Math Research Compass | Brian Hepler

A production data dashboard analyzing mathematical research trends across 290,000+ arXiv papers. This full-stack application uses advanced topic modeling and NLP to map the thematic landscape of modern mathematical research, deployed with professional infrastructure and custom domain.

Overview

Math Research Compass transforms the vast landscape of mathematical research into an interactive, explorable dashboard. By analyzing nearly 300,000 arXiv mathematics papers from the past five years, the application identifies 1,938 distinct research topics and presents them through an intuitive web interface.

Key Features

Interactive Topic Exploration:

Browse 1,938 discovered research topics across 31 mathematical subfields
Dynamic filtering by arXiv categories (algebraic geometry, number theory, etc.)
Detailed topic views with top contributing authors and representative papers
Real-time category distribution analysis

Advanced Analytics:

AI-enhanced topic labeling using Claude for human-readable descriptions
Author productivity rankings and collaboration patterns
Research trend identification across mathematical disciplines
Cross-category thematic analysis

Professional Web Application:

Lightning-fast performance with optimized SQLite database architecture
5x improvement in interactive response times through indexed queries and LRU caching
Custom domain with SSL certificates (mathresearchcompass.com)
Production deployment on Heroku with professional reliability

Technical Architecture

Data Pipeline:

ArXiv metadata ingestion and preprocessing (290K+ papers)
Advanced topic modeling with BERTopic, UMAP, and HDBSCAN clustering
Claude AI integration for enhanced topic labeling and interpretation
Comprehensive data validation and quality assurance

Backend Optimization:

Optimized SQLite database with indexed tables and connection pooling
LRU caching for frequent queries achieving sub-second response times
Efficient data structures supporting real-time filtering and aggregation
Memory optimization for handling large-scale academic datasets

Frontend Development:

Interactive Shiny dashboard with responsive design
Dynamic visualizations using Plotly for data exploration
Intuitive user interface supporting both overview and detailed analysis
Mobile-responsive design for accessibility across devices

Production Infrastructure:

Professional deployment on Heroku with custom domain configuration
SSL certificates and security best practices
DNS management and domain forwarding
Performance monitoring and optimization

Impact and Applications

This dashboard serves multiple audiences in the mathematical research community:

Researchers can identify emerging trends and potential collaboration opportunities
Graduate students can explore active research areas and understand field dynamics
Department administrators can analyze research productivity and focus areas
Funding agencies can assess research landscape and identify investment priorities

Future Development

Planned enhancements include:

Collaboration network analysis with NetworkX for author relationship mapping
Temporal trend analysis showing topic evolution over time
Citation impact analysis (when data becomes available)
Geographic and institutional affiliation analysis

Links

Live Application: mathresearchcompass.com
Source Code: GitHub Repository

Technologies Used

Machine Learning: BERTopic, UMAP, HDBSCAN, Sentence Transformers
AI Integration: Claude API for topic enhancement
Database: SQLite with optimization and indexing
Web Framework: Shiny for Python with Plotly visualizations
Deployment: Heroku with custom domain and SSL
Data Processing: Pandas, NumPy, advanced NLP pipelines