Nets Katz on skipping grades and solving problems

By Will Patel     11/19/24 10:42pm

Nets Katz has always liked numbers. As a child, he played with numbers in his head and quickly learned to add and multiply. Katz’s elementary school grouped students in classes based on test scores. However, Katz didn’t land on the top track.

Despite his parents’ anger, Katz’s placement introduced him to an ambitious math teacher — one who led him to graduate from Rice at 17 and complete a Ph.D. at 20.

“[The teacher] had a large collection of workbooks,” Katz, the W. L. Moody Professor of Mathematics, said. “I went through the entire elementary school curriculum in a year.” 

---

---

Other teachers began to notice. In fourth grade, a high school teacher who coached the math team contacted him. 

“[The math coach] said, ‘I’ve got to have this kid,’” Katz said. “He worked out an arrangement where I would do an independent study in math … at the high school and hoped I would start going to contests.”

Katz’s parents were skeptical about math contests, so he didn’t try one until sizth grade. Ultimately, the competitions were the catalyst that moved him quickly through school.

“I competed in the lowest grade level that I could, which was ninth grade,” Katz said. “When they discovered I was [younger], I was disqualified. But when my school heard, I got a battlefield promotion …  to ninth grade.”

After finishing high school in Grand Prairie, Texas, Katz graduated from Rice with a bachelor’s degree in mathematics. Despite being younger than his peers, Katz enjoyed his experience.

“I found the town where I [grew] up not so intellectually stimulating,” Katz said. “But at Rice, I looked up to my peers. They were people I wanted to talk to. It was exciting.”

Katz graduated from Rice in three years and then received a Ph.D. in mathematics at the University of Pennsylvania. Afterward, he began teaching undergraduate mathematics and working on various research projects, specializing in analysis and combinatorics.

“I’m interested in problems that can be approached with bare hands — problems that have to do with counting things, but where one doesn’t necessarily need exact answers, where it’s alright to have estimates,” Katz said.

In 2015, Katz won the Clay Research Award with Massachusetts Institute of Technology’s Larry Guth for their solution to the Erdős distinct distances problem. In 1946, mathematician Paul Erdős posed the question, aiming to find the minimum number of distinct distances possible between a set number of points in a plane. Almost 70 years later, Katz and Guth proved a solution.

While teaching calculus at the California Institute of Technology, he wrote a book, Calculus for Cranks, which emphasizes practical applications of calculus for scientists and engineers. Katz said the ideas behind his research flow through his classes.

“I want [students] to think analytically,” Katz said. “I present them with a problem, and what [I] want them to do is think about the sources of errors and … break them out and separate them through different techniques.”

After teaching at California Institute of Technology as the IBM Professor of Mathematics, Katz returned to Rice and joined the department of mathematics in 2023.

Yitang Chen, a student in Katz’s MATH 221 class, said he is a helpful professor.

“Though his course is challenging, it is helpful to my math skills,” Chen, a Wiess College freshman, wrote in an email to the Thresher. “I have gone to his office hours [to ask about] some theorems I did not understand ... and he explained them in detail.”

Katz said he looks forward to directing undergraduate research projects at Rice.  

“I’m not very good at staying in one place forever,” Katz said. “And a friend of mine, David Fisher, had been hired here, and … it sounded very exciting. I enjoy directing undergraduate research. I’m really happy when students show interest in that, and [Rice] has resources that lead into research like the directed reading program.”

---