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.
[此贴子已经被作者于2024/5/31 19:01:38编辑过]
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