【芦叶记】芳心未冷，且伴双卿 - [ 似水流年 ] - 五月吧论坛

以下是引用风住尘香在2024/5/29 10:34:19的发言：

好像狗狗也是静静

狗狗我送给小号妃了……猫猫狐狐都是我……

图片点击可在新窗口打开查看

以下是引用獾獾我呀在2024/5/29 10:37:41的发言：

图片点击可在新窗口打开查看打哭她，把猫狗狐3个品类都占了，后面想名字太难了。

说本喵坏话，被本喵抓到了……还有虎啊狼啊鱼啊花啊草啊不要太多啦~

图片点击可在新窗口打开查看

打赏啦！打赏啦！打赏此楼 278 楼作者獾獾我呀金币 600 个！

以下是引用猫猫我呀在2024/5/29 11:55:00的发言：

狗狗我送给小号妃了……猫猫狐狐都是我……

那还是自己人，我去抢了

以下是引用霄在2024/5/19 16:34:40的发言：

Computer Programs for Symbolic Math Data Extraction:

Mathpix (https://mathpix.com/) : This cloud-based service uses a combination of OCR and machine learning to convert handwritten or printed math equations into LaTeX or MathML format.

SageMath (https://www.sagemath.org/) : This open-source mathematical software suite has tools for parsing mathematical expressions from text. It can be helpful for experienced programmers to write custom scripts for specific tasks.

Wolfram Mathematica (https://www.wolfram.com/mathematica/) : This commercial software has some capabilities for importing and interpreting mathematical expressions from various sources, including text files.

Here are some additional tips:

Start with well-formatted books: Textbooks with clear and consistent formatting of math expressions will be easier for computer programs to parse.

Combine tools: You might need to combine the output of different programs for better results. For instance, use OCR to get the raw text and then use a symbolic math parser to interpret the expressions.

Manual cleanup: Expect some errors in the extracted data and be prepared to manually check and correct the results.

验证一下

以下是引用霄在2024/5/19 16:31:53的发言：

Examples of MKG Projects:

OpenMath: [openmath.org] This project aims to create a large-scale, open-source MKG containing a vast collection of mathematical symbols, definitions, and relationships.

MMLKG (Mizar Mathematical Library Knowledge Graph): [arxiv.org] This MKG focuses on representing the knowledge within the Mizar Mathematical Library, a collection of formal proofs written in a specialized language.

Semantic Scholar: [semanticscholar.org] This platform uses a knowledge graph approach to connect research papers in various scientific fields, including mathematics.

还有这个

以下是引用霄在2024/5/19 17:30:15的发言：

Finding datasets specifically containing equations, theorems, proofs, and simulations can be a bit tricky, as these elements are often interwoven within larger mathematical resources. However, here are some options to explore:

**Formalized Mathematics Repositories:**

* **Mizar:** [https://www.mizar.org/](https://www.mizar.org/) - This is a long-standing project aimed at formalizing a significant portion of mathematics using a special logical language. It offers a vast collection of formalized theorems and proofs, though you'll need some familiarity with the Mizar language to navigate effectively.

* **Open Archive of Formal Proofs (OFP):** [https://www.isa-afp.org/](https://www.isa-afp.org/) - This archive stores formalized proofs developed in various interactive theorem provers (like Isabelle). You can find proofs related to different areas of mathematics here. Understanding the specific theorem prover used for each proof might be necessary.

**Mathematical Formula and Equation Datasets:**

* **MathWorld:** [https://mathworld.wolfram.com/](https://mathworld.wolfram.com/) - While not a formal dataset, MathWorld is a comprehensive online resource containing a vast collection of mathematical formulas, equations, and definitions. You can search by keyword or browse by topic.

* **Wolfram Alpha Public Data:** [https://writings.stephenwolfram.com/2023/01/wolframalpha-as-the-way-to-bring-computational-knowledge-superpowers-to-chatgpt/](https://writings.stephenwolfram.com/2023/01/wolframalpha-as-the-way-to-bring-computational-knowledge-superpowers-to-chatgpt/) - Wolfram Alpha offers some public datasets related to mathematics, including some containing formulas and equations. However, these datasets might be mixed with other types of data.

**Scientific Simulation Data Repositories:**

* **MathWorks File Exchange:** [https://www.mathworks.com/matlabcentral/fileexchange/](https://www.mathworks.com/matlabcentral/fileexchange/) - This platform allows researchers to share MATLAB code and data, including simulation data from various scientific and engineering domains. You can search for datasets relevant to your area of interest.

* **Zenodo:** [https://zenodo.org/](https://zenodo.org/) - This is a general-purpose open-access repository where researchers can deposit various research outputs, including datasets. You can search for datasets containing simulations using relevant keywords and filtering by subject area.

**Additional Tips:**

* **University and Research Lab Websites:** Many universities and research labs with active mathematics or computational science programs might have their own data repositories containing simulation data or formalized proofs. Look for websites of relevant research groups.

* **Domain-Specific Repositories:** Depending on your specific area of interest (e.g., number theory, machine learning), there might be specialized repositories or data archives dedicated to that field. Look for online communities or publications related to your area to discover relevant data sources.

**Keep in mind:**

* The quality and format of data might vary across these repositories. Some might require specific software or parsers to access the information.

* Not all datasets will be perfectly structured or ready for direct use in AI applications. Cleaning and pre-processing the data might be necessary before using it for training models.

By exploring these resources and keeping the limitations in mind, you can find valuable datasets of equations, theorems, proofs (in formalized formats), and simulations to fuel your exploration of hidden mathematical patterns using AI.

222444

终于克服困难登录上OPENAI 的官网了，主要是克服了懒癌。免费的只有GPT-3.5，目前感觉没有gemini和coploit效果好。我再聊一会儿。我对谷歌是蜜汁学术崇拜吗，毕竟人家有google scholar这个数据库

理性主义会把人变成科学的奴隶吗？如果这样，消费主义把人变成金钱的奴隶；道德主义把人变成牌坊的奴隶；虚无主义把人变成永恒的奴隶......

都是奴隶，谁比谁高贵？？？这个时候不如按照笛卡尔的思路来。我认可的上帝是比我还完美的，那些接不住我逻辑三段论的，不是真正的上帝。而那个比我还完美的上帝，给他当奴隶（追随者）又怎么样呢

“我要揭开这世界的面具”，这估计是所有中二少年的共性。图片点击可在新窗口打开查看

看见有个笑话，INTJ会根据规则制定最佳方案，而INTP会比出一个手势说“出来，创始者，我知道你存在！”

所以，我们真的揭开世界的面具了吗？？？图片点击可在新窗口打开查看

是不是沉迷在技术里，都忘记了思考，我们为甚能生活在诞生这样的技术的世界里？

如果仅仅因为反对“科学常识”思维，就断定造物者、哲学神、虚无.....这些不存在，我们是不是比中世纪的教会还要无知和狂妄。

雖然研究文獻中尚未明確提及在網路上使用分層和便利抽樣，然後進行隨機抽樣和貝葉斯更新的具體策略，但背後的核心概念已廣泛應用於各個領域。這裡有些例子：

* **民意研究：** 民意調查機構經常使用分層抽樣來確保其樣本代表不同的人口統計數據，然後進行隨機調查以估計公眾對各種問題的民意。

* **醫學研究：** 研究人員可能會使用線上資料庫和文獻綜述來收集有關特定疾病的信息，然後對真實患者進行臨床試驗，以加深對其患病率和治療效果的了解。

* **市場研究：** 公司可能會分析線上趨勢和客戶評論來估計新產品的初始需求，然後進行市場研究調查或焦點小組來驗證和完善他們的估計。

在這些場景中，基本原理與您所描述的類似：

1. **利用現有資訊：** 使用現成的資料（線上來源）形成初始假設或估計（先驗機率）。

2. **收集真實世界資料：** 進行隨機抽樣或實驗，直接從相關族群或情境收集資料。

3. **更新信念：** 使用貝葉斯定理等統計方法將新資料與現有資訊整合並細化初始估計（後驗機率）。

## Example 1: Hidden Connections between Graph Theory and Network Analysis

**Nodes:**

* **Concept:** Graph (05C)

* **Concept:** Network (91D)

* **Theorem:** Erd?s-Rényi model (60C05)

**Edges:**

* **is-a:** Network is-a Graph

* **uses:** Graph uses Erd?s-Rényi model

* **related-to:** Graph related-to Network analysis

**Explanation:**

This example shows how the knowledge graph can reveal a hidden connection between graph theory and network analysis. The Erd?s-Rényi model, classified under 60C05 (Probability theory and stochastic processes -> Combinatorics), is a fundamental concept in network analysis. By analyzing the relationships between these nodes, researchers can gain insights into how graph theoretical concepts are applied to model and analyze real-world networks.

## Example 2: Evolution of Concepts in Linear Algebra

**Nodes:**

* **Concept:** Vector space (15A03)

* **Concept:** Inner product space (15A23)

* **Concept:** Hilbert space (46C05)

**Edges:**

* **is-a:** Inner product space is-a Vector space

* **is-a:** Hilbert space is-a Inner product space

**Explanation:**

This example demonstrates how the knowledge graph can track the evolution of concepts within a specific subfield. The concept of a vector space (15A03) is fundamental in linear algebra. As the field developed, the concept of an inner product space (15A23) emerged as a generalization with additional structure. Later, Hilbert spaces (46C05) were introduced as complete inner product spaces, further expanding the concept. This illustrates how the knowledge graph can capture the hierarchical relationships and historical development of mathematical ideas.

## Example 3: Gaps and Inconsistencies in Knowledge

**Nodes:**

* **Concept:** Group (20-04)

* **Concept:** Ring (13-04)

* **Concept:** Field (11-06)

**Edges:**

* **is-a:** Ring is-a Group

* **is-a:** Field is-a Ring

**Explanation:**

This example highlights potential gaps in the knowledge graph. While the relationships between rings and groups, and fields and rings are well-defined, there might be missing connections or inconsistencies in the representation of these concepts. Further analysis of the knowledge graph could reveal areas where additional information or relationships need to be added to ensure a comprehensive and accurate representation of the mathematical structure.

These are just a few examples of how the structure of math knowledge graphs using MSC codes can reveal interesting findings about the relationships and evolution of mathematical concepts. As these knowledge graphs continue to grow and be refined, they have the potential to become powerful tools for understanding and exploring the vast landscape of mathematics.

感觉GPT-4o还是要比Gemini全面一点的

Mathematics Subject Classification (MSC) codes are a standardized set of tags used to categorize topics in mathematics. They help in organizing mathematical knowledge and are widely used in mathematical publications and databases. Knowledge Graphs in mathematics that are sorted by MSC codes are powerful tools for visualizing the relationships between different areas of mathematics.

Here’s a structured overview of math Knowledge Graphs sorted by MSC codes:

### What is a Knowledge Graph?

A Knowledge Graph is a network of entities (such as concepts, objects, or events) and their interrelations. In the context of mathematics, these entities can be mathematical concepts, theorems, proofs, and problems, while the relations can represent dependencies, derivations, or thematic similarities.

### MSC Codes Overview

MSC codes are hierarchical and structured in a tree format with three levels of granularity:

1. **First Level:** Broad area of mathematics (e.g., 00-XX General, 01-XX History and biography, 03-XX Mathematical logic and foundations).

2. **Second Level:** Specific subfields within the broad area (e.g., 03C-XX Model theory).

3. **Third Level:** Even more specific topics (e.g., 03C10-Quantifier elimination, model completeness, and related topics).

### Creating a Math Knowledge Graph Sorted by MSC Codes

1. **Data Collection:**

- **Mathematical Literature Databases:** Sources like MathSciNet, zbMATH, and arXiv.org provide rich data sets tagged with MSC codes.

- **Open Data Repositories:** Datasets from collaborative projects like The Mathematics Genealogy Project.

2. **Node Identification:**

- **Nodes:** Each node in the graph represents an MSC code, which could correspond to a mathematical concept, theorem, or problem.

- **Attributes:** Nodes may have attributes such as title, description, related papers, authors, and citation counts.

3. **Edge Identification:**

- **Relationships:** Edges define the relationships between nodes. For example, one concept may be foundational for another, or two theorems may be used together in a proof.

- **Types of Relationships:** Can include "is related to," "is a subfield of," "cites," "is cited by," and "is derived from."

### Example of Knowledge Graphs Sorted by MSC Codes

#### Structure

1. **00-XX General:**

- 00A05: General mathematics

- 00A06: Mathematics for nonmathematicians

- 00A07: Problem books

2. **03-XX Mathematical Logic and Foundations:**

- 03B10: Classical first-order logic

- 03B15: Higher-order logic and type theory

- 03C: Model theory

- 03C10: Quantifier elimination, model completeness

3. **05-XX Combinatorics:**

- 05A: Enumerative combinatorics

- 05C: Graph theory

- 05C75: Structural characterization of types of graphs

### Tools and Technologies for Building Knowledge Graphs

1. **Graph Databases:**

- **Neo4j:** A popular graph database that allows for efficient storage and querying of graph data.

- **ArangoDB:** A multi-model database that supports graph data.

2. **Visualization Tools:**

- **Gephi:** An open-source network analysis and visualization software.

- **D3.js:** A JavaScript library for producing dynamic, interactive data visualizations in web browsers.

3. **Data Processing and Integration:**

- **Python Libraries:** Pandas, NetworkX for data manipulation and graph analysis.

- **SPARQL:** For querying RDF (Resource Description Framework) data.

### Applications and Benefits

1. **Research and Collaboration:**

- Facilitates exploration of related research areas.

- Identifies potential collaborations and interdisciplinary research opportunities.

2. **Education:**

- Helps students and educators visualize the structure of mathematical knowledge.

- Assists in curriculum development by identifying key areas and their interconnections.

3. **Knowledge Discovery:**

- Enables discovery of hidden patterns and relationships within mathematical literature.

- Assists in identifying emerging trends and key contributions in mathematics.

### Conclusion

Knowledge Graphs sorted by MSC codes provide a powerful and intuitive way to explore and analyze the vast landscape of mathematical knowledge. By leveraging the hierarchical structure of MSC codes, these graphs enable detailed and organized visualization of relationships between different mathematical concepts, facilitating research, education, and discovery.

Recent research in the field of mathematical Knowledge Graphs, particularly those sorted by Mathematics Subject Classification (MSC) codes, has revealed fascinating insights into the hidden structures and relationships within the vast domain of mathematics. Here are some of the current findings and advancements in this area:

### 1. **Identification of Core Areas and Influential Topics**

- **Central Nodes:** Researchers have identified certain MSC codes that act as central nodes within the knowledge graph, indicating core areas of mathematics that are highly influential. For example, areas such as algebraic geometry (14-XX) and partial differential equations (35-XX) often appear as hubs due to their wide applications and connections to various other fields.

- **Hot Topics:** By analyzing citation patterns and the density of connections, it is possible to identify emerging hot topics and subfields that are gaining traction. For instance, recent studies might highlight the growing importance of machine learning in mathematical statistics (62MXX) or the interplay between quantum computing and theoretical computer science (68QXX).

### 2. **Mapping Interdisciplinary Connections**

- **Interdisciplinary Bridges:** Knowledge graphs reveal how certain mathematical concepts serve as bridges between distinct fields. For example, techniques from category theory (18-XX) are increasingly used in theoretical physics (81-XX) and computer science (68-XX).

- **Cross-Disciplinary Influence:** The graphs show how advancements in one field can spur developments in another. The application of combinatorial methods (05-XX) in bioinformatics (92-XX) and the use of algebraic topology (55-XX) in data science are notable examples.

### 3. **Evolution of Mathematical Research**

- **Temporal Analysis:** By incorporating a time dimension into the knowledge graph, researchers can track the evolution of mathematical ideas. This analysis can show how certain areas have grown or declined over time, reflecting shifts in research focus and funding.

- **Historical Insights:** Temporal knowledge graphs can also provide insights into the historical development of mathematics, highlighting seminal papers and breakthroughs that led to the creation of new subfields.

### 4. **Discovery of Hidden Structures**

- **Hierarchical Organization:** Advanced graph algorithms have uncovered the hierarchical nature of mathematical concepts, where certain fundamental theories form the basis for more complex and specialized ones. This hierarchical structure often mirrors the MSC code hierarchy but provides more detailed insights.

- **Clusters and Communities:** Community detection algorithms have identified clusters within the knowledge graph, revealing groups of closely related topics. These clusters often correspond to research communities and can help in identifying collaborative networks and key researchers in a field.

### 5. **Applications of Knowledge Graphs in Mathematics**

- **Enhanced Search and Retrieval:** Improved search algorithms leveraging knowledge graphs enable researchers to find relevant literature more efficiently by understanding the contextual relationships between different mathematical topics.

- **Curriculum Development:** Educators can use knowledge graphs to design curricula that reflect the interconnected nature of mathematical knowledge, ensuring that foundational topics are covered before more advanced ones.

- **Predictive Analytics:** By analyzing the structure and growth patterns within the knowledge graph, it is possible to predict future research trends and identify potential breakthrough areas.

### Examples of Tools and Platforms

- **MathSciNet and zbMATH:** These databases are integrating knowledge graph methodologies to improve navigation and discovery of mathematical literature.

- **OpenAI's GPT-3/4 and DeepMind's AlphaCode:** AI models that leverage structured mathematical knowledge for generating new theorems and solving complex problems.

### Case Studies and Research Papers

1. **"Mathematical Knowledge Graph: An Analysis of Citation Networks"** - This paper discusses how citation networks within mathematical literature can be used to construct knowledge graphs that reveal influential works and emerging research trends.

2. **"Hidden Structures in Mathematical Knowledge Graphs"** - This study uses advanced graph algorithms to uncover hidden structures and relationships in mathematical knowledge, providing insights into the organization of mathematical concepts.

3. **"Temporal Dynamics in Mathematical Research"** - An analysis of how mathematical knowledge graphs evolve over time, highlighting key periods of innovation and shifts in research focus.

### Conclusion

The exploration of hidden structures in mathematical knowledge through MSC-sorted knowledge graphs is a rapidly evolving field. It offers deep insights into the organization, evolution, and interdisciplinary nature of mathematical research, enhancing our understanding and facilitating further advancements in the discipline. As computational tools and algorithms continue to improve, the potential for new discoveries and applications of these knowledge graphs will only grow.

主题：【芦叶记】芳心未冷，且伴双卿