Gallian, Joseph

Joseph A. Gallian

Adam  J. Kucera

Intro

Born to the parents of a glass factory foreman and a waitress in small town Pennsylvania in 1942, Joseph Gallian  (commonly called Joe)  was never a person meant to go to college. However, after working for three years in a  glass factory,  Joe  enrolled in college.   After successfully completing his undergraduate and doctoral degrees, Joe  moved on to  find a position teaching. After sending applications all across the country, Joe eventually landed at the University of Duluth.  From here he has built one of the most prestigious undergraduate mathematics research opportunities in the country as well as contributing greatly to the mathematical community in the form of mentoring.  Joe  currently lives and works as the chair of the mathematics department in Duluth,  Minnesota.   He is continuing to mentor some of the best mathematically minded undergraduate students in the country.

Early  Life

Joe Gallian describes himself as a class clown throughout his childhood. He often did poorly in most of his classes, but generally excelled in the course that he liked (mainly mathematics) [3].  Although  he barely graduated high school, Gallian  says that  he had a fantastic high school math education. He credits all of his success in high school to a product of his generation. He says:

“My math teachers were outstanding . . . my generation had the great advantage that there weren’t many opportunities for women except in teaching and nursing. . . . That  meant that people like me had the benefit of women who might have joined [other] professions becoming great teachers” ([3]).

Throughout his high school career he often hung out with the neighborhood kids. After

high school, however, most of his friends went on to college. This option was never much of a thought for Gallian,  however, because his father had already secured him a position at the local glass factory that he worked at.  After working for three years, however, he was called to go into the factory and be a ’breaker’. This job required the worker to stand under a large sheet of glass as it was stretched and then break it off at a scored location. This job payed extra, but there was often injuries.  After being trained on a newer machine, Gallian  told himself that he was going to be OK  with breaking. The next day, however, he was no longer in training and seniority dictated that he work on the oldest, and most dangerous machine. After breaking for three hours on his own, Gallian  experienced the worst thing that  could

happen to a breaker, the glass exploded.  The glass shattered, leaving Gallian  holding one piece, the other in free fall like a large guillotine. Luckily,  Gallian  was not seriously injured during this accident, but he realized just how dangerous breaking was.  He called over the foreman and recalls the following exchange:

. . . I called the foreman over and said, ”I’m  leaving–I’m going home. He said, ”You mean you're not even finishing your shift?”;  and I said, ”I'm  going home.”  He said, ”If  you walk off, you lose your job.  Do you realize this?”  And I said, ”I’m  going home and”–here’s the exact quote–’I’m not a married guy; I want all my parts.  I don’t want to lose any fingers or kneecaps–I want all my parts!”  It  was kind of morbid.  Say  someone lost a kneecap; the rst thing he would do is figure out how much he’d get.  You got paid if you got injured; an eyeball might be worth $5000, a finger $1500. They  had a formula.  I said, ”I  don’t want any $5000 or $1500. I want all my parts”  ([3])

Coming home four hours earlier than planned, Gallian’s father immediately knew some- thing was wrong.  He immediately became incredibly angry.   His father had never had a job outside of the factory,  and in that  time no connections almost always meant no job. In an attempt to diffuse the situation, Gallian  threw out the only thing he could think of,

”how ’bout if I go to college?” [3]. The result surprised even Gallian.  His father immediately calmed down and called the factory to say that he wasn’t going to be coming in the following day.  The next day Gallian and his father drove up to Slippery Rock College, where three of his best friends were in their 4th year. With only just graduating high school, Gallian wasn’t sure if they would admit him.  However, after sharing his experiences  in the glass factory, the admissions person surprised him.  They let him in on probation [3].

The college didn’t have any dorm space, but through an advantageous connection forged by his mother, his landed in an off campus house with two senior math majors. This math majors, it turned out, encourage Gallian  to become interested in higher mathematics.  Not because they were very good at it, but because they were very bad. Gallian,  in an attempt to understand what they were talking about,  picked up an algebraic book and not only understood it,  but  began tutoring his housemates.  After several semesters  of exploring upper level mathematics,  learning how to  study, and getting  married, Gallian began to look into life after getting his undergraduate. At  the time Gallian  was at school, the only professions for a person interested in math was an education degree. During his sophomore year, however, Slippery Rock offered a liberal arts degree. Under the tutelage of a favorite teacher, he switched to a liberal arts degree in mathematics.  This worked out in Gallian’s favor and he applied to several different universities  in pursuit of a doctorate in math.

He was first accepted into the university at Kansas.   He excelled in that  program and soon became interested in infinite group theory.   After his first master’s thesis adviser left Kansas for Michigan State,  he wrote his master’s thesis with one of his colleagues working in the same area.  However, one day his new adviser came in and announced that  he was also leaving for Michigan State.  Knowing that he wanted to work in infinite group theory, he decided to apply elsewhere and ended up at Notre Dame [3].

After  having his adviser at  Norte Dame leave for New Zealand,  Gallian  published his thesis with an adviser who gave him a good problem, but little support.  This worked out, in large part, to be in Gallian’s  favor.  “He  gave me almost no help beyond giving me the problem, but that worked to my advantage, because when I eventually got to Duluth,  there was nobody to work with. But I was already used to working on my own” ([3])

Mentoring

In June  of 1972, Gallian  was still working at Notre Dame after two unsuccessful years of looking for a different position. However, a position in Duluth opened up when the original hire backed out.  The university called Gallian and two others up to campus for an interview. During  the  interview, among many other topics,  a  discussion about senior mathematics projects for undergraduates came up. When asked about if there were any tractable problems in finite group theory for undergraduates, Gallian replied that there was lots of them. After being selected for the faculty position at Duluth,  Gallian  devoted a lot of time and energy and time into the student projects. This was a precursor to his great work with the Research Experience for Undergraduates (REU)  program  [3].

The summer of 1976 was the first year that Gallian started recruiting talent from across the country.   This came in the form of a program called an Undergraduate Research Participation program (URP). This program was more of a literature search than research, but Gallian  applied anyway and received the grant.   The  largest benefit of this program for Gallian  and the future Duluth  REU   program was the exposure that  Duluth  received by recruiting talent from MIT, Princeton, and Harvard  [4].

Every year since 1977, with the exception of one, there has been a ten-week REU  program in mathematics at  the University of Minnesota Duluth.   Through 2012, the program has seen 194 students (not counting multiplicity) and produced over 190 papers that have been published in professional-level  journals.  The ma jority of these papers have been in graph theory, number theory, and field theory  [2].

The vast amount of success at the Duluth  REU  is often cited as the reason to attempt an REU  at Duluth.  Gallian,  however, has found a different meaning. “. . . you can still get a lot out of an REU  experience even if you don’t have anything on paper to show for it.  . . . if they go through the research process and learn something, that’s a success” ([4])

Gallian  is not only known for his amazing work with the REU  program at Duluth,  he is also the author of several survey papers in the field of abstract algebra. The survey papers on a specific topic that Gallian has written has been cited over 500 times via Google Scholar [1]. In his own words:

I liken my surveys to what someone who loves football and knows a lot about football but does not have the physical capacity to play in the NFL. So instead, he becomes a coach.  He still contributes to the sport by helping others become better players, but he doesn’t have to be a player himself. ([1])

Conclusion

Undergraduate mathematics education is the driving force behind much of the innovation and progress in higher level mathematics. Gallian,  in the respect, is an esteemed conductor. He has built an REU  program from the ground up that has been internationally recognized for its ability to foster amazing undergraduate mathematics research. Gallian is truly a role model for undergraduate  professors in the way he gives good problems to great students and allows them to build their own solutions. “I’m  not a whiz kid.  I’m not an incredibly strong mathematician, but my talents match up with what strong students don’t have.”  ([4])

References

[1]  Joseph Gallian.  private communication, 2013.

[2]  Joseph Gallian.  The vita of joseph gallian, aug 2013.

[3]  Deanna Haunsperger.  A  break for mathematics:  An  interview with joe gallian.   The

College Mathematics  Journal, 39:174–189, 2008.

[4]  Sara  Robinson.   In  the mix at  model reu:  Creative  mentor, talented students, hand- matched problems, jul 2005.