 80.2 | 43.2 | 72.0 | 64.7 | 54.7 | 74.4 | 61.8 | 14.3 | 14.1 | 12.1 | 23.4 | 23.1 | 17.4 | 29.2 | 28.5 | 40.5 | 34.2 | 45.3 | 35.5 |
| 11-20 | 55.0 | 55.7 | 70.1 | 61.5 | 67.0 | 61.9 | 42.7 | 48.8 | 64.3 | 59.0 | 53.3 | 53.6 | 27.8 | 23.5 | 20.4 | 33.1 | 32.4 | 27.4 | 26.2 | 30.0 | 36.9 | 40.2 | 45.6 | 35.8 |
| 21-30 | 67.8 | 61.1 | 81.7 | 75.4 | 70.7 | 71.4 | 52.0 | 57.9 | 69.6 | 71.2 | 59.6 | 62.1 | 39.0 | 27.8 | 28.8 | 47.1 | 46.8 | 37.9 | 35.7 | 41.1 | 49.0 | 56.6 | 52.3 | 46.9 |
| 31-40 | 62.0 | 51.3 | 67.7 | 67.7 | 70.2 | 63.8 | 44.2 | 51.1 | 61.1 | 59.7 | 53.5 | 53.9 | 35.5 | 25.6 | 22.8 | 42.4 | 40.2 | 33.3 | 36.2 | 33.6 | 44.2 | 49.7 | 52.1 | 43.2 |
| Setting | Comparison | BLEU (%) | Sig. | |
| Simple transcription Without textual context | GPT–Gemini | 10.57 | ||
| GPT–DeepSeek | 15.15 | |||
| GPT–Claude | 4.62 | .099 | ||
| GPT–Grok | 2.60 | .339 | ||
| Simple transcription With textual context | GPT–Gemini | 19.40 | ||
| GPT–DeepSeek | 7.46 | .022 |
| Category | Feature | Count | % | Examples |
| Structural | Brackets/grouping | 113 | 94.2 | , , |
| Structural | Fractions/divisions | 49 | 40.8 | , |
| Structural | Superscripts/exponents | 50 | 41.7 | , |
| Structural | Subscripts/indices | 74 | 61.7 | , |
| Operator | Basic operators | 100 | 83.3 | , , , , |
| Operator | Integrals | 4 | 3.3 |
| Simple transcription | Extended transcription | ||||||
| Category | Feature | Cov. | Without text. context | With text. context | Without text. context | With text. context | |
| All | All formulas | 120 | 100.0 | 69.3 | 57.9 | 29.0 | 40.4 |
| Structural | Brackets/grouping | 113 | 94.2 | 67.7 | 57.5 | 29.8 | 40.3 |
| Structural | Fractions/divisions | 49 | 40.8 | 68.4 | 57.6 | 33.1 | 41.7 |
| Structural | Superscripts/exponents | 50 | 41.7 | 67.3 | 56.6 | 33.5 | 43.1 |
| Structural | Subscripts/indices | 74 | 61.7 | 66.0 | 55.5 | 31.5 | 42.2 |
| Simple transcription | Extended transcription | ||||
| Category | Feature | Without textual context | With textual context | Without textual context | With textual context |
| Structural | Brackets/grouping | 37.9 | 32.8 | 23.8 | 23.9 |
| Operator | Basic operators | 5.3 | 7.7 | 19.1 | 19.1 |
| Formatting | Punctuation/separators | 20.7 | 13.2 | 8.6 | 9.9 |
| Symbol | Latin letters | 7.5 | 7.2 | 11.9 | 13.4 |
| Structural | Fractions/divisions | 6.9 | 16.0 | 7.9 | 9.3 |
Language Model Generation Evaluation
Language model generation evaluation measures the quality, reliability, diversity, and task fit of outputs produced by language models.
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