Quote
“Pure mathematics is, in its way, the poetry of logical ideas.”
—Albert Einstein
Quote
“Any sufficiently advanced technology is indistinguishable from magic.”
— Arthur C. Clarke
Hi there, I’m Juan 👋
I’m a Mathematics graduate from the University of Waterloo, passionate about tackling challenging problems at the intersection of software and mathematics.
Currently Working On
- Developing a multiplayer poker game as a full-stack project.
- Learning about Generative AI from the IBM specialization on coursera.
- Working on a fullstack freelance project with React and Next.
Experience
- I interned at Versa Networks as a cloud developer, working on cybersecurity microservices within an API-driven data protection cluster.
- I also interned at Catalyst Technologies as a backend developer, contributing to the integration of blockchain technologies in the agricultural industry to manage carbon rebates earned through sustainable farming practices.
- I worked at SYMX.AI as a software developer, leveraging AWS technologies and communication protocols to integrate IoT functionality into mining drills, enhancing operator training and improving mechanical efficiency through data-driven cloud analytics.
Fun Facts
- I absolutely love martial arts and have recently participated in over 30Â grappling competitions.
- I work part-time supporting people with mental disabilities at a non-profit organization called L’Arche.
Notes
Note on Notes
These notes are intended as a personal reflection of my learning and therefore are a perpetual work in progress—they’ll never be finished. They started off as my computational mathematics notes compiled from my coursework at the University of Waterloo and are slowly transitioning more into software and AI.
Why Obsidian?
Obsidian is the note-taking tool used to create these notes. Its linking system is similar to that of Wikipedia, aiming to organize information by concepts rather than book chapters. In this way, information forms a graph with meaningful connections between ideas.
Since I started jiujitsu, I realized that knowledge is best applied when it is well-organized. As an aspiring mathematician, it felt natural to structure my own thoughts, interpretations, and frameworks—flawed as they may be—as abstract concepts that can be readily applied to different situations—a fundamental principle of mathematics.
Homomorphisms
The organization of ideas in Obsidian follows a more dynamic approach to knowledge storage. For instance, the concept of homomorphisms is defined as “a mapping between objects of the same type that preserves structure.” Yet, this idea transcends mathematics.
An application of the concept: Consider a car and a small truck: there is a mapping between them, preserving the essential structure of a chassis with four wheels.
A philosophical reflection: Though our lives unfold in unique ways, they share a common underlying structure shaped by universal themes—joy, grief, loss, growth, and more. When someone says, “I can relate to that person,” they have found a homomorphism between their experiences. Indeed, as Joseph Campbell wrote, “All the gods, all the heavens, all the hells are within you.”