--- license: other license_name: dgn-math-benchmark-research-use license_link: https://huggingface.co/datasets/ORCHORDS/dgn-math-problems pretty_name: DGN Math Benchmark tags: - mathematics - math - math-benchmark - benchmark - evaluation - eval - reasoning - text-to-math - math-reasoning - latex - algebra - trigonometry - geometry - inequalities - word-problems - worked-solutions - english - english-translation - textbook-derived - mixed task_categories: - text-generation - question-answering language: - en size_categories: - 10K Every printed answer in this dataset was checked with a real symbolic engine (SymPy). > Where the engine produced a concrete counterexample, the answer was either replaced by a > recomputed value that the engine then re-verified (`corrected`), or the row was kept with > the printed answer and flagged (`refuted`). Where the check was inconclusive the row is > flagged `suspected` and is **not** counted as a book error. Nothing was silently corrected, > and every row says in `answer_status` exactly how much its answer was checked. ## What this is An English-language mathematics benchmark for evaluating language models on problem solving. Problems are given in LaTeX, every item carries a worked solution, and the final answer is stored in the standard MATH convention (`\boxed{...}`), so the dataset drops straight into the usual math harnesses. ## Configs | config | rows | what it is | |---|---|---| | `full` | 12,554 | every problem, every column, including the unverified ones | | `qa` | 12,554 | the minimal MATH-style columns: problem, answer, metadata | | `verified` | 2,132 | **the scored split** - only rows whose answer the engine confirmed | | `core` | 3,617 | the scanned algebra book (11 chapters) | | `books` | 8,417 | the additional problem books | | `synthetic` | 520 | generated problems with computed, re-checked answers | Each config has a deterministic 85/15 train/test split (seed 42), stratified by source and chapter. ## Columns (`full`) | column | type | meaning | |---|---|---| | `id` | string | stable identifier, e.g. `algebra_core.1.122` | | `problem_id` | string | the problem number as printed in the book | | `source` | string | which collection the problem comes from | | `source_title` | string | human-readable name of that collection | | `chapter` | int | chapter / topic number | | `chapter_title` | string | chapter / topic name | | `group` | string | difficulty group printed in the book (A / B / C) | | `difficulty` | string | the difficulty glyph printed in the book (`□` easy, `■` hard) | | `problem` | string | the statement, LaTeX, inline `$...$` and display `$$...$$` | | `solution` | string | the worked solution, ending in the boxed answer | | `final_answer` | string | the gold answer as bare LaTeX (no `$`, no `\boxed`) | | `final_answer_boxed` | string | the same answer as `\boxed{...}` | | `answer_status` | string | `verified` / `corrected` / `refuted` / `suspected` / `disputed` / `unverifiable` / `no-gold` / `synthetic-verified` / `synthetic-unverified` | | `verification_note` | string | what the engine checked and what it found | | `page` | int | the printed page the problem is on | ### Answer status | status | count | meaning | |---|---|---| | `verified` | 1,924 | the engine substituted the answer back into the problem and it held | | `corrected` | 17 | the printed answer was refuted and replaced by a re-verified recomputation | | `refuted` | 60 | the engine found a concrete counterexample: the printed answer does not hold | | `suspected` | 114 | the recomputed answer differs from the printed one, but no counterexample was found - **not** counted as a book error | | `disputed` | 102 | a third read of the scanned page disagreed with the bulk transcription | | `unverifiable` | 3,969 | outside the reach of automatic checking | | `no-gold` | 5,848 | the source page carries no printed answer for this problem | | `synthetic-verified` | 191 | generated template; the printed statement was parsed, solved and compared with the printed answer | | `synthetic-unverified` | 329 | generated template; the answer is a derived quantity no engine could re-check - not scored | `verified` means the engine substituted the answer back into the problem and it held. `corrected` means the printed answer was refuted and replaced by a recomputed answer that the engine then re-verified. `refuted` means the engine produced a **concrete counterexample** - the printed root fails the equation, the printed tuple satisfies no equation of the system, or the printed interval misses a point that satisfies the inequality. `suspected` means the recomputed answer differs from the printed one but no counterexample was found; a difference in a radical's scope can look the same, so these are **not** counted as book errors. `disputed` means a third independent read of the scanned page disagreed with the bulk transcription. `unverifiable` means the printed answer exists but is outside the reach of automatic checking - word problems, open-ended proofs, and answers that are not a number or a set. `no-gold` means the source page carries no printed answer for that problem. Only `verified`, `corrected` and `synthetic-verified` rows are scored. ## Answer format The convention is the one used by the MATH dataset and by the standard evaluation harnesses: * inline mathematics is written `$...$`, display mathematics `$$...$$` * the gold answer is stored twice: `final_answer` holds the bare LaTeX (`\frac{3}{4}`), `final_answer_boxed` holds `\boxed{\frac{3}{4}}` * the `solution` column ends with the boxed answer, so a harness that extracts the last `\boxed{...}` from the solution gets the same string * decimals use a point, never a comma * there is no mixing of `\(...\)` and `$...$` delimiters ```python from datasets import load_dataset ds = load_dataset("ORCHORDS/dgn-math-problems", "verified", split="test") print(ds[0]["problem"]) print(ds[0]["final_answer_boxed"]) ``` ## Scoring The scoring model, the comparison tiers and a reporting template are documented in `BENCHMARKING.md` at the root of this repository, and implemented in `evaluate_benchmark.py`. In short, a prediction is compared with the gold answer at four strengths - exact string, numeric, symbolic and set equivalence - and the strictest tier that decides the item is the one that is reported, so a model cannot be rewarded for a merely numerically close answer. ```bash python evaluate_benchmark.py \ --dataset hf_dataset/data/verified/test-00000-of-00001.parquet \ --predictions predictions.jsonl \ --out report.json ``` ## How the data was produced 1. **Transcription.** The scanned books were transcribed page by page with a vision model into structured JSON, twice, with the two passes arbitrated by SymPy. The additional books were transcribed from their page images with the same pipeline. 2. **Verification.** Every answer was checked with SymPy: back-substitution into equations and systems, exact endpoint evaluation for inequalities, symbolic evaluation for limits and integrals, numeric identity testing for proofs. 3. **Adjudication.** Every flagged answer was re-read a third time, directly from the page image, and only corrections that the engine could confirm were written back. 4. **Generation.** The synthetic slice is produced by templates that compute the answer with SymPy and then re-check it; an item that fails the re-check is dropped. ## Provenance and rights The problems are drawn from Russian-language university entrance-exam mathematics problem books and problem collections that are publicly available on the postypashki.ru site. All rights in the underlying texts remain with their authors and publishers; this repository redistributes transformed, machine-checked English transcriptions for research and evaluation purposes and makes no claim of original authorship of the problem statements. `license` is therefore `other`. The `answer_status` and `verification_note` columns exist so that any user of this benchmark can see exactly how much trust each item's answer has earned.