Balancing Math Breakthroughs and Motherhood: An Inspiring Journey

When the Wolf Foundation recently announced the recipients of the 'Krill Prize' for young and promising Israeli researchers, many were surprised that one of the winners was Dr. Chaya Keller, a mathematician from Ariel University. Beyond her prestigious role, she is also a mother of 11.

For those who know Chaya closely, this is no surprise. She has made groundbreaking contributions to geometric mathematics globally but believes this does not conflict with raising her own children. Yes, she has a family life and a husband who also works in mathematics, in closely related fields.

A Mathematical Path

"Currently, I live in Jerusalem," Keller introduces herself. "As a child, I attended 'Noam Bnot' school in Kiryat Moshe and then continued at Horev Ulpana. I studied for my bachelor's degree in mathematics and computer science at the women’s Jerusalem College in Beit Hagan and pursued my master's and doctoral degrees at the Hebrew University. I did my postdoctoral research at Ben-Gurion University and the Technion, and since 2019, I've been a faculty member at Ariel University."

Interestingly, Keller did not feel a particular connection to math during her childhood and preferred literature and creative writing classes. "During my teenage years, especially in the high school, I started to be drawn to the exact sciences, particularly mathematics," she shares. "A central figure that influenced me was my high school math teacher, David Tzchor, who shaped generations of students and showed us the beauty of mathematics beyond what was required for the matriculation exam."

What does combinatorial geometry involve? Can you elaborate on that?

"Certainly," says Keller, clearly enjoying her professional work. "It is a field that deals with geometric objects like points, lines, spheres, and more, and the possible connections between them."

To simplify the topic, Chaya chooses to discuss a specific problem she tackled with partners – the 'Ringel Problem.' "Over 200 years ago, cartographers discovered that a world political map could be colored using just four colors, ensuring that two bordering countries never share the same color. Mathematicians hypothesized that this property isn't unique to our world's borders but applies to any planar map. This was confirmed, but it took nearly 200 years to prove: only in the 1970s, thanks to computers, mathematicians Appel and Haken from the University of Illinois formally proved it."

Keller emphasizes that such problems interest not only map colorists but are also relevant in many other fields, like frequency assignment for cellular antennas, task distribution among processors working in parallel, and more. Consequently, in recent decades, many researchers have been interested in coloring problems where other objects, not just maps, are colored. "One of the most famous challenges was posed by German researcher Gerhard Ringel in 1959. He asked: 'How many colors are needed to color any group of tangent circles, ensuring that two intersecting circles have different colors?'"

"Researchers soon realized that four colors were insufficient but hypothesized that five might suffice. However, this problem remained unsolved for over 60 years. Recently, in a joint project with four other researchers from various global universities – Prof. Shakhar Smorodinsky from Ben-Gurion University, Ph.D. student James Davis from the University of Waterloo in Canada, Dr. Linda Kleist from the Braunschweig University of Technology in Germany, and Prof. Bartosz Walczak from Krakow University in Poland – we found the solution. Interestingly, the hypothesis was incorrect: not only are five colors inadequate, but even a million colors wouldn't suffice. We demonstrated that no finite number of colors is enough for every set of such circles. To prove this, we constructed a series of examples – circle arrangements that cannot be colored with five, six, or even seven colors. These arrangements can be described mathematically but not demonstrated in reality, as even the setup needed to prove five colors are insufficient contains more circles than there are particles in the universe."

What is the Krill Prize you were recently awarded?

"The Krill Prize is awarded annually by the Wolf Foundation to young Israeli researchers from research universities in Israel who achieve significant breakthroughs in the fields of exact sciences, life sciences and medicine, engineering, and agriculture. The award is a significant professional milestone in the academic progress of the researcher, so it carries much prestige in Israel’s research academia," Keller explains.

First and Foremost, I'm a Mom

As a professional, you're also a mom of 11 kids. How do you balance work and home life? What's your secret?

"I don't believe there's a single best answer to this question, not only because different people have different needs but because even for an individual, the answer varies over time and different life stages. Of course, there are times when family matters take time and mental space away from research, and times when research occupies thoughts even beyond working hours.

"From experience, I learned it's not worthwhile to try working when the kids surround me at home because it's often just frustrating and usually unsuccessful. So, I try to work in the morning when the kids are at school or in the evening after the little ones go to bed. On days when I teach at the university, I stay in the office after classes to work, and during those times, my husband is with the kids. Throughout my academic journey, I felt I had great divine assistance, and things worked out much better than I expected. There were also times I almost gave up on continuing in academia, and it was my husband who encouraged and supported me, believing more than I did that it was worth continuing and there was no reason to despair."

Do you think your children have paid a price for your professional engagement over the years?

Surprisingly, my field of work is quite convenient for a mom of kids. The amount of teaching hours, both as a faculty member and during my Ph.D., is significantly less than a teacher's, for instance, and aside from occasional work meetings and attending one or two seminars, almost all work can be done from home. Even during my studies, starting from my master's degree, the number of frontally taught hours per week was quite small. In reality, on many days, I work from home all day, and so I can be with the kids from when they come home from school until they go to sleep. Of course, this isn't the case in every academic field; it's unique to my area, which doesn’t require lab presence, etc., and also the manner of working with colleagues I’ve worked with over the years. I see this as another piece of the special divine assistance I was fortunate to receive.

Keller speaks calmly and collectedly, which leads me to think this might be the secret. When I press on what is still challenging about the work, she ponders slightly before responding: "Unlike many professions where you stop thinking about work once you get home until the next morning, research can occupy thoughts for prolonged periods, regardless of standard work hours. However, I don't see this negatively, as it's part of the charm and experience of research. On the other hand, sometimes it can be burdensome when it clashes with life commitments and mental space for the kids."

Mom, Career, Kids

How do your kids view your work? Are they aware of what you do? Do you share it with them?

"The kids are interested, as expected, in significant milestones in my spouse's and my progress – like completing a Ph.D., obtaining a position, promotion, and interesting anecdotes from professional life. They are less interested in the mathematical research itself, even in those parts simple enough to explain to non-professionals.

"I don't see special importance in sharing the details of my research and work with the kids if they're not naturally interested, nor do I see any reason for the kids to lean specifically towards mathematics or related subjects. On the contrary – we aim not to push the kids in a specific direction and allow each child to find their unique role in the world based on their passions and skills. In the meantime, it doesn't seem like any of our children are heading towards mathematical research.

"By the way, my husband's and my research areas aren't very far apart, so we have the pleasure of sharing not just the final results but also the details of the research. Once, during the Corona lockdown, we collaborated with five colleagues through Zoom from different universities. It was a bit challenging with all the kids at home, and some geometric models we built from LEGO bricks as part of modeling the problem we were working on became a fascination for our kids at that time."

What tip can you give mothers wanting to advance their careers but are concerned about family impact?

"It's hard to believe there's one piece of advice suitable for everyone, but I can say that when I faced decisions where there could be a conflict between academic progress and family, I tried to think from a perspective of two, five, or even decades down the line: what will I think in the future about the decision I have to make now? Which of my choices hold long-term value, and which are just temporary challenges? I think this perspective sometimes helped me make decisions that I later was glad I made, and of course, the most important advice for any mother – be content with yourself and your choices, undoubtedly driven by the desire to do the best."