📘 Project Euler: Mathematical Explorations

This repository is a mathematical and computational exploration of selected Project Euler problems, designed to bridge rigorous mathematical reasoning with computational implementation.

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🎯 Purpose and Philosophy

"Mathematics is the art of giving the same name to different things." — Henri Poincaré

The purpose of this project is not only to find numerical answers, but to understand the structure, proofs, and asymptotic behaviors that lie beneath each problem.

Each solution is built upon a dual foundation:

1. Formal Mathematical Analysis (LaTeX) — proofs, lemmas, propositions, and theorems;
2. Computational Realization (Python / Jupyter) — verified algorithms and empirical validation.

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🧩 Structure of the Repository

PROJECT-EULER/
├── .vscode/                   # Environment configuration
├── .github/workflows/         # LaTeX CI/CD pipeline (GitHub Actions)
├── data/                      # Optional datasets
├── docs/                      # Mathematical write-ups in LaTeX
├── notebooks/                 # Jupyter notebooks for exploration
├── src/python/                # Core algorithmic implementations
├── tests/                     # Future mathematical/algorithmic validations
├── pyproject.toml             # Dependency and environment control
└── .gitignore

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🧠 Mathematical Focus

Each notebook and LaTeX document focuses on:

• The underlying recurrence relations or combinatorial structures of the problem;
• The proof of correctness for derived formulas or algorithms;
• The asymptotic growth and analytical behavior of resulting sequences;
• The relationship between discrete and continuous models (e.g., sums vs. integrals, discrete recursions vs. differential analogs).

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⚙️ Environment Setup

Languages & Tools

• 🐍 Python 3.12 (with uv, numpy, sympy, jupyter)
• 📘 VS Code (extensions: Python, Jupyter, LaTeX Workshop)
• 📄 LaTeX (MiKTeX + SumatraPDF)
• ⚙️ GitHub Actions (for automated LaTeX builds)

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🔬 Research Perspective

This repository treats computational mathematics as an experimental science:

• Hypothesis generation from numerical patterns;
• Proof verification through symbolic reasoning;
• Construction of efficient algorithms inspired by theorems;
• Asymptotic and structural analysis of recursive systems.

It aims to evolve into a library of mathematical mini-papers, each combining theoretical rigor with reproducible computational evidence.

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🧮 Long-Term Vision

To create a Mathematical Atlas of Project Euler problems — each entry containing:

• A theorem-driven formulation;
• Analytical and computational solutions;
• Cross-references to known results in number theory and combinatorics.

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📜 License

Released under the MIT License. Free for academic and educational use with proper attribution.