a² + b² = Ibbotson²

He can be found in his classroom in the basement of the Academy Building drawing the loxodromic spiral in complex analysis on a blackboard, wearing a fez or throwing board markers. He can also be seen lamenting the lack of sushi with his students in front of Wetherell Dining Hall. From the intellectual, to the random to the downright wacky, math instructor Jeff Ibbotson does it all.While completing a dual major in math and physics at the State University of New York at Buffalo, Ibbotson described how blowing up a physics lab in his third year felt like the subject was calling to him. From there he fell in in love with real analysis.“So that was it,” Ibbotson said. “I followed it and it seemed like almost everything else I could learn by myself- I could go to the library, I could read books, I could learn the history, but math really seemed to be something that you needed some level of instruction so the further I went the further I discovered how fascinating the ideas were.”Ibbotson graduated early, finished his undergraduate degree work in three and a half years and almost immediately accepted the position of graduate assistant. However, he was discouraged by his students’ apathetic attitudes towards the subject he loves teaching—abstract algebra and real analysis. He recounted spending most of his time speaking in large lectures, not having as much contact with students as he would have liked.“The students didn’t feel the same way as I did about [abstract algebra and real analysis], they really disliked them, and even though they learned to enjoy them eventually, it was hard,” Ibbotson said. “For me I felt like I spent most of the time speaking in large lectures, and I wasn’t having as much contact with students as I would have liked to.”Although during these years Ibbotson was living in Exeter, without knowledge of the academy. “Someone told me there was this school up the road. So I sent them a letter and here I am,” he said simply of his arrival at the Academy.“I often pinch myself about how lucky I am to teach strong students and people who are interested in learning,” Ibbotson said. “What we do in terms of Harkness teaching forces students to select themselves as people who are engaged in talking about ideas and really think deeply about stuff. That is all I have ever wanted—to be able to teach such students.”Fellow math instructors spoke of Ibbotson’s aptitude in the field of advanced mathematics and the positive influence on the mathematics department.“Mr. Ibbotson is a very collegial member of the department. He is well informed, he reads widely and voraciously. He is a very capable mathematician, well versed in many aspects of the subject,” math instructor Phillip Mallinson said.Math department chair Eric Bergofsky expressed similar sentiments and complimented Ibbotson’s wide range of knowledge. “He is a top-level mathematician. He has a PhD in mathematics, and he has a huge base of knowledge across a lot of areas,” he said. “He has brought that expertise to us in the department by teaching at all levels, but particularly at the highest levels, like the 500 and 600 range.”“Mr. Ibbotson has broad intellectual interest, and in our department, his expertise about the history of mathematics invariably works its way into our discussions,” math instructor Richard Hardej said.Students used a plethora of words to describe classes with Ibbotson, from funny and helpful to interesting.“I especially liked the fact that Mr. Ibbotson was a playful teacher after a student had finished presenting a correct solution,” Dai Yang ‘12, who took four advanced math classes with Ibbotson, said. “He would not hesitate to change the parameters of the problem and ask questions that would lead to insightful generalizations of the problem we had just solved.”Lower Alex Wei agreed and said that even Ibbotson’s digressions are insightful. “His classes are always fun; there’s always unexpected and exciting to look forward to,” he said. “A lot of times he talks to us about interesting aspects of math; even though it’s going a little off-topic, I still find those discussions interesting. I want to have him as a teacher for more math classes, maybe game theory.”The learning environment— which includes a paper bat, self-selected quotes and two full shelves of books, reflects Ibbotson’s eccentric and thoughtful personality.“He is always passionate and very knowledgeable, and equally fun loving and energized about life,” Hardej said. “Conversations with Mr. Ibbotson invariably include the serious and not so serious; he can be zany and irreverent, but also introspective.”Ibbotson noted how much math means to him and the extent to which he has changed during his 18 years of teaching at the Academy.“To me math means a way of looking at the world — looking at the world through a certain set of lenses — being able to use quantitative patterns as well as qualitative ones. And really at this point in my life almost everything I see or do is related to math,” Ibbotson said. “So I have become math, in some way.”“I think teaching at Exeter has really opened my eyes about looking at problems. I now have a much more open mind,” Ibbotson added. “I see what students are capable of reasoning without having all these tools- without even having the algebraic facility and still figuring it out. So it has changed for me—I started doing algebra in my head and really thinking deeply about what’s really involved in the questions. I am just trying to find the simple purpose of the problem and go on from there.”