DeepMath-103K: A Large-Scale, Challenging, Decontaminated, and Verifiable Mathematical Dataset for Advancing Reasoning
Paper • 2504.11456 • Published • 12
Datasets:
Tasks:
Text Generation
Modalities:
Text
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parquet
Languages:
English
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10K - 100K
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question stringlengths 24 2.83k | final_answer stringlengths 1 136 | difficulty float64 4 10 | topic stringclasses 80
values | r1_solution_1 stringlengths 2.77k 86.6k | r1_solution_2 stringlengths 2.64k 85.4k | r1_solution_3 stringlengths 2.53k 100k |
|---|---|---|---|---|---|---|
Verify that the distance from the function \( f = x \) to the set \( Y = \{ f \in C[0,1] : \int_0^1 f = 0 \} \) is 0.5, given that \( Y \) is a closed subset of \( X = \{ f \in C[0,1] : f(0) = 0 \} \). | 0.5 | 6.5 | Mathematics -> Calculus -> Integral Calculus -> Applications of Integrals | Okay, so I need to verify that the distance from the function f(x) = x to the set Y, which consists of all continuous functions on [0,1] that integrate to zero, is 0.5. Y is a closed subset of X, where X is the set of continuous functions on [0,1] with f(0) = 0. Alright, let's break this down step by step.
First, I kn... | Okay, so I need to verify that the distance from the function f(x) = x to the set Y, which consists of all continuous functions on [0,1] that integrate to zero, is 0.5. And Y is a closed subset of X, where X is the set of continuous functions on [0,1] that vanish at 0. Alright, let me start by understanding the problem... | Alright, let's see. The problem is to verify that the distance from the function f(x) = x to the set Y, which consists of all continuous functions on [0,1] with integral zero, is 0.5. Y is a closed subset of X, where X is the set of continuous functions on [0,1] that vanish at 0. The distance is measured in the supremu... |
Let $T$ be a continuous linear operator. Suppose $(u_n)$ is a sequence that converges weakly to $u$, denoted as $(u_n) \rightharpoonup u$. Additionally, assume $T(u_n) \rightharpoonup T(u)$ and there exists a subsequence $(u_{n_k})$ such that $T(u_{n_k}) \rightarrow T(u)$. Does it follow that $T(u_n) \rightarrow T(u)$? | No | 8.5 | Mathematics -> Algebra -> Linear Algebra -> Linear Transformations | Okay, let me try to figure this out. So the question is about whether a continuous linear operator T preserves the convergence of a weakly convergent sequence, given some additional conditions. Let me recall the definitions and see how they fit together.
First, we have a sequence (u_n) that converges weakly to u, deno... | Okay, let's see. The problem is about whether a continuous linear operator T preserves strong convergence under certain conditions. We have a sequence u_n that converges weakly to u, and T(u_n) also converges weakly to T(u). Additionally, there's a subsequence u_{n_k} such that T(u_{n_k}) converges strongly to T(u). Th... | Okay, let's see. I need to figure out whether, under these conditions, the whole sequence \( T(u_n) \) converges strongly to \( T(u) \). The problem states that \( T \) is a continuous linear operator, \( u_n \) converges weakly to \( u \), \( T(u_n) \) converges weakly to \( T(u) \), and there's a subsequence \( T(u_{... |
"Let $a, b, c, d$ be a permutation of the numbers $1, 9, 8, 4$. Define $n = (10a + b)^{10c + d}$. Ca(...TRUNCATED) | \dfrac{5}{6} | 7 | Mathematics -> Algebra -> Intermediate Algebra -> Exponential Functions | "Alright, so I need to solve this problem where we have a permutation of the numbers 1, 9, 8, 4 assi(...TRUNCATED) | "Okay, so I have this problem here where I need to calculate the probability that 1984! is divisible(...TRUNCATED) | "Okay, so I need to find the probability that 1984! is divisible by n, where n is defined as (10a + (...TRUNCATED) |
"Let \\( A \\) be a C* algebra of operators on a Hilbert space \\( H \\). Determine if there exists (...TRUNCATED) | Yes | 9 | Mathematics -> Differential Equations -> Partial Differential Equations (PDEs) | "Okay, so I need to figure out if there's a vector x in a Hilbert space H such that the set Ax is de(...TRUNCATED) | "Okay, so I have this problem about C* algebras and whether there's a vector x in a Hilbert space H (...TRUNCATED) | "Okay, so I need to figure out if there's a vector x in a Hilbert space H such that the set Ax, wher(...TRUNCATED) |
"Determine the limit of \\( \\frac{\\pi(x)}{x} \\) as \\( x \\to \\infty \\), where \\( \\pi(x) \\) (...TRUNCATED) | 0 | 8 | Mathematics -> Number Theory -> Prime Numbers | "Okay, so I need to figure out the limit of π(x)/x as x approaches infinity. π(x) is the prime cou(...TRUNCATED) | "Okay, so I need to figure out the limit of π(x) divided by x as x approaches infinity. Hmm, π(x) (...TRUNCATED) | "Okay, so I need to find the limit of π(x)/x as x approaches infinity, where π(x) is the prime cou(...TRUNCATED) |
"Consider a sequence $(r_n)$ resulting from infinite coin flips, where $R_n=1$ if $r_n$ is a head an(...TRUNCATED) | 1 | 8 | Mathematics -> Applied Mathematics -> Statistics -> Probability -> Other | "Okay, so I need to figure out whether the probability that the sum of R_n/n converges is equal to 1(...TRUNCATED) | "Okay, so I have this problem here where we're considering a sequence of coin flips, right? Each fli(...TRUNCATED) | "Alright, so I need to figure out whether the probability that the series ∑(Rₙ/n) converges is e(...TRUNCATED) |
"Consider a locally path connected space $X$. If every open subset $U \\subseteq X$ is semi-locally (...TRUNCATED) | Yes | 8.5 | Mathematics -> Other | "Okay, so I need to figure out if a locally path-connected space X, where every open subset U is sem(...TRUNCATED) | "Okay, so I have this problem here: if X is a locally path connected space, and every open subset U (...TRUNCATED) | "Okay, so I need to figure out whether a locally path-connected space X, where every open subset U i(...TRUNCATED) |
"Let $E \\subset \\mathbb{C}$ be a set such that for any sequence of distinct elements $(e_n)_{n \\i(...TRUNCATED) | Yes | 8 | Mathematics -> Algebra -> Intermediate Algebra -> Complex Numbers | "Okay, let me try to figure out this problem. So, the question is: If a set E in the complex numbers(...TRUNCATED) | "Okay, so I have this problem here: Let E be a subset of the complex numbers such that any sequence (...TRUNCATED) | "Okay, so the problem is asking if a set E in the complex numbers must be countable if every sequenc(...TRUNCATED) |
"Let $S$ be an algebraic smooth surface over $\\\\mathbb{C}\\\\). Suppose there is a fibration $p: S(...TRUNCATED) | Yes | 9 | Mathematics -> Algebra -> Abstract Algebra -> Field Theory | "Okay, let me try to work through this problem. So, we have a smooth algebraic surface S over the co(...TRUNCATED) | "Okay, so I need to figure out whether each m-canonical map φ_{mK} contracts a fiber f of the fibra(...TRUNCATED) | "Okay, let's try to tackle this problem step by step. So, we have a smooth algebraic surface S over (...TRUNCATED) |
"Is the space \\(X = \\prod_{t \\in \\mathbb{Z}} \\mathbb{R}\\), with the product topology \\(T\\), (...TRUNCATED) | No | 8.5 | Mathematics -> Geometry -> Differential Geometry -> Other | "Okay, so I need to figure out if the space \\( X = \\prod_{t \\in \\mathbb{Z}} \\mathbb{R} \\), equ(...TRUNCATED) | "Okay, so I need to figure out if the space \\( X = \\prod_{t \\in \\mathbb{Z}} \\mathbb{R} \\), equ(...TRUNCATED) | "Okay, so I need to figure out if the space \\( X = \\prod_{t \\in \\mathbb{Z}} \\mathbb{R} \\), equ(...TRUNCATED) |
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DeepMath Hard Diverse 15k — A
15,000 questions, one of two disjoint, distribution-matched halves of a hard and diverse 30,000-question selection from DeepMath-103K.
Companion half: storagestuffnobody/DeepMath-Hard-Diverse-15k-B. Together the two repositories contain all 30,000 selected questions exactly once.
Contents
The train split preserves all seven original fields: question, final_answer, difficulty, topic, r1_solution_1, r1_solution_2, and r1_solution_3. No questions, answers or solutions were rewritten. provenance/rows.jsonl maps each row to its original DeepMath source row and embedding cluster.
This half has mean supplied difficulty 7.6198, median 8.0, and 87.10% scoring at least 7.
Selection and balancing
The parent selection used question-only EmbeddingGemma-300m embeddings and 128 full-data spherical k-means clusters. It retained 30,000 unique questions while requiring every supplied topic and cluster to retain at least half its original percentage. Difficulty was prioritized, with constrained farthest-first selection to improve within-cluster diversity. The parent mean difficulty is 7.6198, compared with 6.0571 in the full source.
For these halves, nearby embeddings were paired within cluster/topic/difficulty buckets, with leftovers paired within clusters. One member of each pair goes to each half. Every embedding cluster and joint bucket differs between halves by at most one question. Topic count differences are at most 2, and difficulty-bin count differences at most 1. Pair orientations also reduce embedding-centroid differences. Integer rounding allows small deviations from the parent's proportions.
Both halves have exactly 15,000 rows, are disjoint, and preserve all parent records unchanged. Public hashes, mappings and balance statistics are under provenance/. Difficulty labels and mathematical correctness were not independently re-evaluated. Embedding matching is approximate and also reflects wording and format.
Source and attribution
Source: zwhe99/DeepMath-103K, revision 5cf055d1fe3d7a2eb19719ac020211469736ae44. The upstream dataset card declares the MIT license; that declaration is retained here. Credit: Zhiwei He and collaborators, DeepMath-103K (2025). Original questions, labels, final answers and R1 solutions are preserved.
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