In Conversation with Dr. Ján Mináč

Dr. Jan Minac in a classroom

Photo credit: Mitch Zimmer

“Many scientists are looking for beauty,” observes Mathematics Professor and Western Fellow, Dr. Ján Mináč. “We are governed by beauty and harmony.”

Born into a family of writers, artists, and film makers, Mináč first realized his love of mathematics at age twelve when he came across a book about prime numbers. Since then, he continues to be compelled by a wide range of topics in pure and applied mathematics; however, while Mináč is motivated by a deep appreciation for numbers and formulas, his creative, multidisciplinary outlook transcends any singular area of study. A recipient of the 2013 Canadian Mathematical Society Excellence in Teaching award, Mináč approaches teaching and research with a storyteller’s sensibility.

“In science,” he explains, “we are looking for a story. We better comprehend important scientific facts if we can embed them into a story. This story and a possible explanation can sometimes be stunning. Albert Einstein found a spectacular explanation of gravitation using curvature in time-space. This explanation of gravitation is a most wonderful, gripping story. It is a milestone in our understanding of nature. Einstein worked extremely hard to uncover the story of gravitation.”

"In science, we are looking for a story. We better comprehend important scientific facts if we can embed them into a story."

Mináč uses mathematics to tell a story about the human brain. His expertise in Galois Theory--an algebraic concept that sheds light on symmetries in mathematics and in nature—drives his contributions to the “Mathematics of Neural Networks” theme, which he leads alongside Theme Leader Dr. Lyle Muller (Department of Mathematics) and Western Fellow Dr. Marieke Mur (Department of Psychology, Computer Science).

As a Western Fellow with the Western Academy, Mináč's goal is to use mathematical principles to discover new ways of understanding the formation of memory, memory loss, and other neurological conditions. Other important goals include the consideration of a new way of understanding the dynamical systems of large networks and related fundamental problems in discrete mathematics, number theory, Galois theory, and dynamical systems.

This interview has been edited and condensed.

What challenges drive your work?

My answer is mystery: the mystery of nature, the mystery of the human mind, the mystery of prime numbers.

When I was twelve years old, I was incredibly interested in prime numbers. With prime numbers, there is a huge mystery, because on the one hand, there is a lot of regularity in them, but on the other hand there is complete chaos. I love this tension. This paradox is a great hurdle and it is extremely interesting to me. Right now I am extremely excited that we are studying how memories are encoded in a possibly highly sophisticated way.

When I was learning about how Einstein saw gravitation, I was so awed! I learned about it as a very young person, it was so amazing to me. When we are studying brain function, we are studying both the physical interactions between neurons occurring in a given space and we are also recording a time schedule of these interactions. As in Einstein’s theory of relativity there seems to be a very deep mathematical concept of time-space which governs the ways in which memories are encoded in our brains.

What crucial issues do you hope to address in your work with the Mathematics of Neural Networks theme?

 "As in Einstein’s theory of relativity there seems to be a very deep mathematical concept of time-space which governs the ways in which memories are encoded in our brain."

This is incredibly interesting. We are tackling a very important theme in our lives. How do you form memories? And how do you keep memories? We know that so many people these days suffer from Alzheimer’s and from other forms of dementia. This is a huge problem. If one can understand with the help of sophisticated mathematics how memories are encoded and how we can retrieve them this would be an enormous advance. Naturally I am excited by the potential to help resolve this problem.

Please describe an interesting, transformative, or memorable insight or moment of discovery that you have shared with another Western Academy Scholar.

Nearly my entire adult life I was a mathematician working on some fundamental questions in mathematics, and I loved it. I was always interested in physics and [neural] connection, but I didn’t work actively in this area. I saw Lyle [Muller]’s research, and I knew he was coming [to Western], and I knew who he was, and I saw he was doing interesting research related to communications between neurons. And this interested me mathematically; I was thinking there is something which I can mathematically investigate using my interests and tools for studying various forms of symmetries and patterns.

Lyle said to me “Ján! That’s perfect! That’s amazing!”

Meeting with Lyle was absolutely crucial. It was an amazing thing. It opened the possibility of better understanding how neurons communicate together and how to decipher this communication. My research matches with his. Lyle is a broad scientist and he knows a great deal about brain function. My emphasis is on symmetry and mathematics and studying patterns, and this works well with Lyle’s goals and aspirations. This was absolutely perfect. And then we got this theme [at the Western Academy] with young people, excited and happy!

It is absolutely wonderful! From that time on, we have worked extremely closely. What we are trying to achieve is to indeed understand memories using communication patterns, and its applications to the study of epilepsy and dementia. If we can make a contribution, it would be enormous.

What has been your strangest or most unexpected research discovery?

One of the most fascinating things in mathematics and in science and art is when you can connect things that look incredibly distant and are in fact connected. Some things that seem impossible to reach, but they are in fact connected and thus approachable. It is the most strange, fantastic feeling, you know? I had a complicated immigration from the former Czechoslovakia. There were difficult conditions and for many years I tried to escape. I was stateless for years, and then I came to Canada, and I was finally able to do mathematics.

"One of the most fascinating things in mathematics and in science and art is when you can connect things that look incredibly distant and are in fact connected."

When I was studying for my PhD at Queen’s University and later as a postdoc, I found a link between Galois theory and quadratic forms that was extremely unexpected. People were very surprised. In fact, it was published [as a paper called “Witt Rings and Galois Groups” (1996)] in a mathematical journal, the Annals of Mathematics. This was my dream work with Michel Spira, who was at the time a PhD student at the University of California, Berkeley.

The Annals of Mathematics is one of the most prestigious mathematical journals in existence today. Because of its prestige and tradition, it has a reputation as the very best mathematical journal. Professor Andrew Wiles together with Professor Richard Taylor published Wiles’ famous proof of Fermat’s Last Theorem in the Annals in 1995. Just one year later in 1996, Professor Wiles [one of the editors of the Annals] accepted my joint paper with Michel Spira for publication.

This paper was precisely about this connection, which was the most unexpected discovery: the connection between symmetries and families of quadratic forms. But the point is that now we are obtaining many other connections like this; there are similar [discoveries] about symmetries in the brain. These are the most creative, exciting and dramatic times in my life.

Interview by Lindsey Bannister