I'm a mathematician with a strong interest in mathematical reasoning, structure, and formal thinking, and how these ideas can be translated into tools that help us understand the world more rigorously — and, ideally, improve it.
My background sits at the intersection of pure mathematics, applied modeling, and data-driven reasoning, with a growing focus on AI systems that reason mathematically, not just statistically.
- Representation theory, algebraic topology, and mathematical structure
- Topological Data Analysis (TDA) and geometric perspectives on data
- Mathematical reasoning, proof, and formal methods (Lean-curious)
- Math-first AI, interpretable models, and research-driven tooling
- Teaching, exposition, and making advanced mathematics accessible
- Developing and experimenting with Topological Data Analysis (TDA) pipelines in Python
- Exploring connections between pure mathematics and AI-assisted reasoning
- Building public-facing math projects, problem-solving tools, and research-style writeups
- Preparing for graduate study with the goal of pursuing a fully funded PhD
- Thinking seriously about how applied math and AI can impact medicine, education, and governance
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Altered Chain — a personal research lab and writing platform where I explore math, reasoning, and AI-adjacent ideas through essays, visual explanations, and computational experiments
https://www.alteredchain.com -
Undergraduate research in representation theory, including computational exploration with GAP
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Modeling and dynamical systems projects motivated by real-world phenomena
I'm open to:
- Research-oriented projects involving mathematics, data, or reasoning systems
- Exploratory work at the intersection of math, AI, and formal methods
- Educational or tooling projects that help people think mathematically
If you care about rigor, clarity, and building things that actually reason — we’ll probably get along.
- 📧 Email: jguzmanmarcos@gmail.com
- 🌐 Website: https://www.alteredchain.com
Feel free to reach out or fork anything here if our interests overlap.