1. Introduction to FAIR Principles

The FAIR principles, first published in 2016 by Wilkinson et al., provide a framework for optimizing the reuse of scientific data. FAIR stands for Findable, Accessible, Interoperable, and Reusable.

"The FAIR principles focus specifically on data management and machine-friendly accessibility aspects with emphasis on metadata, rather than broader research transparency."

These principles are designed to support knowledge discovery and innovation both by humans and machines, to increase the value of accumulated digital research objects, and to enable automation in scientific processes.

2. The Importance of FAIR in Mathematics

Mathematics research generates a wide variety of data types that benefit from structured management approaches. The implementation of FAIR principles in mathematics:

• Enables verification, reproduction, and extension of research findings
• Facilitates new investigations and hypotheses testing
• Supports the combination of data from multiple sources to uncover novel insights
• Enhances cross-disciplinary collaboration and knowledge transfer
• Accelerates the pace of scientific discovery through efficient data reuse

As noted in the Scientific Data journal (2024): "The main goal is to make the scientific community more transparent and efficient by making it significantly easier to re-use previous research results. This openness not only facilitates collaboration within the mathematical community but also enhances cross-fertilization with other fields, fostering interdisciplinary approaches that can lead to new discoveries and innovations."

3. Categories of Mathematical Research Data

Mathematical research encompasses diverse data types that require specialized management approaches:

4. Detailed FAIR Principles

5. Practical Implementation Guidelines

For Findability

1. Use persistent identifiers: Register your mathematical research outputs (datasets, software, papers) with services that provide DOIs or other persistent identifiers
2. Create comprehensive metadata: Include relevant mathematical subject classifications, keywords, abstract, author information, and related works
3. Ensure identifier visibility: Make sure the persistent identifier is prominently displayed in the metadata and is machine-readable
4. Select appropriate repositories: Choose repositories with good indexing and search capabilities specific to mathematical content

For Accessibility

1. Utilize standard protocols: Make data accessible via standard web protocols that support mathematics (e.g., with proper rendering of equations)
2. Consider access controls: If access restrictions are necessary, implement them at the data level while keeping metadata openly accessible
3. Ensure long-term access: Partner with institutional repositories or discipline-specific archives that commit to long-term preservation
4. Plan for data discontinuation: Establish protocols for maintaining metadata even if the underlying data becomes unavailable

For Interoperability

1. Adopt standardized formats: Use established formats for mathematical content (e.g., LaTeX, MathML, standard formats for matrices and other mathematical objects)
2. Implement controlled vocabularies: Utilize the Mathematics Subject Classification (MSC) and other standardized terminology
3. Enable semantic relationships: Explicitly document relationships between different mathematical objects, proofs, and theorems
4. Support machine readability: Structure data and metadata to facilitate automated processing

For Reusability

1. Provide detailed documentation: Include comprehensive information about the context, methodology, and potential applications
2. Select appropriate licenses: Choose licenses that facilitate reuse while respecting intellectual contribution (e.g., Creative Commons licenses)
3. Document provenance: Clearly describe the origin, validation methods, and transformations applied to the data
4. Follow community standards: Adhere to established practices within specific mathematical subdisciplines

6. Current Challenges in Mathematics

The implementation of FAIR principles in mathematics faces several discipline-specific challenges:

1. Metadata standardization: Lack of uniform metadata standards across different branches of mathematics
2. Persistent identifier adoption: Inconsistent use of persistent identifiers for mathematical objects
3. Data-metadata distinction: Often unclear separation between mathematical data and its descriptive metadata
4. Machine-readable formats: Limited availability of machine-readable formats for complex mathematical structures
5. Standardized vocabulary: Absence of comprehensive controlled vocabularies that span all mathematical subfields
6. Provenance documentation: Difficulty in documenting complex chains of mathematical reasoning in standardized formats

These challenges are reflected in the current state of mathematical data repositories, with most systems fulfilling the FAIR principles for findability and accessibility but showing lower compliance rates for interoperability and reusability.

7. Recommended Repositories

8. FAIR Compliance Checklist

Use this checklist to assess and improve the FAIR compliance of your mathematical research data:

9. References

1. Wilkinson, M. D., et al. (2016). The FAIR Guiding Principles for scientific data management and stewardship. Scientific Data, 3, 1-9.
2. Conrad, T. O. F., et al. (2024). Making Mathematical Research Data FAIR: Pathways to Improved Data Sharing. Scientific Data, 11:676.
3. Leipzig, J., et al. (2021). The role of metadata in reproducible computational research. Patterns, 2, 100322.
4. Pampel, H., et al. (2013). Making Research Data Repositories Visible: The re3data.org Registry. PLOS ONE, 8, e78080.