Arithmetic of curves, network for women in number theory earn Rachel Pries national honor

Asking Rachel Pries to choose her favorite prime number would be like asking someone to choose between their pets or their children. She loves them all so.

Rachel Pries
Rachel Pries, professor of mathematics

It’s this deep-seated passion for the fundamental theory of numbers that has propelled Pries, professor in the Department of Mathematics at Colorado State University, to the title of Fellow of the American Mathematical Society. The society named Pries among its 63 newest fellows earlier this month.

“I love my work, and I can do the work that I love – that’s such an amazing thing to be able to say about your life,” said Pries, who joined the CSU faculty in 2003.

As an American Mathematical Society inductee, Pries was honored “for contributions to arithmetic geometry, and for service to the mathematical community.”

Arithmetic geometry

Pries’s research is a hybrid of number theory and algebraic geometry. Broadly, she studies shapes and symmetries, and the algebraic equations that describe those shapes. In particular, she studies sets of curves, or what’s called moduli spaces of curves. “You can think about the geometry of an equation, but you can also think about the geometry of the moduli space,” Pries said. “It’s like a whole universe that’s keeping track of these different equations.”

She sees numbers not as complex or real – as most people do – but more like numbers on a clock, where after 12, you’re back at 0 again. This is known as modular arithmetic.

Modular arithmetic falls under number theory, which includes the study of prime numbers and their properties. A prime number is an integer greater than 1 with no positive divisors other than 1 and itself. So that’s 2, 3, 5, 7, 11, 13, 17, etc. (According to Euclid, there are infinitely many prime numbers.)

Women in Number Theory

The AMS citation also honors Pries’ work in bringing women in mathematics into closer partnership across the world. In 2008, she was instrumental in launching a community called Women in Number Theory that organizes scholars into research collaborations through conferences and other events. The group has evolved into 200 to 300 women working together to make breakthroughs in the field of number theory.

“For me the investment was huge, but I also feel that I’ve benefitted enormously both from making friends, and by being able to develop new research directions I would not have been able to do individually,” Pries said of the effort.

Pries’ formal induction ceremony will take place in January at the Joint Mathematics Meetings in San Diego.