Patterned symmetry

When most people glance at wallpaper, complex mathematics is probably not the first thought that springs to their minds. But Prof. Daniel (Dani) Wise, a newly hired scientist in the Department of Mathematics, is far from typical. Using the analogy of wallpaper patterns, Prof. Wise explains the considerably knottier mathematical field of geometric group theory—a fascinating subject that explores repeating patterns in complex spaces. 

“Imagine a room decorated with patterned wallpaper,” he posits. “The design—whether it’s animals, flowers, or abstract shapes—repeats itself in a regular way. And one can work out, mathematically, the rules that govern this pattern.”

While wallpaper patterns are relatively simple, confined to the flat, two-dimensional world, Prof. Wise studies far more complex patterns, or groups, which exist in intricately twisted, curved, and higher-dimensional spaces. These patterns stretch beyond the familiar geometry of our everyday world, challenging our understanding of space itself.

Cube collection

Early in his career, Prof. Wise began developing a novel approach to studying geometric group theory, one that would prove to be a breakthrough in the field. He was able to break down the complicated patterns into simpler blocks by taking a section of a group and reimagining it as being composed of “cube complexes”—a collection of high-dimensional cubes. 

“It’s like solving a difficult puzzle by breaking it into manageable pieces, which then reveals a greater underlying order,” he explains. “As I continued working on my idea and building it up, and as it got more and more complicated—for a long time, nobody understood what I was talking about. When they finally did, they said it would never work, that it couldn’t be true.”

Prof. Wise’s perseverance paid off when everything began falling into place, leading to a series of significant papers co-authored with colleagues. His cube complex approach provided a groundbreaking way to simplify and organize these complicated patterns and enabled mathematicians to understand the enigmatic world of 3-manifolds, a key area in modern mathematics. 

A 3-manifold is a space that appears three-dimensional when you zoom in to any point. Imagine the air around a knotted rope or even the universe itself—both are examples of 3-manifolds. From an external perspective, the universe may seem to have a curved and finite shape. However, for anyone inside the universe, it feels like ordinary 3D space—flat and infinite in all directions, regardless of its overall structure. 

A new home

Now at the Weizmann Institute, Prof. Wise is eager to continue exploring these mathematical ideas and to seek collaborations that may bridge the gap between abstract theory and practical innovation.

“Being at Weizmann is such an amazing opportunity,” he says. “I feel as though I have all these avenues open to me for exploring deep questions and forging connections with amazing scientists from different disciplines.”

Moving to Rehovot marks the culmination of years of longing to live and work in Israel, a country that has always felt like a second home. His wife, Yael—an Israeli professor of English and Jewish Studies—shares his strong ties to the region, and their family has often divided their time between North America and Israel. Over the years, they have spent three sabbaticals in Israel, the last of which was immediately after the beginning of the war when Prof. Wise was at the Weizmann Institute as a visiting professor. Now, two of their four children live in Israel as well.

Love for the land

When he came to Rehovot, he recalls thinking, “This is it. The environment at Weizmann is incredible—the students I’ve worked with are exceptionally talented and eager to learn. It’s inspiring to teach young people at the start of their careers, knowing they’ll go on to do amazing things. And not to mention, I’ll never need to buy citrus ever again!”

Though raised in New York, Prof. Wise’s roots in Israel run deep. His mother is Israeli, and his grandfather founded, alongside David Ben-Gurion, the International Bible Contest (“Chidon HaTanach”)—a worldwide competition on Jewish biblical texts for middle school and high school students. His grandfather was also among the pioneers of Kibbutz Tirat Zvi in the Beit She’an Valley, founded in 1937 in pre-state Israel. 

These connections have instilled in him a profound sense of belonging and a love for the land and its people, and he is determined to immerse himself in the language and culture: “Though English is my native tongue,” he says, “I insist that my colleagues at Weizmann speak to me only in Hebrew. If they don’t, I’ll respond in my terrible French!”

Education and select awards

• BA, Yeshiva University (1991)
• PhD, Princeton University (1996)
• Postdoctoral Fellow, University of California, Berkeley (1996-1997)
• The E. H. Moore Research Article Prize (2022), awarded by the American Mathematical Society (AMS); Lobachevsky Medal from Kazan State University, Russia (2019); CRM-Fields-PIMS Prize (2016), the premier Canadian research prize in mathematical sciences; Guggenheim Fellowship (2016); the Canadian Mathematical Society’s
• Jeffery-Williams Prize (2016); the Oswald Veblen Prize in Geometry, awarded by the AMS (2013); Fellow of the Royal Society of Canada (2014) and Fellow of the Royal Society of London (2018).

Appointments

• Assistant Professor, Cornell University (1997-2000)
• Visiting Assistant Professor, Brandeis University (2000-2001)
• Assistant Professor, Associate Professor, and Full Professor, McGill University (2001-2024)
• Visiting Professor, The Hebrew University of Jerusalem (2008-2009), Technion-Israel Institute of Technology (2016), Sorbonne University (2022), Weizmann Institute of Science (2023)