A Puzzling Professor

Byron Walden, an assistant professor of mathematics at SCU, draws on his knowledge of numerical analysis to create crossword puzzles for The New York Times.


A love of words adds up to a hobby as a crossword puzzle creator

While crossword puzzles may seem more the domain of a wordsmith than a math whiz, SCU Assistant Professor of mathematics Byron Walden has used his knowledge of number analysis to fashion a hobby as a creator of newspaper puzzles.

“My grandmother and dad were crossword enthusiasts, so I got started as a kid. I specifically remember my dad letting me help him on one for the first time, when I was about 7.”

“The process of constructing the puzzle is somewhat more mathematical in that you look at the letters as symbols and you consider various combination probabilities,” says Walden, who did his undergraduate studies in mathematics at Vanderbilt University and earned a doctorate in math from Yale. “For example, if you’re deciding between using AMEN and XMEN, you have to be thinking that there are more crossing words that have an A than an X. On the other hand, if that were the last letter of the crossing word, the number of options with the two letters is a bit more even.

“If possible, I’d try for XMEN anyway,” muses Walden, “since the word is more interesting.”

As of May, Walden has had three puzzles published in The New York Times—the first in 1997 and the other two this year. He’s also had several published in The New York Sun, the daily newspaper most famous for the “Yes, Virginia, there is a Santa Claus” editorial. Many of the Times’ puzzles and all of the Sun’s get republished in book form eventually.

Walden says his love of crossword puzzles developed at a young age. “My grandmother and dad were crossword enthusiasts, so I got started as a kid,” he says. “I specifically remember my dad letting me help him on one for the first time, when I was about 7. The first entry was a five-letter word for ‘salty water.’ I wrote in ‘OCEAN,’ but my dad saw that the correct answer was ‘BRINE.’ I remember being very annoyed at the puzzle, since ‘OCEAN’ seemed fine to me. I suspect that annoyance was what got me interested.”

Like most crossword constructors, Walden works on a freelance basis, submitting his puzzles to an editor. That person will change some of the clues and the answers to achieve a desired level of difficulty and to avoid repetition of clues from recent puzzles. The Times pays $100 for a daily puzzle and the Sun—”not coincidentally,” Walden says—pays $101. “Those are at the high end of the scale,” he adds.

“These days, the words that go into crosswords are often generated by a computer working from a large list of words to find ones that fit,” he says. “For people who do this for a living, the art is in developing a good list of words and finding good clues. I’m just a hobbyist, so I fit words in by hand-metaphorically, that is—since I do type on a computer.”

While some puzzles have themes, Walden’s favorites to construct and solve are the themeless puzzles. “I either start with words with interesting letters and/or interesting clues and try to make a nice grid—the fewer black squares the better,” he says.

At Santa Clara, where Walden has taught since 1997, his primary research interest is in complex analysis, which he describes as “calculus using complex—that is, real and imaginary—numbers. I use complex analysis as a tool to get information about the geometry of planar figures.”

For the past three years, Walden has served on the questions committee for the Putnam Exam, the nation’s most prestigious college math exam. Since the late 1970s, the distribution and grading of the Putnam has been administered at SCU and directed by Professor Leonard Klosinski.

Walden says he does not bring his hobby into the classroom. “There’s a bit too much in the curriculum to cover for that,” he says. But he does offer advice on how to be a better puzzle solver. “Many newspapers follow the convention that Monday puzzles are easiest, increasing in difficulty until Saturday,” Walden says. He suggests that the advice of fitness trainers can come in handy. “Repetition until failure. Pretty soon, you’ll be able to get through the whole week.”

Adam Breen is the editor of Santa Clara Magazine

A printer-friendly version of the online crossword puzzle is also available.

To complete the crossword puzzle, print out this page and fill it in as best you can. When you are ready to check your answers, click on the purple box below that says Answers.

Always Turn Toward the Sun

How has the pandemic affected what kids know? SCU’s Kirsten Read is researching what happened when less people read to our kids.

Trauma Paves the Way

Can we stop poor outcomes by tracing trauma’s path in the brain? SCU’s Lindsay Halladay wants to map it.

What We Don’t Know

Clinical Professor of Law Thiadora “Dori” Pina has made it her mission to mentor and empower first-generation students at the law school.

Generation Un-Grind

Now that hustle culture has crashed and burnt us all out, how are young people viewing their future work?