For Western professor Ján Mináč, “there is no greater joy than understanding something that looked mysterious before.”
And Mináč’s been experiencing – and spreading – joy throughout his career, as a globally renowned expert of Galois theory, an area of mathematics that studies the relationships between groups of numbers and generalized numbers and how they can be transformed or rearranged.
Ján Mináč (Keri Ferguson/Western News)
His research, advancing how certain groups of numbers (called fields) relate to each other through their symmetries (called groups), allows researchers to deeply understand solutions of algebraic equations and differential equations. This theory also allows scholars to study large data efficiently.
There are many applications of this theory in mathematics, physics and chemistry, with promise of further application in a number of new areas, including neuroscience and artificial intelligence. Here, Galois theory may reveal patterns that might not otherwise be evident.
Mináč’s outstanding contributions in mathematical research will be recognized this June, when he receives the Jeffery-Williams Prize, the highest research honour awarded annually by the Canadian Mathematical Society (CMS).
Being selected as the 2025 recipient is a “huge and humbling” experience for Mináč.
“The people who won before me are larger than life, they’re my heroes,” he said. “It is a great honour, not just for me, but for my wonderful collaborators, students and our entire team.”
It’s also a win for Western. Mináč is the first Western researcher to earn the prestigious prize, which was created in 1968 to honour Ralph Jeffery and Lloyd Williams, two influential CMS board members. The inaugural prize recipient, Irving Kaplansky, was one of Mináč’s early mentors at the Mathematical Sciences Research Institute and in the department of mathematics at the University of California, Berkeley, where Mináč trained as a postdoctoral fellow.
Mináč’s colleague in the department of mathematics, professor Chris Kapulkin is also being honoured by the CMS. Kapulin’s work in homotopy theory is being recognized with the 2025 Coexter-James Prize, which was last awarded to a Western faculty member in 1992, when current professor emeritus Rick Jardine received the award.
Guided by Galois
Mináč’s interest in Galois theory started with a story he read as a young boy, growing up in the former Czechoslovakia. It was the biography of Évariste Galois, a young French mathematician and political activist, who made the groundbreaking discovery of group theory, confounding his older contemporaries.
Before his tragic death at the age of 20, in a duel over a woman, Galois developed a way to understand the hidden patterns and symmetries in numbers, solving a longstanding problem of understanding solutions of polynomials of degree larger than or equal to five. Reading about this dramatic discovery had a profound impact on Mináč, leaving him hungry for more information.
At the time, it was difficult to obtain the original works of Galois. After a lot of hard work and determination, Mináč eventually had the collected works of Galois shipped from Paris.
“From that time on, I fell in love with Galois theory,” Mináč said. “It is extremely beautiful and powerful, with many open questions. For mathematicians, questions are very important.”
Professor Ján Mináč’s “contagious energy, generosity in sharing ideas and ability to engage and inspire others” was noted in his nomination for the Jeffery-Williams Prize, awarded annually by the Canadian Mathematical Society. (Mitch Zimmer)
Using math to unlock mysteries of the mind
Galois theory remained top of mind for Mináč while he earned his bachelor’s and master’s degrees in mathematics from Comenius University in Czechoslovakia. It then became the focus of Mináč’s doctoral research when he emigrated to Canada to attend Queen’s University, in Kingston, Ont. to study with well-known Canadian mathematician Paulo Ribenboim. There, Mináč made an unexpected and important discovery about the connection between families of quadratic forms and certain Galois groups, which are sets of symmetries. In this way, he discovered new vocabulary and a novel way of studying both quadratic forms and Galois groups.
Mináč continued his groundbreaking work at Berkeley, where, with Michel Spira, he extended his previous work in a unique way. Their work was later published in influential mathematical journals, including the Annals of Mathematics. This paper was published in 1996, one year after Andrew Wiles and Richard Taylor published their famous proof of Fermat’s Last Theorem in the same journal.
In 1989, Mináč joined the department of mathematics at Western, where he made further important contributions, including studying how certain mathematical tools called Massey products, influence the structure of absolute Galois groups.
In 2012, Nguyen Duy Tân came to Western as a postdoctoral fellow, working with Mináč. Together they listened to a lecture by American mathematician Kirsten Wickelgren and shortly afterwards, they made the discovery about an extension of her work with Michael Hopkins. This discovery led them to further develop the theory of Massey products in Galois cohomology.
“This is a beautiful concept which borrows the ideas of algebraic topology to Galois theory,” Mináč said.
Along with Tân, Mináč proposed a new conjecture, now known as the Mináč-Tân Conjecture. This conjecture was proved in a number of cases by Mináč and Tân and several other researchers. In each case, where this conjecture was proved, researchers are gaining new insights into the mysteries of absolute Galois groups.This conjecture is still not fully proved, which is exciting for Mináč, as the research continues.
A two-time recipient of Western’s Distinguished Research Professorships, Mináč’s contributions have resulted in more than 115 publications in esteemed academic journals.
In 2022, he was chosen as an inaugural fellow in the Western Academy for Advanced Research alongside Lyle Muller and Marieke Mur, working under the theme of computational neuroscience.
Mináč’s expertise in sophisticated mathematics aligns well with Muller’s background. Together, with Muller’s team, which includes Alex Busch, Roberto Budzinski and Tung T. Nguyen, they are making progress developing novel methods of studying dynamical systems related to networks. Their joint work includes studying how memories are encoded, holding promise for a better understanding of Alzheimer’s and other forms of dementia.
“This is such interesting and important work. How does one keep their mind healthy? Dementia is such a concern. If there is anything we can do to better understand and help, that would be incredible,” Mináč said.
‘It’s the climb’: Inspiration through collaboration
Working across disciplines with colleagues and students has been a rewarding experience for Mináč.
“I love collaborating. It is amazing. It allows you to speak, share ideas and clear your mind.”
The process, he said, is like mountain climbers scaling a summit together. “You get one step up and there’s someone there to help you climb further.”
And Mináč is in the perfect position to lift the next generation, with his “contagious energy, generosity in sharing ideas and his ability to engage and inspire others.”
Those traits, noted by his Jeffery-Williams award nominators, also helped him earn the 2013 CMS Excellence in Teaching Award and two University Students’ Council and Alumni Western Teaching Awards of Excellence. He also was a recurring recipient of Western’s Teaching Honour Roll Awards of Excellence from 2007 to 2018.
Coming from a family who embraced the arts, it’s not uncommon for Mináč to thrust students into a scene from Shakespeare or Sherlock Holmes, embedding mathematical concepts into stories that engage, inspire and enhance learning.
“Professor Mináč’s insights and understanding of the structure of absolute Galois groups make learning a wonderful experience, because of the depth of his knowledge and the flexible approaches he uses to understand a problem. Watching him work is like watching a magician; what looks like an ordinary hat will suddenly turn into something unexpected and exciting.” -nominator, Jeffery-Williams prize submission
Students and younger researchers have an equally powerful effect on Mináč.
“I feel energized working with young collaborators. We are making breakthroughs, but we are not at the final breakthrough, which is exciting. This work is opening gates for many other fascinating explorations. The story’s never-ending.”
