Learning has been one of the most consistent themes throughout my life. On this page, I share the subjects that I, Ryan Montazer, am currently studying and exploring. My interests have changed and expanded over time, but the desire to understand difficult ideas, explore unfamiliar subjects, and connect knowledge across different fields has remained constant.
My educational background is primarily in mathematics, engineering, and applied mathematics. However, my current learning extends beyond formal academic disciplines. It includes language, history, mathematical logic, systems thinking, artificial intelligence, and other subjects that help me better understand both the world and my own direction within it.
This page presents the areas that currently receive most of my attention. Some are practical priorities, while others are long-term intellectual projects that I have wanted to pursue for many years.
French
Learning French is currently one of my highest practical priorities. After moving to Montréal, learning the language became an important part of better understanding Québec, communicating with people, and integrating more fully into the local community. My goal is to steadily build confidence in speaking, listening, reading, and everyday communication.
Gödel’s Incompleteness Theorems
Gödel’s incompleteness theorems have fascinated me since I first encountered mathematical logic and set theory during my undergraduate studies in pure mathematics.
The theorems address profound questions about formal mathematical systems, proof, truth, and the limits of what can be established from a fixed collection of axioms. I have understood their general meaning for many years, but one of my long-term goals is to reach a deeper and more technically satisfying understanding of the proofs.
My current objective is what I think of as a second level of understanding: moving beyond popular explanations while not necessarily attempting to specialize in mathematical logic professionally. This means carefully studying the necessary background, including formal systems, computability, arithmetization, self-reference, and the structure of Gödel’s argument.
This is not a project I expect to complete quickly. It is a long-term intellectual journey connected to my broader interest in mathematics, logic, philosophy, and the foundations of knowledge.
Fundamentals of Mathematics
One of my long-term mathematical goals is to reorganize my understanding of calculus from a foundational perspective.
Having studied, taught, and applied calculus extensively over the years, my objective is no longer to learn the subject itself. Instead, I want to identify and organize the small collection of fundamental definitions and major theorems from which the rest of differential and integral calculus naturally follows.
I enjoy viewing mathematics as a coherent logical structure rather than a collection of formulas and techniques. Much like writing a book from scratch, I want to reconstruct the subject from its foundations, arranging the ideas into a clear and elegant framework that reflects the underlying structure of the discipline.
Will Durant, History, and Civilization
History has increasingly become an important part of my learning.
I am particularly interested in Will and Ariel Durant’s broad account of human civilization. Their work connects political events with philosophy, religion, science, literature, art, economics, and everyday life. This wide perspective appeals to me because it presents history not simply as a sequence of rulers and wars, but as the development of civilizations and ideas.
Listening to and reading history also gives greater context to my travels. Places become more meaningful when I understand the societies, conflicts, beliefs, and historical changes that shaped them.
My goal is not to memorize every date or event. I want to develop a coherent mental framework for understanding major civilizations, historical periods, and the recurring forces that influence societies over time.
Systems Thinking
Systems thinking has become an important way for me to connect ideas from different areas of my life. My background in mathematics, engineering, software, business, health, and history often leads me to look for relationships rather than isolated facts.
I want to continue developing this perspective so I can better understand complex problems, make better decisions, and recognize the common patterns that appear across different disciplines.
Artificial Intelligence and Emerging Technology
Artificial intelligence is both an intellectual interest and an increasingly practical area of study for me.
My background in mathematics, numerical modelling, programming, and software engineering gives me several ways to approach the field. I am interested not only in how AI tools can be used, but also in the mathematical and computational ideas behind them, their limitations, and their broader effects on education and work.
AI is particularly relevant to my teaching and educational business. It can influence how educational material is created, how students practise, how technical content is organized, and how small businesses operate more efficiently.
Last update: July 2026
-Ryan Montazer