Columbia Mathematics Professor Mohammed Abouzaid has been named a 2017 recipient of the prestigious New Horizons in Mathematics Prize. The $100,000 award recognizes the achievements and raises the profiles of early-career physicists and mathematicians.

“We’re thrilled,” said Columbia Mathematics Chair Henry Pinkham. “Mohammed works in a very important area of mathematics. This award is further evidence that he’s a star in the field around the world and it brings a lot of prestige to the math department here at Columbia.”

Abouzaid, who joined Columbia in 2012, studies subfields of mathematics known as topology and geometry. Topology is the study of geometric properties and spatial relations that are not affected by the continuous change of shape or size of figures. In other words, topology is the study of the shape of space. Geometry studies the relative arrangement of objects in spaces using quantitative measurements such as angles and distances.

“Basically, I study topological objects using geometric techniques,” Abouzaid said, adding that a simplified example of his work is finding ways to measure objects, such as a coffee mug or a donut, with the techniques one would use to measure objects with a more geometric shape.

Abouzaid’s research focuses on symplectic topology. In symplectic topology, one puts a rich and interesting extra structure on a space, which opens up many more ways of studying it via geometric tools. This structure is closely related to ideas in physics that arise from studying the behavior of atoms and other elementary particles. Abouzaid’s work contains new insights into this subject and its relation with both physics and other areas of mathematics.

"Certain patterns just exist and we try to understand them for their intrinsic value without having in mind how they might have an impact on society or what practical applications they might have in the next few years or decades,” Abouzaid said. “Trying to explain why I study mathematics is like trying to justify other artistic pursuits. The great range of modern-day applications of mathematics to real-world problems has grown out of centuries of such inquiry by men and women who pursued the mysteries that arise in mathematics and studied them for their aesthetic beauty. I hope that future generations will view the work I and my colleagues are doing in a similar light."

Abouzaid received his Ph.D. from the University of Chicago in 2007 and was subsequently a Research Fellow of the Clay Mathematics Institute from 2007 to 2012, during which time he was also a postdoctoral fellow at MIT. He joined Columbia as an associate professor of mathematics four years ago.

He is one of four mathematicians to receive the New Horizons in Mathematics Prize this year from the Breakthrough Prize Foundation, founded by Sergey Brin of Google; Anne Wojcicki of 23andMe; Jack Ma of Alibaba and his wife, Cathy Zhang; Yuri Milner, an internet entrepreneur, and his wife, Julia Milner; and Mark Zuckerberg of Facebook and his wife, Priscilla Chan. Now in its fifth year, the Breakthrough Prize – Silicon Valley’s munificent science prize – honors paradigm-shifting research and discovery in the fields of fundamental physics, life sciences and mathematics. Across all categories for this year, the foundation awarded $25 million to honor both outstanding career achievement and emerging talent.

*—By Jessica Guenzel*