John Neuberger 1934-2020

My memories of John

I had been in Denton for about a week, after arriving from Amsterdam as a one-year Visiting Assistant Professor, when John Ed Allen (who was Chair of the department at the time) introduced me to John Neuberger. John kindly offered to loan me his mountain bike for the duration of my stay, so that I could get around town, because I did not yet possess a car. It was a very nice bike, and the frame was a perfect fit: John was the only person in the department taller than I. The bike was a lifeline in those first few months, as I moved from a hotel to another kind colleague’s home and finally to an apartment just across the street from campus. After I purchased my first (used) car, the bike changed from an essential mode of transport to a recreational tool.

Little could John or I know at the time that I would stay in the department for, well, basically forever. After that first year, I returned the mountain bike to John and bought my own, a light blue Specialized, which still adorns my garage today.

I gradually came to know John as one of the most colorful (and, some might say, controversial) members of the department. John was always generous with his time, and loved to talk about mathematics or tell stories about his many travels and people he had met. Once I and several other colleagues were invited to a party at his house. When I was ready to leave, John and his wife Barbara followed me to the door and continued telling stories. An hour later, I was back in my car.

John loved research and teaching. Perhaps others will touch on his scholarly achievements; I will briefly comment on his teaching. John was an inspiring educator who taught “Texas style”, in the footsteps of his mentors at the University of Texas. He emphasized applications and was an early adopter of technology in the classroom. In classes such as linear algebra and differential equations, he made sure that his students learned to code in C++ or Mathematica. On the other hand, he de-emphasized formal syllabi, program requirements and grades. If somebody wanted to learn mathematics, that was enough for him. I remember a time, back when tenure-track faculty still routinely taught calculus, when John was assigned the job of calculus course coordinator. At the mandatory coordinating meeting before the start of the semester, John walked into the room, said something to the extent of: “This is the textbook, you have to make a syllabus, give three exams or so and a final. Any questions?”, and that was the meeting.

John’s relaxed attitude about formal requirements concerned especially the graduate program, and this sometimes led to fierce disagreements with other faculty. I myself got a first-hand view of this when I became chair of the Graduate Affairs Committee. Those who served with me on the committee at the time will know what I’m alluding to, but I will omit the details here.

Around the time John went on modified service, I met him in the stairwell. Reminiscing on his career, he said: “Research, I enjoyed every moment of. Teaching, most of it. But committee meetings, none, not a single minute.” This last statement seemed somewhat contrary to experience, since John himself was known to drag out meetings with long monologues, where it sometimes took a trained ear to discern his actual view of the issue at hand. A former department chair once famously pointed a water pistol at him in a faculty meeting, threatening to pull the trigger if he exceeded his allotted speaking time. On another occasion, we had a qualifying exam committee meeting in John’s spacious office to discuss a borderline candidate. He basically held us hostage for an hour: I remember being trapped between the table and a window. Toward the end of the meeting it slowly transpired that he agreed with what had been the majority opinion all along!

John had a long and distinguished career. His last PhD student, Jason “Monty” Montgomery, graduated when John was 80. The last few years must have been difficult as both his mental and physical health slowly declined. Despite the differences he had with others in the department, he will be missed.

Pieter Allaart
December 19, 2020

I have many fond memories of John.  I first met him at my UNT job interview in 1997, and even in that sort of stressful situation, I could tell that he was very kind.  Later on, after I had been at UNT for a few years, I remember that he offered to make an appearance at my son’s fifth birthday party in his Ford Model A.  My son was pretty interested when he and Barbara drove up in it.  (Or maybe I was the one who was interested ...)

John was one of the core members of UNT’s PDE group.  At some point he learned that my father-in-law was also in the PDE business and invited him down for a talk.  As we were walking to the seminar room, John asked me to introduce him.  I had never introduced anyone for a talk, and moreover had never paid any attention to any of the introductions at talks I had been to, so I didn’t know what introductions were supposed to be like.  I thought all these PDE people already knew each other, so I just said “today my father-in-law will talk about PDEs”, and left it at that.  After the talk they were teasing me about it, and I have always remembered John telling me that I “needed some sensitivity training.”  (Note to younger faculty: at that time, the concept of trainings was only a joke.)

I also remember going to a big party at John and Barbara’s beautiful house, which I was glad to get a chance to see.  They lived on Ridgecrest, a spiral-shaped street that goes around 720 degrees, starting from Pennsylvania, crossing both Southridge and Pennsylvania four times each, alternating between the two, and ending in a T-intersection with its own midpoint.  By way of warning everyone not to get lost, John told the story of Gian-Carlo Rota’s visit to UNT and his attempt to attend the party John threw for him.  It is a famous piece of UNT lore – I believe it culminates in Rota making a call from a gas station pay-phone.  John concluded with clear and mathematically precise directions, featuring crucial landmarks, but nevertheless, I got thoroughly lost.

John was a warm and enthusiastic person, always willing to talk about math – even algebra.  I will miss him.

Charles Conley

My Memories of John Neuberger

John was not concerned about how people dressed. I mention two stories to illustrate this.

When I arrived at UNT, students registered in the Coliseum. Each department had a table that included two faculty members to answer questions and help advise students. One student talked to John about taking second semester calculus. John asked who the student had for the first semester. The student said that he could not remember the professor’s name, but he did remember that his professor only wore one pair of pants and two shirts all semester. John replied, “That could be almost anyone.” Can you guess who the mysterious professor was?

Another story I remember hearing from a faculty member at a different university took place when John was a student at UT. At the time, most students dressed up more than they do today. But not John, he wore jeans every day. UT had a day they called ranch and farm day when students were to wear clothes appropriate for farm work. That day, and only on that day, John wore a suit.

The space which is now offices 417A and 417B used to be the lunchroom. I enjoyed having my lunch there and talking to the other faculty members. John was often there and I remember listening to his stories and discussing his philosophy about teaching. These conversations gave me insight that I used the rest of my career on how to be an effective educator. I didn’t always agree with his point of view, but he made me think carefully about what being a successful educator means.

When the lunchroom was made into offices, Alfonso Castro and I were assigned to offices 417A and 417B. Alfonso and I are both short, so it was no surprise that the doors to our offices were short and John’s office door right next to ours was nine feet tall! This was an observation the three of us enjoyed and often mentioned.

John had a good sense of humor. I don’t remember the circumstances, but after a meeting in San Antonio, I rode back with John to Austin where my brother lives. As we drove through Austin at some point the landscape became hillier and John explained to me that parts of Austin have a much older geological development than others and that we just crossed into the older area. He then mentioned that is was odd that the houses don’t look any older.

As department chair, I went to several meetings where I met other chairs. At these meetings I met several of John’s former students both when they were undergraduates and graduate students. Without exception, they had only very positive comments regarding John. Typically, they mentioned his optimism and his encouragement. Many said that John helped them develop the self confidence they needed to succeed.

John loved to ride bicycles. He did not always ride his bike to work, but it was not unusual to see his bike in his office. I remember seeing him out riding many times through our neighborhood which is not far from where John lived in Denton. When he turned 70 he told me that each year it takes him just a few seconds longer to ride a mile.

John had an interesting opinion about federal grants. Although he applied for some, he did not apply for many. He told me that instead of giving large grants to well established researchers, he would rather have the NSF give small grants to many mathematicians who are just starting their careers. He looked at funding young researchers to attend conferences and to have some summer support as an investment in the future that would yield good results in the long run, even if some of the recipients did not pan out to be good researchers.

When I first came to UNT in 1983 I was interested in using computers in my research. I learned that John was using computers in his research as well and we used to talk about programming. At home I had an 8086 based IBM PC with a floppy disk for storage. When John got a new laptop, he gave me his old one, allowing me to have a computer at home, at work, and when I travelled. I mention this as just one example of John’s generosity and support.

John was also a good mentor and colleague to others who worked in his area. When I was chair, we attempted to build a strong group in differential equations, based on John’s presence here at UNT. Other tenure/tenure track faculty members who worked in differential equations while I was a member of the department include Joe Iaia, Alfonso Castro, Santiago Betelu, and Nick Alikakos. Unfortunately, both Alfonso and Nick moved on to other opportunities and Santiago switched to an adjunct position and became a consultant. Although UNT does not have a large strong group in differential equations as John’s legacy, the department does have a scholarship fund in his name.

Neal Brand

I enjoyed very much talking to John about mathematics and I highly valued my discussions with him. John was a genuine mathematician caring about each aspect of mathematics, primarily learning and research. For him these two faces of mathematics formed an inseparable unity. He has frequently emphasized that not only students but also faculty learn and they do this primarily by doing research. John’s primary area of research was differential equations which is a field with a strong applied flavor. He however valued both applied and pure mathematics, and frequently emphasized that many breakthrough discoveries and achievements in applied mathematics were done in the field of pure math.

John liked to work on highly challenging problems. He was for many years preoccupied with the famous Jacobian conjecture. He did not prove it but it was an unforgettable experience to see and hear him speak about it with the sparks in his eyes. He also thought about the Riemann hypothesis, trying to make some progress by considering an appropriate continuous version of it and to apply the theory of differential equations. The conversations with him about this topic inspired me to think about Newton’s method generated by the Riemann Zeta function and to investigate its dynamics. This is a long-term work in progress which may shed some light on the structure of basins of attraction to zeros of the Zeta function.

I was not only inspired by John’s research and conversations with him but I personally found it very encouraging that John received his doctoral degree in the same year that I was born. I do hope that John will be remembered in our department for many long years to come.

Mariusz Urbanski

John always seemed larger than life to me which is partly due to the fact that I’m 5’ 5’’ and John seemed to be about 6’ 10’’ but it is also due to the exuberance with which John carried himself through life. I was amazed at how he often was a “full speed ahead” kind of a person and how he had this energy that just seemed to last and last. I recall going to a conference at Texas A&M with John and we had to walk about a half mile from our hotel to the Math Department. Now I like to think of myself as someone who walks quickly but despite being 30 years younger there was just no keeping up with John. I had to run to catch up with him!  I assume it would have looked quite comical to any observer.

John and Barbara were always super welcoming to me (and everyone else) and I greatly appreciate their inviting me over for dinner on many occasions. One of the first times I was there, a brass band came through the door and started playing tunes!  I seem to remember “Yellow Submarine” as one of the songs.  I think the story was that John had done some favor for someone in the College of Music and their repayment was the brass band.

John had an old Model-A Ford in his garage which I was able to take a ride in. He also had this big whale of a car from the 1950’s and that was fun to experience as well. I remember John showing us some pictures when he was a bit younger posing in front of his super cool looking car and all I could think of was James Dean and that rebel-like look that John had in his eyes. I liked hearing about John’s growing up in Iowa and the one room schoolhouse that he went to. I had only seen this occur in movies or on TV so it was fascinating to hear about what that was really like. Then John and his family moved to Brownsville, Texas when he was young. Can you imagine growing up in Texas before AC was common?

I can’t think of anyone who would have been better as an ambassador for mathematics than John. His enthusiasm was so contagious that I can easily see him acting like Butch and Sundance in their final scene – it seemed that John could be outnumbered 100 to 1 but if he really believed in something he would come out with guns ablazing and ready to take on the world.

John had a fun, mischievous side too. I remember John complaining about the bureaucracy of academia. UNT was a lot smaller when I got to UNT in 1991 and I remember there was a faculty meeting where John said something like, “Do you have any idea how many vice presidents UNT has?  17(!)  Why on earth does UNT need 17 vice presidents? And some of them are pretty dim bulbs too!”

There’s this great photo of Ronald Reagan where he is in a circle of about 10 people. It’s clear that someone (I assume Reagan) has just told a joke and everyone is laughing hysterically. I can easily picture this being photo shopped with John in the place of Ron because to me that was the type of person John was. He wanted everyone to be a friend. Not a bad way to go through life if you ask me.

Joe Iaia

Recollections about John Neuberger

I first met John while I was a graduate student at the University of Texas around 1967. We had the same advisor, H. S. Wall. John was already a full professor at Emory University in Atlanta. John and his wife Barbara were true friends.

One of the first things one noticed about John was that he was friendly, kind and generous. Moreover, he was a very positive person and once he decided to try something, he would doggedly pursue it.

In the 1977, the mathematics department at North Texas had two positions. They quickly decided to offer one of them to John. The other was offered to me. I was an associate professor of mathematics at the University of Florida in Gainesville at the time. I talked with John and of course the members of the math department at North Texas about the possibility. It was an exciting time. The academic vice president at North Texas, Miles Anderson, and the department chair, John Allan both said that they wanted the mathematics department to be as strong as possible and they thought that if John and I came this would be great – music to our ears. So we started on a great adventure of some 40 years. The department members were enthusiastic also. John and I taught two courses each semester (well, we ran more courses than that to work with our graduate students.) I remember John Mohat, who taught four courses each semester, saying in a meeting that our job was to do research and teach and develop our students. He thought that was an equitable division of labor. Many people in the department felt the same. So, we all were in the adventure together.

John had some strong opinions about teaching and research. He had advised several doctoral students before going to North Texas. Students were allowed to flounder around with problems. Of course, he (and I) had learned this from our advisors. So, John was comfortable wandering in the dark until the first dawning of light. Not only was this good training for students, but was excellent training for tackling unsolved and perhaps difficult problems when one had to start from the beginning.

John had a long and strong career consulting. Some of the finest minds quickly realized his intelligence and persistence. To John there was no difference between pure and applied mathematics, there was just mathematics – an opinion which I share.

Dan Mauldin
December 31, 2020

I first learned of Professor John W. Neuberger when studying nonlinear semigroups as a graduate student. His formula for the exponential of a nonlinear semigroup got me very interested in following his work.

I first met John in person at a meeting in Oklahoma State University. When one of the organizers of that meeting introduced me to John I could not believe how kind he could be to a recent Ph.D. considering his mathematical stature. Right after his talk I asked him about connections of his work with symmetric positive systems that I was studying at that time. His encouraging reply was a big boost for my beginning career as an independent researcher. At that time, I was working in Mexico which made it convenient for John to visit me. Actually, he was invited to Mexico by universities other than mine which allowed me to interact with John on several occasions. In one of those occasions my boss, Samuel Gitler, invited John, I and the corresponding wives for dinner to a very fancy restaurant in the Zona Rosa. It only took a quick exchange of platitudes for the conversation to turn into a dialog between John and Samuel because John knew quite a bit about a family of polynomials that show up in cohomology theory which was Sam’s specialty. After dinner we walked around the Zona Rosa while their mathematical conversation went on and on.

On another occasion, while John was visiting Mexico invited by a university other than mine and accompanied by his wife Barbara and his daughter Sandra, I invited them to go to Puebla. An archeological feature of the Puebla area is the Cholula pyramid. This pyramid is so large that Spaniards preferred to cover it with dirt to make it look like a mountain rather than destroying it. The pyramid was eventually discovered and a tunnel was built to allow people to see the different stages of construction of the pyramid. The tunnel is about five feet tall and rather narrow. When we arrived at the pyramid, I proceeded to get into the tunnel followed by Barbara, Sandra, Miryam (my wife), others and John. I felt very bad to have suggested that part of the excursion when I exited the tunnel and saw John coming last almost crawling. His height not always worked in his favor but he was a truly good-sport.

My time at UNT was made many times more pleasant and productive because of John’s presence. He really knew the meaning of mentor and colleague. By the time I arrived at UNT John had developed a large group of graduate students interested in the general area of Analysis and Partial Differential Equations.

Immediately John found a way for me to start a seminar that included graduate students McCabe, Dawson, Lee, Kurepa and Unsurangsie. The first three students completed their doctoral dissertations with John and the last two with me. From that point on there was a constant stream of well qualified students that have gone on to pursue successful careers. John’s contagious energy and optimism made every event so much more exciting. Two consecutive grants from the Texas Advanced Research Program, new results, papers published, etc., every day John renewed the energy of the least optimistic in the group.

My last in person reunion with John was in November of 2017 when Miryam and I visited the Neuberger’s in their retirement place. By that time John’s physical health had deteriorated quite a bit but his mind was sharp as a tack. The three days we spent together our conversation was 99% devoted to understanding the connection between his amazing characterization of local semigroups in his paper “A linear condition determining local or global existence for nonlinear problems” (2013) with blow up phenomena. John’s approach to determining when a local flow is global is by appealing to the linear semigroup defined in the phase space in the spirit of Lie group theory. His approach, for example, addresses precisely The Clay Institute Millennium Problem on the Navier-Stokes equation. It is too bad that life did not give us John for a few more years for maybe we would be celebrating the solution to one of the main questions in mathematics.

Alfonso Castro
McAllister Professor, Harvey Mudd College
January 2nd., 2021