Dr. Abdalla Mansur is a mathematician, researcher, and educator based in Kingston, Ontario, Canada. With a Ph.D. in Mathematics from Queen’s University, his work focuses on dynamical systems and differential equations, with particular interest in N-body problems—a field that studies how multiple objects interact under gravitational forces.
His academic journey has taken him across multiple countries, including Canada, Libya, the UAE, and Saudi Arabia. Over the years, he has held teaching and research positions at Laurentian University, the Royal Military College of Canada, Al Ain University, Imam Abdulrahman Bin Faisal University, the University of Toledo, the Higher Colleges of Technology in Abu Dhabi, and the University of Bani Waleed in Libya. Currently, he serves as an assistant professor at the Libyan Center for Engineering Research and Information Technology.
Dr. Mansur is deeply passionate about exploring mathematics as the hidden structure of the universe, making complex theories more accessible to students, and leveraging modern technology—especially AI and computational tools—to expand the limits of mathematical research.
In this in-depth Q&A, he shares his unique perspective on mathematics, education, and the way numbers define the world around us.
What first drew you to mathematics?
Mathematics always felt like a puzzle to me—one that actually had solutions. Unlike subjects that rely on memorization or interpretation, math is about finding answers through logic and reasoning. As a child, I was fascinated by how numbers could describe everything from simple equations to the movement of planets.
Over time, I realized that mathematics isn’t just about solving problems—it’s about discovering the hidden rules that govern reality. Whether in physics, engineering, or finance, math provides a structure that allows us to understand and predict the world.
PhD Research in Mathematics: From Queen’s University to Global Impact
Many people see mathematics as abstract and disconnected from daily life. How do you respond to that?
I hear this all the time, especially from students who struggle with math. The truth is, mathematics is everywhere. It’s in the way our phones connect to networks, how Google ranks search results, and even how cities optimize traffic lights.
Nature also follows mathematical principles. The Fibonacci sequence appears in sunflowers, pinecones, and galaxies. The golden ratio shapes everything from architecture to human faces. Even something as simple as the way a credit card company calculates interest is based on mathematical formulas.
What’s frustrating is that many educational systems teach math as a set of mechanical rules rather than a way of thinking. If people saw math as a tool for understanding patterns rather than just a subject they need to pass, they might appreciate it more.
Your research focuses on dynamical systems and differential equations. Why are these fields important?
Dynamical systems are all around us. They describe how things change over time—whether it’s the orbit of planets, the spread of diseases, or the fluctuations of financial markets.
Differential equations allow us to model these systems. For example, in physics, we use them to describe motion and force. In biology, they help predict how populations of animals grow or decline. In economics, they analyze market trends.
I’m particularly interested in N-body problems, which involve studying how multiple objects move under gravitational forces. This research has applications in space exploration, satellite trajectory planning, and astrophysics. Even though these equations have been studied for centuries, they remain a challenging and fascinating area of mathematics.
How has teaching in different countries influenced your perspective on mathematics education?
It’s been an eye-opening experience. In some countries, math education is highly theoretical, focusing on proofs and formal reasoning. In others, it’s more applied, emphasizing how math connects to real-world problems.
One of the biggest challenges I’ve faced as an educator is adapting my teaching style to different learning cultures. Some students are used to memorization and repetition, while others thrive on problem-solving and exploration. I try to strike a balance by showing both the rigor of mathematical proofs and the practical applications of mathematical models.
The key, I’ve learned, is to make math relatable. When students see how mathematical principles impact their daily lives, they engage with the subject in a much deeper way.
You recently conducted a workshop on LaTeX for researchers. Why do you think writing skills are important in mathematics?
Mathematics isn’t just about solving equations—it’s about communicating ideas. Many brilliant mathematicians struggle to explain their work clearly, which limits how others engage with their research.
LaTeX is an essential tool because it allows researchers to write complex mathematical papers with precision. Unlike word processors, it ensures that formulas, graphs, and citations are formatted properly, which is crucial for academic publishing.
Beyond LaTeX, I encourage my students to develop strong writing skills. A well-explained theorem is just as valuable as the theorem itself. If no one understands your proof, it doesn’t matter how groundbreaking it is.
What role do you think artificial intelligence (AI) will play in mathematical research?
AI is already transforming mathematics. We’re seeing machine learning models that can analyze massive datasets, generate mathematical proofs, and even predict outcomes in ways that were impossible before.
One of the most exciting developments is how AI assists in theorem discovery. Programs like DeepMind’s AlphaTensor have shown that AI can find new, more efficient ways to perform matrix calculations—something mathematicians have studied for decades.
That said, AI is a tool, not a replacement for human intuition. It can process information at incredible speeds, but it doesn’t understand meaning the way we do. The best results come when AI and human mathematicians work together—combining computational power with creative problem-solving.
Have you ever faced a major failure in your career? How did you overcome it?
Early in my teaching career, I struggled with engagement. I knew my subject well, but I wasn’t reaching students the way I wanted to.
One turning point came when I realized that students need to see why math matters before they can truly connect with it. I started using real-world examples, interactive problem-solving, and a more conversational approach.
Over time, I found that making small adjustments—like using data from students’ favorite sports teams or analyzing trends in social media—made a huge difference. The experience taught me that even the most technical subjects need human connection to be meaningful.
What advice would you give to students struggling with mathematics?
First, don’t fear mistakes. Mathematics is about exploration. Every great mathematician has failed hundreds of times before making a breakthrough.
Second, focus on understanding, not memorization. Instead of just memorizing formulas, try to see why they work. Ask yourself, “What problem is this equation solving?”
Finally, find connections to things you enjoy. If you like music, study the math behind sound waves. If you’re into technology, explore cryptography and coding. Math is everywhere—you just have to look.
What’s next for you?
I want to continue exploring how mathematical models can help solve real-world problems, from climate change to economic stability. I’m also working on making advanced math more accessible by using technology and interactive tools.
Teaching will always be a part of my journey. I believe that education is one of the most powerful ways to make an impact. Whether through research, mentorship, or writing, I hope to help others see the beauty of mathematics—not just as numbers, but as a way to understand the universe.