ORCHORDS/dgn-math-problems

DGN Math Benchmark

12,557 question-answer pairs - 1,989 of them with an engine-verified answer and therefore usable as a scored benchmark. 3,620 problems come from scanned books, 8,417 from additional problem books, 520 are generated and machine-checked.

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	12,557	every problem, every column, including the unverified ones
qa	12,557	the minimal MATH-style columns: problem, answer, metadata
verified	1,989	the scored split - only rows whose answer the engine confirmed
core	3,620	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	1,781	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	66	the engine found a concrete counterexample: the printed answer does not hold
suspected	102	the recomputed answer differs from the printed one, but no counterexample was found - not counted as a book error
disputed	122	a third read of the scanned page disagreed with the bulk transcription
unverifiable	4,100	outside the reach of automatic checking
no-gold	5,849	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

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.

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.