Mathematics

Found in translation: Technology helps students, prof decipher 18th century mathematician's works

October 2, 2006

When the international mathematics community celebrates the 300th anniversary of the birth of famous Swiss mathematician Leonhard Euler in 2007, they’ll have additional insights into his genius thanks to the work of Rowan University students and their professor.

Under the supervision of longtime mathematics professor Tom Osler, student Lucas Willis has translated from French one of Euler’s writings, published in the 1760s. The duo’s scholarly work, which was completed this summer, has been published on a Dartmouth University web site dedicated to Euler (pronounced “Oiler”) and his work.

Another of Osler’s students, Walter Jacob, a senior mathematics major who was a two-time silver medalist in the national Latin exam in high school, is currently translating another paper of Euler’s, published in 1741 in Latin.

And two additional students, Kristen L. McKeen and Edward Greve, have just begun translating two more of Euler’s papers from French, according to Osler.

Throughout his lifetime, Euler published a remarkable 866 scholarly papers. Most of the papers, which make up a full quarter of all of the papers published in science and mathematics combined in the 18th century, are in French, Latin and German, according to Osler.

“Only about 8 percent of his papers have been translated into English,” says Osler.

To read Euler, Osler, who doesn’t speak French, Latin or German, would follow the mathematical equations and try to decipher Euler’s message.

“I was struggling with the mathematics,” says Osler. “Euler is brilliant. You have to really work at it. Because I don’t speak the languages, I would read his papers and follow them through the equations.”

Osler mentioned his Euler dilemma one Friday in class. Willis, an Honors physics and math major with a minor in French, got right to work. By the following Monday, he had completed half of the translation, Osler said.

“I thought, ‘My goodness, do I deserve students like this?’” Osler says, noting that, in some cases, what he surmised Euler was saying in the paper wasn’t what he was saying at all, according to the translation Willis provided.

Like other students currently working on translations with Osler, Willis used a PDF of the original Euler paper that was posted online to do the translation for “Remarks on a beautiful relationship between direct as well as reciprocal power series,” which was originally printed in the journal Memoires de l’academie des sciences de Berlin in 1768.

The Euler archive deems the translation “both faithful and highly readable.” The duo took the work to a higher level by including a section-by-section synopsis of the paper, which evaluates the Riemann zeta function, according to Willis.

“The Riemann zeta function has been studied intensely for the past 150 years,” says Osler. “Riemann showed that mastery of this function’s hidden structure would reveal facts critical to the branch of mathematics called number theory.

“The most important unsolved problem in mathematics today is the Riemann hypothesis, and it concerns this zeta function.”

The role of modern-day technology in accessing Euler’s 18th century work wasn’t lost on Willis, 20, who clearly relished the chance to work with Osler to uncover the great mathematician’s theories, theories he was then able to share with his delighted professor.

“Once you start thinking about it through a historical perspective, it really was kind of a groundbreaking thing,” Willis said. “First, you have this old, old text, which is tough to read. And the spelling has changed over the last 250 years.

“In my French studies, I hadn’t really learned math terms. So a lot of the words weren’t so easy to find.

“Dr. Osler is very specific about wording and he was very particular about it being clearly written,” continued Willis, a third-year student with senior standing at Rowan. “By the end of our work, I was really in awe of Euler’s whole paper.”

Osler was in awe as well.

“This translation is the result of a happy collaboration between student and professor,” Willis and Osler wrote in the paper’s preface. “Together we struggled to understand this brilliant work.”

Though he’s just begun his translation from Latin of Euler’s “Approximation to the sums of convergent series” paper, Jacob has had similar experiences thus far.

“It’s pretty amazing that, through the advent of the Internet, subjects from hundreds of years ago can be brought to light now,” says Jacob, who has his sights set on graduate school and a career as a mathematics professor. He’s hopeful he’ll be able to use his translation to teach his future students.

“These are real gems in Euler’s work that we’re uncovering. He’s such an interesting historical character.”

Though his collaboration with Willis marked the first translation Osler had accomplished with a student, it was one of an impressive 25 collaborations he’s had with students, mostly undergraduates, since 1999.

In his classes, Osler regularly seeks out students who have an interest in publishing works in scholarly journals. His collaborations with them have been published in prominent journals including the College Mathematics Journal, Mathematics and Computer Education, the International Journal of Mathematical Education in Science and Technology, Mathematics Magazine, and The Mathematical Spectrum.

For the 66-year-old Osler, who has been a full Rowan professor for a quarter-century, the thrill in the collaborations is two-fold. It’s a joy, he says, to work with students, to see them get excited about mathematics. But equally important is that students are able to make solid, scholarly contributions to the discipline, he says.

“I enjoy sharing my excitement about mathematics with good students who have enthusiasm. It magnifies the enjoyment for me immensely. It’s just a wonderful joy,” says Osler, who has taught at the university level for 45 years.

“This type of work is very important to our world of scholarship,” he continued. “And it’s an opportunity for our students to make a contribution to the world of scholarship. There’s a great need to help mathematicians communicate with each other.

“Through our collaborations, we’re thinking of new and exciting ways to deal with things taught in mathematics. And we’re writing about them. Journals are always looking for new applications.”

Like Euler, Osler, himself, is no slouch when it comes to publishing. After publishing a remarkable 14 research papers the five years after he earned his doctorate, Osler took a break from publishing until the early 1990s. Inspired, he says, by his collaborations with students, he has published 70 papers in just the past seven years.

Though he’d like to reach 100 published papers before he retires (and the lifelong runner says he has no plans to slow down), Osler downplays his exploits in mathematical terms.

“I’m up to 86,” he says. “I’m not Euler. I’m 10 percent of Euler.”