# Mathematics

Goedel-Prover is an open-source large language model specializing in automated theorem proving. It significantly enhances the efficiency of automated mathematical problem solving by translating natural language mathematical questions into formal languages (such as Lean 4) and generating formal proofs. The model achieved a success rate of 57.6% on the miniF2F benchmark, surpassing other open-source models. Its key advantages include high performance, open-source extensibility, and a deep understanding of mathematical problems. Goedel-Prover aims to advance automated theorem proving technologies and provide powerful tool support for mathematical research and education.

OpenThinker-32B is an open-source reasoning model developed by the Open Thoughts team. It achieves robust reasoning capabilities by expanding data scale, validating reasoning paths, and scaling model size. The model excels in reasoning benchmarks for mathematics, code, and science, surpassing existing open data reasoning models. Its key advantages include open-source data, high performance, and scalability. The model is fine-tuned based on Qwen2.5-32B-Instruct and trained on a large-scale dataset, aiming to provide researchers and developers with a powerful reasoning tool.

Confucius-o1-14B is an inference model developed by the NetEase Youdao team, optimized based on Qwen2.5-14B-Instruct. It employs a two-stage learning strategy that automatically generates reasoning chains and summarizes step-by-step problem-solving processes. This model is aimed at the education field, particularly suitable for K12 math problems, helping users quickly acquire correct problem-solving strategies and answers. Its lightweight nature allows it to be deployed on a single GPU without quantization, reducing the barrier to use. Its reasoning capabilities have demonstrated outstanding performance in internal evaluations, providing robust technical support for AI applications in education.

The OKMath AI Math Solver is an advanced AI-driven tool designed to deliver precise solutions to math problems for students. This product harnesses powerful AI technology, combined with a vast database of over 10 million math practice problems, utilizing self-trained AI models and multiple cross-validation algorithms to ensure accurate answers for each query. Key advantages include high accuracy, detailed step-by-step explanations, and a wide range of covered math problems. OKMath is suitable not only for student learning and homework assistance but also for teachers' instructional support and parents' tutoring efforts. Its goal is to provide a comprehensive math learning tool for learners at all levels, helping them better understand and master math concepts.

PRIME-RL/Eurus-2-7B-PRIME is a language model with 7 billion parameters, trained on the PRIME methodology with the aim of improving reasoning abilities via online reinforcement learning. Starting from the Eurus-2-7B-SFT model, this model was fine-tuned using the Eurus-2-RL-Data dataset. The PRIME methodology employs an implicit reward system, fostering an emphasis on the reasoning process during output generation, rather than focusing solely on the results. This model has demonstrated exceptional performance in various reasoning benchmark tests, achieving an average improvement of 16.7% over its SFT version. Key advantages include enhanced reasoning capabilities, lower data and resource requirements, and outstanding performance in mathematical and programming tasks. It is well-suited for scenarios requiring complex reasoning abilities, such as programming and mathematical problem solving.

Teach Me Anything is an online learning platform focused on delivering diverse knowledge videos. The platform uses engaging video formats to help users learn about various fields, including science, mathematics, and natural phenomena. Its main strengths lie in the diversity and engaging nature of the content, which can stimulate users' interest in learning. Background information reveals that the platform aims to make complex knowledge easier to understand and remember through visual means. Currently, the platform is free, catering to all users looking to expand their knowledge base.

YuLan-Mini is a lightweight language model developed by the AI Box team at Renmin University of China. With 240 million parameters, it achieves performance comparable to industry-leading models trained on larger datasets, despite using only 1.08 terabytes of pre-trained data. The model excels in mathematics and coding domains, and to facilitate reproducibility, the team will open-source relevant pre-training resources.

Math Tutor on Groq is an AI math tutoring project powered by Groq, utilizing the xRx framework 8090, Whisper, the Llama 3.3 70b model, and Elevenlabs TTS technology to engage in real-time dialogue with students about math questions. Groq's high-speed processing allows for near-instantaneous responses to complex problems, providing a seamless learning experience. This project can also solve algebra and calculus problems using an internal math engine, delivering solutions as context to the AI for enhanced response accuracy.

The RLVR-GSM-MATH-IF-Mixed-Constraints dataset focuses on math problems, containing various types of math questions and corresponding answers for training and validating reinforcement learning models. Its significance lies in helping develop smarter educational tools that enhance students' abilities to solve math problems. The product background information indicates that this dataset was released by Allenai on the Hugging Face platform, containing the GSM8k and MATH subsets, as well as IF Prompts with verifiable constraints, licensed under MIT License and ODC-BY license.

QwQ (Qwen with Questions) is an experimental research model developed by the Qwen team, aimed at enhancing artificial intelligence's reasoning abilities. It embodies a philosophical spirit, approaching every question with genuine curiosity and skepticism, seeking deeper truths through self-questioning and reflection. QwQ excels in mathematics and programming, particularly in addressing complex problems. Although it is still learning and evolving, it has already demonstrated significant potential for deep reasoning in technological domains.

AI Homework Helper is an online tool designed to assist students in solving their homework problems. Users can upload images or PDFs of their assignments, and the AI instantly provides accurate solutions and step-by-step explanations. Whether it's math, science, or other subjects, this tool helps students learn and solve problems more effectively.

FrontierMath is a mathematical benchmarking platform designed to test the limits of artificial intelligence in solving complex mathematical problems. Created by over 60 mathematicians, it spans the full spectrum of modern mathematics, from algebraic geometry to Zermelo-Fraenkel set theory. Each problem on FrontierMath requires expert mathematicians to invest hours of work, and even state-of-the-art AI systems like GPT-4 and Gemini can solve less than 2% of the problems. This platform provides a genuine assessment environment, with all problems being novel and unpublished, eliminating the common data contamination issues found in existing benchmarks.

Photomath is an educational app that scans math problems to provide detailed solution steps and explanations, aiding users in comprehending mathematical concepts. The app supports math learning across all educational stages, from elementary to university, covering subjects like algebra, geometry, trigonometry, statistics, and calculus. Photomath not only helps users solve homework problems but also offers learning resources and articles to alleviate math anxiety and enhance learning efficiency.

Yuan2.0-M32-hf-int8 is a mixture of experts (MoE) language model featuring 32 experts, of which 2 are active. By adopting a new routing network—the attention router—it enhances the efficiency of expert selection, resulting in an accuracy improvement of 3.8% compared to models using traditional routing networks. Yuan2.0-M32 was trained from scratch on 200 billion tokens, with its training computation demand being just 9.25% of that required by a dense model of equivalent parameter size. This model is competitive in programming, mathematics, and various specialized fields while utilizing only 3.7 billion active parameters, which is a small portion of a total of 4 billion parameters. The forward computation per token requires only 7.4 GFLOPS, just 1/19th of what Llama3-70B demands. Yuan2.0-M32 outperformed Llama3-70B in the MATH and ARC-Challenge benchmark tests, achieving accuracy rates of 55.9% and 95.8%, respectively.

Yuan2.0-M32 is a mixture of experts (MoE) language model featuring 32 experts, of which 2 are active. It introduces a new routing network—an attention router—to improve the efficiency of expert selection, resulting in a 3.8% accuracy boost over models using traditional routing networks. Yuan2.0-M32 was trained from scratch using 200 billion tokens, with a computational cost only 9.25% of that required by similarly parameterized dense models. It demonstrates competitive performance in coding, mathematics, and various professional fields, with only 370 million active parameters out of a total of 4 billion, and a forward computation requirement of just 7.4 GFLOPS per token, which is only 1/19th of Llama3-70B's requirements. In MATH and ARC-Challenge benchmark tests, Yuan2.0-M32 outperformed Llama3-70B, achieving accuracies of 55.9% and 95.8%, respectively.

Yuan2.0-M32 is a mixed expert (MoE) language model featuring 32 experts, out of which 2 are active. It introduces a novel routing network—attention routing—to improve expert selection efficiency, achieving a 3.8% increase in accuracy. The model is trained from scratch using 2000B tokens, with a training computational load only 9.25% of that required by a dense model with the same parameter scale. It demonstrates competitive performance in coding, mathematics, and various specialized fields, utilizing just 3.7B active parameters, with a per-token forward computation requirement of only 7.4 GFLOPS, which is 1/19 of what Llama3-70B demands. It surpasses Llama3-70B in MATH and ARC-Challenge benchmark tests, achieving accuracy rates of 55.9% and 95.8%, respectively.

MathGPT Pro is an advanced AI math solver designed to provide fast and accurate solutions to math problems for millions of students worldwide. It can handle a broad range of mathematical topics, including algebra, equations, derivatives, and integrals, thus enhancing students' learning efficiency and performance. Its underlying technology combines the latest AI algorithms to ensure both efficiency and accuracy, making it suitable for anyone needing math assistance. MathGPT Pro features an intuitive user interface that supports image recognition and voice input, enabling users to perform calculations anytime, anywhere.

Numina Math 7B is an AI math model developed by the Numina organization, focusing on solving high-difficulty math problems, particularly in the field of math competitions. The model ranked first in the AI Math Olympiad, demonstrating its strong ability to solve complex math problems. Numina is a non-profit organization dedicated to promoting the development of humans and artificial intelligence in the field of mathematics.

This GitHub repository contains training and inference code to replicate our winning solution in the AI Mathematics Olympic (AIMO) Progress Prize 1. Our solution consists of four main parts: a recipe for fine-tuning DeepSeekMath-Base 7B for use in solving math problems using Tool Integrated Reasoning (TIR); two high-quality datasets of about 10 million math questions and solutions; an algorithm for generating solution candidates with coding execution feedback (SC-TIR); and four carefully selected validation sets from AMC, AIME, and MATH to guide model selection and avoid overfitting the public leaderboard.

NuminaMath is a database and model designed for training the state-of-the-art math language models (SOTA math LLMs). It comprises 860k+ pairs of math competition problems and solutions, where each solution is templatized using chain of thought (CoT) reasoning. In addition, there are 70k+ math competition problems, whose solutions are generated by GPT-4 through tool integrated reasoning (TIR). NuminaMath provides a valuable resource for educators and students by offering high-quality math problems and solutions, which helps them improve their mathematical thinking and problem-solving abilities.

AI Math Solver is an online tool powered by the math AI and math GPT model (such as GPT-4), designed to provide a wide range of math problem solutions. It leverages advanced AI technology to provide comprehensive step-by-step solutions for students and teachers, enhancing understanding of mathematical concepts and problem-solving abilities. The product background is the need for efficient problem-solving tools in mathematical learning, positioned to offer high-quality educational support for free.

AI Math Notes is an open-source interactive graphing application that allows users to draw mathematical equations on a canvas. The application leverages multimodal large language models (LLMs) to calculate and display the results. Developed using Python, it utilizes the Tkinter library for creating the graphical user interface and PIL for image processing. It was inspired by Apple's 'Math Notes' showcased at the 2024 Worldwide Developers Conference (WWDC).

Qwen2 is a series of pre-trained and instruction-tuned models that support up to 27 languages, including English and Chinese. These models have excelled in multiple benchmark tests, particularly demonstrating significant improvements in coding and mathematical capabilities. Qwen2 supports a context length of up to 128K tokens, making it suitable for handling long-text tasks. Moreover, the Qwen2-72B-Instruct model exhibits comparable safety performance to GPT-4, significantly outperforming the Mistral-8x22B model.

Mistral-22b-v0.2 is a powerful model that demonstrates excellent mathematical and programming abilities. Compared to V1, the V2 model has significantly improved coherence and multi-turn dialogue capabilities. This model has been re-adjusted to remove censorship and can answer any question. The training data primarily includes multi-turn dialogues, with a particular emphasis on programming content. Additionally, the model has agent capabilities and can execute real-world tasks. Training utilized a 32k context length. When using the model, please adhere to the GUANACO prompt format.

Grok-1.5 is an advanced large language model with exceptional capabilities in long text comprehension and reasoning. It can handle long contexts up to 128,000 tokens, far exceeding the capabilities of previous models. Grok-1.5 excels in tasks such as mathematics and coding, achieving high scores on numerous established benchmarks. Built upon a robust distributed training framework, the model ensures efficient and reliable training processes. Grok-1.5 is designed to empower users with powerful language understanding and generation capabilities, facilitating various complex language tasks.

Yi-9B is one of the next-generation open-source bilingual large language models developed by 01.AI. Trained on a dataset of 3T, it demonstrates strong capabilities in language understanding, common sense reasoning, and reading comprehension. It excels in code generation, mathematics problem solving, common sense reasoning, and reading comprehension, ranking among the best open-source models of its size. It is suitable for personal, academic, and commercial use.

AutoMathText is a comprehensive and meticulously planned dataset containing approximately 200GB of mathematical texts. Each item in the dataset is autonomously selected and rated by the state-of-the-art open-source language model Qwen, ensuring high standards of relevance and quality. This dataset is particularly suitable for fostering advanced research in the intersection of mathematics and artificial intelligence, as an educational tool for learning and teaching complex mathematical concepts, and as a foundation for developing and training AI models dedicated to processing and understanding mathematical content.

AI Math is a free online AI-powered math solution that helps you overcome math difficulties and provides 99% accurate solutions. It can handle various math problems, including arithmetic, algebra, geometry, trigonometry, calculus, combinatorics, and statistics probability. AI Math not only provides answers but also guides you with step-by-step explanations to help you understand the solving process. Accessible anytime, anywhere, AI Math is a powerful support system for both educators and students.

Internlm2 Math 7b is a mathematics model based on the Hugging Face platform, primarily used for solving math problems. It can handle a variety of math problems, including algebra, geometry, and probability statistics. Using this model can provide accurate mathematical calculations and answers, helping users learn and understand mathematical knowledge. Internlm2 Math 7b offers a simple and easy-to-use API interface, which can be easily integrated into other applications. This model is based on deep learning technology and has high accuracy and reliability. It is suitable for educational scenarios such as mathematics auxiliary learning and homework help.

AlphaGeometry is a cutting-edge AI system for solving geometry problems that surpasses existing technologies. It combines the predictive capability of neural language models with the reasoning power of a rule-driven inference engine to tackle complex geometrical challenges. Utilizing a neuro-symbolic approach, AlphaGeometry consists of a neural language model and a symbolic reasoning engine that work together to discover proofs for intricate geometrical theorems. By generating one billion random geometrical object graphs and deriving all relationships from them, AlphaGeometry ultimately yields 100 million unique training samples, 9 million of which include additional constructions. AlphaGeometry's language model can provide insightful suggestions when faced with geometry problems from international mathematics competitions. This system marks the world's first AI model capable of reaching the bronze medal level at the International Math Olympiad.