The Stuggles of a Female Mathematician
I have written down some thoughts about my struggles in a male-dominated part of the world. I think these thoughts would be of interest to young women just starting out. Women have made great strides since my days but some of my stories could still be worth writing down, reviewing and perhaps reading. This effort was prompted by a request to do a STEM interview with high school students.
BUT think of this post as a draft for now. I wanted to capture steps in my life without worrying about how it reads. If I were to publicize this post I would want to make changes. But for now read it as a series of steps in my life that have brought me to my current position, one in which I am happy to be marrying two passions in my life: art and math.
Early Careers
The stories of my life careers include choosing between architecture and mathematics in my freshman year of high school. Aptitude scores indicated that a career as an architect would be a good one for me. But our HS counselor told me that women do not succeed as architects so I didn't think further about this direction. I sometimes wonder what a career in architecture would have been like. I am happy to see that my son chose to study architecture, but even happier that he was able to switch careers to one in which he utilizes his skills in computers in a different direction, while still keeping his connections to the world of architecture.
Other career choices for me involved choosing between art and math upon entering college; I chose math for a few reasons - it would provide a better living among others. I had grown up very poor so that I never could have the luxury of not studying or working.
By the time I entered college, I was no longer swayed by the attitude that certain fields were forbidden from women. Perhaps this was maturity or perhaps we were beginning to enter a new phase in women's rights. In any case, the field of Mathematics challenged me; I was happy to begin to compete in this male-dominated world.
After college though, I did spend two years as a Peace Corps volunteer, as a 'Profesora de las Mathematicas' en La Escuela Normal de Chimbote in Peru. I loved teaching 'new math' and I returned to continue in graduate school so that I could become a college teacher. I married and began full-time graduate school at NYU at the Courant Institute of Mathematics. And four years later, one week after I received my PhD, my son, Joshua, was born.
That year I struggled with a new position on the faculty of a NYC college while taking care of a new baby. I felt that college teaching would provide a way of combining motherhood and working since I only needed to teach for 12 hours (though of course, many more hours were required to prepare for class and do research). And it did for ten years while gaining tenure and new ranks. But that first year was a struggle; I wanted to spend more time with Joshua. So I cut back on the hours for one semester and that helped. The next few years were easier. This was the period of Women’s Liberation; I was determined to have a career and a family. I was happy for society's support, so different from the environment women had endured just a few generations earlier. And Joshua's father supported me fully.
Change in Direction
Other struggles in the development of my career involved dealing with a (hearing) disability that became a reason to change my career from teaching to computer programming; it actually was a very good move for me. People can change directions. But another driving force behind my change in career at this point was monetary. The college felt that it was okay to pay very little; it was expected that faculty members would have a spouse making money (whether female or male). This wasn't fair and it bothered me (and others). I loved my job but it was time to try something else.
In addition, the personal computing industry was beginning to explode. Part of my academic job included computer courses and soon I was immersed in what these new computers could provide. This was the early 80's with the advent of computers such as the Commodore 64, initially built in a garage. I think it had less than a megabyte of memory. But it had games and it had the popular Excel Spreadsheet. Spreadsheets intrigued me with how data could be presented and organized. It's said that spreadsheets helped speed the rise of computers. Of course, word processing programs also helped. This era had not yet reached the internet, but in the academic environment and research areas we began to see its promise. During this period I was teaching students how to program in Basic (and Fortran). We developed artificial intelligence simulations. In any case these were exciting times for computers. This was another reason I considered changing jobs.
Startup Company
A friend had started a Compiler Design Company and that was intriguing to me. And I began to work part time at first. I was the 6th person hired. I primarily worked with computer programmers right out of college. We were all going to become millionaires. The main idea behind the company was a universal compiler design and we grew in 4 years to over 100 employees. It was an exciting time, in a company that began in a basement and moved to a full floor in a high rise on the Avenue of the Americas. But the competition was tough and when it was clear that the company would soon be bankrupt I changed to the corporate world, one I never thought would be mine. Moreover, it was a job in the belly of the beast - in the technical subsidiary of the New York Stock Exchange. And so, another phase began.
A New Phase
I arrived at the NYSE at the end of 1986. And then the stock market crash of October 1987 hit us. The thrill of being in the center of such activity began to take over though. I worked hard but we had personnel issues during this trying period and management began to change. I was on the short list to become a manager but was passed over for more corporate types. But I was beginning to find areas that interested me enough that I began to make a mark.
An important step in my career involved solving a significant online computer problem, a computer logic bug that caused the NYSE exchange to close down for a few hours. All my male colleagues were running around like chickens without their heads on. They were going in circles, just talked about the problem and getting nowhere; they did not concentrate on the issue at hand. I hunkered down for many hours well into the wee hours of the morning, pouring over the code until I tracked down the problem. Its solution gained me some (favorable) notoriety and probably was the main cause of my rise in the ranks. This became another exciting period; we had money to hire excellent consultants and we began to re-design and implement major programs used by hundreds of brokers and specialists at the center of financial dealings on Wall Street. We also provided oversight and surveillance so I learned a lot about the 'underworld' of trading and the financial underpinnings of our country. I progressed from a computer programmer position to management and then two months before 9/11 to a Vice Presidential position. I spent 9/11 and the days after that in the board room discussing tactics with other officers, the chairman of the NYSE and Washington DC. In addition, I worked with my staff on the logistics of getting our employees home and then back again so that we could re-open the exchange 5 days later. And underlying the effort we made was the worry about how our world had changed.
One item to note is that a decision was made to increase the computer security for the NYSE by creating remote computer monitor sites. This included using my brand new corner office to house many monitors. Soon my office was filled with blinking lights. If needed we were ready for the specialists and brokers to descend on our offices in order to conduct business. As an aside, I heard that years later, these backup sites were moved to New Jersey. But in the meantime these blinking lights reminded me hourly of the changes we were undergoing.
As a personal aside, my overriding concern was my son, working in SoHo at an architectural firm. On 9/11 after many attempted phone calls I heard from him that he was okay!! Beginning on that day though, I realized that his world would be different. Fortunately he was too old to be drafted at age 28 (my second concern now that I knew he had not done something unexpected like having a meeting at the Trade Center). And I could concentrate on work.
Defining Moments
At this defining moment the world changed overnight dramatically. The stress of the new environment with budget crunching -as well as the blinking lights- began to take its toll. The main stress was due to increased security though, with six checkpoints to go through every morning. I needed something else to preoccupy me. I began to address the issue again of the Art versus STEM world.
And I found painting!! I began to paint with a passion in the evenings and on the weekends and my life changed. I finally began a career in art. I figured out a way to retire early and I began to paint full time. I read many art books and took numerous classes and I painted for hours every day. We moved to Santa Fe and found talented artists everywhere (it is said that every other person you meet in Santa Fe is an artist.) I began to show in a small gallery in Albuquerque and then one right on Canyon Road in Santa Fe. I felt that I had made it. But I continue to work at my painting. There is so much to learn and this has become my new passion.
Art and Math
But again I am struggling with the choice between art and math, between painting and solving logical problems, this time of an large website. I have been spending a majority of my hours as the volunteer Webmaster, developing and maintaining a website for a group of 300-500 members, the Plein Air Painters of New Mexico (www.papnm.org). Do I concentrate now on improving my painting skills or solving logical problems? I enjoy solving the problems that arise. But I miss the painting - and its challenges.
Perhaps there's a way to marry both sides of the brain.
Since I began painting full time almost twenty years ago in that defining moment after 9/11, I am constantly amazed at the connections between art and math. I remember vividly how excited I was at a first 'lecture/demo' for me by a wonderful artist/instructor (Keith Gunderson), when he pointed out how the golden mean underlies the design of so many famous paintings. This was one of my topics in both the Introductory Course to College Mathematics and the advanced Abstract Algebra Course for math majors. Mathematics can explain underlying patterns in nature and in art in many different ways.
Throughout my development as a painter, it seems that I see connections over and over again, from simple calculations of a vanishing point to the use of underlying grids in a painting to help with design; from the suggestion of unequal measures to maintain interest in a painting to the use of aerial perspective. Other topics such as Informal Design, Fibonacci Series, Golden Spirals, Dynamic Symmetry, Radical Impressionism, Fractals, Mandelbrot Series, Self-referential Forms, Moebius Strip, Knot Theory, Braid and Group Theory have inspired me to look at Art in a different way. The book, "Godel, Escher and Bach: An Eternal Golden Braid", provided examples in many of the college classes I taught with its connections in math and in logic, art and music.
The Visual Presentation of Data
Another topic of interest while I was working on Wall Street in the computer world is that of "Envisioning Information". See the works of Edward Tufte, Professor Emeritus at Yale. It was important to present the data underlying the flow of information at NYSE to the traders in a way that was understandable and attractive. And now I have been working on presenting information to the members of the Plein Air Painters of New Mexico on the website in a way that is attractive but understandable. Working with computer information and the presentation of data is a continued interest.
Pandemic
In terms of my work, the adjustment during the pandemic has not been difficult. Painting and solving computer problems are solitary activities. I enjoy painting with others but it's okay to be alone. In fact, I now find that working in the studio can be easier than painting outdoors "en plein air".
The visual presentation of the pandemic data has been intriguing me also and I spend many hours pouring over the graphs and other data visualization techniques in an attempt to see which seemed to work most effectively.
Painting is an activity that can help everyone during the pandemic. Painting has become meditative for me. I am happy that this passion has served me so well over the past couple of decades. I have painting pal friends everywhere. And I continue to do research, now in the area of Art. It has such a long fascinating history.
So little to do and so much time....
And besides all this, I want to spend time working on this blog, Radical Impressionist: A Mathematician Paints.
Karen Halbert Sept 30, 2020
Corrections made to typos, Aug 29, 2021 and Jan 5, 2022
