Building a Semantic Search Engine and Open-Status Classifier over the ResearchMath-14k Dataset

['In this tutorial, we work with the amphora/ResearchMath-14k dataset, a collection of research-level mathematics problems mined from arXiv. We load the dataset, inspect its structure, and explore how the problems are distributed across mathematical fields and open-status categories. We then move beyond basic analysis by extracting field-specific keywords, generating semantic embeddings, visualizing the problem landscape, clustering related problems, and building a simple search engine over the dataset.

Also, we train a classifier to predict problem status from embeddings and detect closely related or near-duplicate problems.', 'We begin by installing the required libraries and importing the tools needed for analysis, visualization, embeddings, and data handling. We also set the main configuration values, including sample size, random seed, and embedding model. This gives us a clean setup before we start working with the ResearchMath dataset.', 'We load the amphora/ResearchMath-14k dataset from Hugging Face and convert it into a pandas DataFrame.

We inspect the number of rows, available columns, and a few sample records to understand the dataset structure. We then keep only problem statements of meaningful length so that subsequent analysis works on useful text. We explore the dataset by checking how problems are distributed across open-status labels and mathematical fields.

We visualize the status counts, field counts, and problem lengths to quickly get an overview of the corpus. We also create a heatmap to see how open-status categories vary across different math fields.', 'We use TF-IDF to find the most important terms within each top-level mathematical field. We group the dataset by field and extract the strongest keywords or phrases that represent each group.

This helps us understand what topics and terminology dominate different areas of research in mathematics. We sample the dataset and convert each mathematical problem into a semantic embedding using a SentenceTransformer model. We reduce the embeddings into two dimensions using UMAP, or PCA if UMAP is unavailable, and visualize the problem landscape by field.', 'We build a semantic search function that retrieves the most similar research problems for a given query.

We then train a classifier on the embeddings to predict each problem’s open-status label. Finally, we compute similarity across all embedded problems to detect the closest pair and identify near-duplicate or strongly related problem statements. In conclusion, we have a complete workflow for analyzing research-level mathematical problems using modern NLP and machine learning tools.', 'We started with dataset exploration, then used TF-IDF, sentence embeddings, dimensionality reduction, clustering, semantic search, and classification to understand the corpus’s structure from multiple angles.