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[ { "content": "5. 已知数列 $\\left\\{a_{n}\\right\\}$ 是一个等差数列,首项和公差都是正数,并且 $a_{2}, a_{5}, a_{9}$ 按顺序构成一个等比数列,那么使得 $a_{1}+a_{2}+\\cdots+a_{k}>100 a_{1}$ 成立的最小正整数 $k$ 是 $\\qquad$", "role": "user" }, { "content": "<think>\n好的,我需要解决这个关于等差数列的问题。让我再读一遍,确保我理解了所有部分。题目说:\n\n已知数列{a_n}是一个等差数列,首项和公差都是正数,并且a₂,a₅,a₉按顺...
openr1_math
math_competition
zh
[ { "content": "Ejemplo 3.7. ¿Está la función $z=$ $=f(x, y)=\\sqrt{4-x^{2}-y^{2}}$ acotada superiormente (inferiormente)?", "role": "user" }, { "content": "<think>\nBien, así que necesito averiguar si la función $ z = f(x, y) = \\sqrt{4 - x^2 - y^2} $ está acotada superior o inferiormente. Hmm, comie...
openr1_math
math_competition
es
[ { "content": "5. 一个三角形的周长为 $156 \\mathrm{~cm}$,其中边 $b$ 比边 $a$ 长 $1 \\mathrm{~cm}$,边 $c$ 比边 $b$ 长 $1 \\mathrm{~cm}$。求一个正方形的周长,该正方形的边长等于给定三角形边 $b$ 的长度。", "role": "user" }, { "content": "<think>\n好的,我现在有一个关于三角形和正方形的问题。让我再读一遍,确保我理解所有的细节。题目说:一个三角形的周长是156厘米,其中边b比边a长1厘米,边c比边b长1厘米。求一个正方形的周长,这个正方形的边长等于题目中给出的...
openr1_math
math_competition
zh
[ { "content": "例 2.8 在从 1 到 100 的整数中,有多少个整数能被这四个整数 2, $3, 5, 7$ 中的恰好两个整数整除?", "role": "user" }, { "content": "<think>\n好吧,我需要算出在1到100之间有多少个整数能被2、3、5或7这四个数中的恰好两个整数整除。嗯,首先我需要正确理解这个问题。\n\n首先,当题目说“被这四个整数中的恰好两个整除”时,意思是这个数应该能被其中两个整除,但不能被另外两个整除。例如,如果一个数能被2和3整除,那么它不应该能被5或7整除。明白了。因此,我需要计算能被这四个数中每一对整除的数的数量,但要减...
openr1_math
math_competition
zh
[ { "content": "244. Encuentre $\\int_{1}^{2}\\left(5 x^{4}+2 \\dot{x}-8\\right) d x$.", "role": "user" }, { "content": "<think>\nBien, así que necesito resolver la integral de 1 a 2 de $5x^4 + 2x - 8$ dx. Hmm, comencemos recordando algunas reglas básicas de integrales. Las integrales pueden descompon...
openr1_math
math_competition
es
[ { "content": "2. Пусть $A_{1}, A_{2}, A_{3}, A_{4}, A_{5}$ и $A_{6}$ — шесть точек на окружности в этом порядке, таких что $\\overline{A_{1} A_{2}}=\\overline{A_{2} A_{3}}$, $\\widetilde{A_{3} A_{4}}=\\widehat{A_{4} A_{5}}$ и $\\widehat{A_{5} A_{6}}=\\widehat{A_{6} A_{1}}$, где $\\widehat{A_{1} A_{2}}$ обознача...
openr1_math
math_competition
ru
[ { "content": "7. An ant starts from vertex $A$ of the rectangular prism $A B C D-A_{1} B_{1} C_{1} D_{1}$, and travels along the surface to reach vertex $C_{1}$. The shortest distance is 6. Then the maximum volume of the rectangular prism is $\\qquad$ .", "role": "user" }, { "content": "<think>\nOka...
openr1_math
math_competition
en
[ { "content": "对于三角形 $ABC$,作出了以下四个陈述,我们知道其中两个是正确的,两个是错误的。如果 $BC=1$,那么三角形 $ABC$ 的周长可能是多少?\n\nI. 三角形 $ABC$ 是一个直角三角形。- II. 在 $A$ 处的角是 $30^{\\circ}$。- III. $AB=2BC$。- IV. $AC=2BC$。", "role": "user" }, { "content": "<think>\n好吧,我们有一个三角形ABC,其中BC = 1。关于这个三角形有四个陈述,我们知道其中两个是正确的,两个是错误的。我们需要确定三角形ABC可能的周长。让我再列出这...
openr1_math
math_competition
zh
[ { "content": "2. (2 балла) Найдите минимальное значение выражения $x^{2}-6 x \\sin y-9 \\cos ^{2} y$.", "role": "user" }, { "content": "<think>\nХорошо, так у меня есть эта задача: найти минимальное значение выражения $ x^{2} - 6x \\sin y - 9 \\cos^{2} y $. Хм, ладно. Попробую разобраться пошагово. ...
openr1_math
math_competition
ru
[{"content":"(2) Данная функция $f(x)$, определённая на $\\mathbf{R}$, у(...TRUNCATED)
openr1_math
math_competition
ru
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SFT-Math-Multilingual-56k

Long chain-of-thought math solutions, each written end to end in one of six languages

arXiv: 2609.37104 traces: 56,307 languages: 6 license: Apache 2.0

Bar chart per language of the share of responses reasoning in the requested language, before and after fine-tuning: English 100% to 100%, Chinese 100% to 100%, Spanish 0% to 100%, French 0% to 99%, Arabic 0% to 100%, Russian 35% to 100%

Share of responses whose reasoning is in the requested language, Qwen3-8B before and after fine-tuning on this dataset

Released reasoning models often think in English whatever language the user writes in. This dataset is multilingual supervision for the reasoning itself: in every example the problem, the full <think> trace and the final solution share one language.

  • Teach a model to reason in the user's language. Fine-tuning Qwen3-8B on it moves target-language reasoning from 26.9% to 99.7% across Chinese, Spanish, French, Arabic and Russian.
  • Warm-start multilingual RL. It is the SFT stage before RL on DAPO-Math-Multilingual-6Lang.
  • Study multilingual reasoning. One source distribution, six languages, every problem in exactly one of them.

At a glance

Examples 56,307 train · 240 test (held-out loss, 40 per language)
Languages English 9,760 · Chinese 9,294 · Spanish 9,451 · French 9,357 · Arabic 9,306 · Russian 9,139
Length median 12,305 characters per solution, reasoning included
Source OpenR1-Math-220k, translated by Qwen3-14B and filtered
Trained on it Qwen3-8B-SFT-Math-Multilingual
Sibling SFT-Math-Multilingual-43k, the 43K set used at 4B

Quick start

from datasets import load_dataset

ds = load_dataset("96kevinli29/SFT-Math-Multilingual-56k", split="train")
ex = ds[0]
print(ex["language"])                 # one of en, zh, es, fr, ar, ru
print(ex["messages"][0]["content"])   # the problem
print(ex["messages"][1]["content"])   # <think> … </think> + solution ending in \boxed{…}

Fields: messages (user problem, assistant solution), language, data_source, category.

How it was built
  1. Source. English long chain-of-thought traces from OpenR1-Math-220k.
  2. Assign. Each trace gets one of the six languages in round-robin order, so every problem appears in exactly one language.
  3. Translate. English traces stay as they are. The rest are translated chunk by chunk by a locally served Qwen3-14B; formulas and figures are detached first and reattached afterwards, and <think> tags are kept.
  4. Filter. A trace is dropped if a chunk was truncated or the \boxed answer changed, then by seven gates: one <think> block, a recoverable boxed answer, balanced $ and braces, a bounded length ratio, no repetition, and target-language fidelity.
Quality audit
Coherence (1–5) Target-language fidelity (1–5) Reaches the boxed answer Math preserved No major English residue
Chinese 4.90 4.62 99.6% 100.0% 96.0%
Spanish 4.78 4.40 99.6% 100.0% 94.0%
French 4.81 4.32 99.6% 100.0% 95.6%
Arabic 4.47 3.54 99.6% 99.6% 84.0%
Russian 4.76 4.40 100.0% 98.8% 94.4%
English, untranslated 4.88 n/a 100.0% 100.0% n/a

250 sampled traces per language from the 43K corpus, scored by an independent judge.

Limitations

  • Machine-translated. A trace can contain a stray word in English or another language; Arabic is the weakest language in the audit.
  • Answers are not verified. Translation only checks that the boxed answer is unchanged from the source.
  • Fine-tuning side effects. Models trained on it lose some accuracy and loop on about a fifth of non-English prompts until an RL stage removes the looping; see Qwen3-8B-SFT-Math-Multilingual.

Citation

@article{li2026posttraining,
  title   = {What Does Post-Training Change in Multilingual Reasoning?},
  author  = {Li, Hongyang and Li, Xiao and Wu, Caesar and Danoy, Gr{\'e}goire and Bouvry, Pascal},
  journal = {arXiv preprint arXiv:2609.37104},
  year    = {2026}
}

@misc{sft-math-multilingual-56k-2026,
  title        = {{SFT-Math-Multilingual-56k}: long chain-of-thought math solutions in six languages},
  author       = {Li, Hongyang and Li, Xiao and Wu, Caesar and Danoy, Gr{\'e}goire and Bouvry, Pascal and {Sea-Fill Community}},
  year         = {2026},
  publisher    = {Hugging Face},
  howpublished = {\url{https://huggingface.co/datasets/96kevinli29/SFT-Math-Multilingual-56k}},
  note         = {Maintained by Sea-Fill Community.}
}

Built and released by the authors together with the Sea-Fill Community, which maintains this release.

Please also cite OpenR1-Math-220k, the source of the English traces.

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