ORCHORDS/dgn-math-problems

DGN Math Benchmark

12,592 mathematics problems, built and machine-verified by us. 2,755 of them carry an answer that a symbolic engine confirmed, and those form the scored split.

Every answer in this dataset was put through a real computational 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 original answer and flagged (refuted). Where the check was inconclusive the row is flagged suspected and is not counted as an error in the source. 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, 5,105 of the 12,592 items carry 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	12,592	every problem, every column, including the unverified ones
qa	12,592	the minimal MATH-style columns: problem, answer, metadata
verified	2,755	the scored split - only rows whose answer the engine confirmed
core	3,617	the main collection: algebra, trigonometry, progressions, logarithms, inequalities
extended	8,455	the extended collections: entrance algebra, the full syllabus, parameters, trigonometry, plane geometry
exercises	520	machine-made exercises whose answers are computed and re-checked

Each config has a deterministic 85/15 train/test split (seed 42), stratified by collection and chapter. A problem that is printed more than once - in two chapters of one collection or in two collections - keeps all of its copies in the same half, so no problem of the test half was in the train half.

Columns (full)

column	type	meaning
id	string	stable identifier, e.g. dgn.core.1.122
problem_id	string	the number of the problem in its collection
collection	string	which collection the problem comes from (core, algebra, syllabus, ...)
source	string	the benchmark this problem belongs to (dgn_math)
source_title	string	the title of the benchmark
chapter	int	chapter / topic number
chapter_title	string	chapter / topic name
group	string	group of the problem inside its chapter, as printed in the source (A, B, C); empty when the source names no group
difficulty	string	difficulty mark of the problem (□ easy, ■ hard); empty when the source prints no difficulty mark
problem	string	the statement, LaTeX, inline $...$ and display $$...$$
solution	string	the worked solution; where the row carries an answer it ends 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
verification_note	string	what the engine checked and what it found
page	int	the page of the source material the problem comes from

Answer status

status	count	meaning
verified	2,705	the engine substituted the answer back into the problem and it held
corrected	50	the original answer was refuted and replaced by a re-verified recomputation
refuted	68	the engine found a concrete counterexample: the answer does not hold
suspected	271	the engine found a difference, but it is not settled whether the source or the transcription is at fault - not counted as an error in the source
disputed	85	a third read of the source disagreed with the bulk transcription
unverifiable	4,228	outside the reach of automatic checking
no-gold	5,185	the source carries no answer for this problem

verified means the engine substituted the answer back into the problem and it held. corrected means the original answer was refuted and replaced by a recomputed answer that the engine then re-verified. refuted means the engine produced a concrete counterexample - the root fails the equation, the tuple satisfies no equation of the system, or the interval misses a point that satisfies the inequality. suspected means the engine found a difference but it is not settled whether the source or the transcription is at fault - a difference in a radical's scope can look the same, and a page that has not been read again cannot decide it; these are not counted as errors in the source. disputed means a third independent read of the source disagreed with the bulk transcription. unverifiable means an answer exists but is outside the reach of automatic checking - word problems, open-ended proofs, and answers that are neither a number nor a set. no-gold means the source carries no answer for that problem.

Only verified and corrected 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 of every row that carries an answer 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. Collection. The problems were collected, translated into English and written out as structured JSON with LaTeX, twice, with the two passes arbitrated by SymPy.
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 source, and only corrections that the engine could confirm were written back.
4. Exercises. The machine-made exercises are produced by templates that compute the answer with SymPy and then re-check it; an item that fails the re-check is dropped. A second, independent verifier per topic re-derives every answer from the published statement without using the generator, and a negative test makes sure that a perturbed answer is rejected.

What was left out, and what is still missing

An item is only published when it is an exercise with a statement that can be read off the page. 358 printed items were left out because they are not exercises at all - a figure and its caption, a section heading, a table of contents, a page of exposition, or the answer key of a chapter, whose answers are published with the exercise they belong to. 3 further items were left out because their statement could not be recovered with certainty.

Four limitations are worth knowing about:

• a statement that runs over the foot of a page was recovered by reading the page again; where the missing words could not be read with certainty, the item was left out rather than published with a guessed question;
• a page of the source can print two exam variants side by side, and the two blocks use the same numbers. Where that happened, one of the two blocks was kept and the other left out, so around sixty printed exercises are not in this release;
• a printed exam variant carries the statements of all of its tasks in one place and their answers in one numbered key. Every such variant was split into its own tasks, so that each task carries its own answer. Where the key could not be read off the page with certainty, the tasks are published without an answer rather than with the answer of a neighbouring task;
• two collections contain a handful of items whose statement stands in two collections. They are kept in the same half of the split, so no problem of the test half was in the train half.

Origin and rights

The English statements, the structured extraction, the answer verification and this curation are ours. The statements themselves are third-party Russian-language university entrance mathematics material published on postypashki.ru; rights in those texts remain with their authors and publishers, so license is other and this release is for research and evaluation use.

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.