Mathematics

Mathematicians are Needed in Industry

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Gregory_Coxson
Greg Coxson

At this point in my career, I have worked at a number of organizations, usually technology companies with military contracts. I am convinced that mathematicians strengthen organizations, and sometimes make revolutionary changes, often in small ways that are not celebrated as often as they should.

My first job was at the Center for Naval Analysis in Alexandria, Virginia. CNA performs long-range studies for the Navy, and is one of the oldest military Operations Research firms. I was working for a crusty old radar engineer, who wanted me to perform Monte Carlo analysis of Russian missile raids. This required thousands of runs of the program. One day, I needed to consult with a mathematician on another floor. I was surprised to find that he knew the simulation I was spending my days with. But what really amazed me was when we started discussing specifics. At that point, he pulled out a big binder containing tables of every possible combination of inputs to the model, and the associated outputs. He had invested the time one week to run all the possibilities and compile them. Having done this, he did not need to run the model for hours a day; instead he had just to pull out the binder and find the right row to pull out the results. It impressed me that this approach was much more efficient.

Later in my career, when I was working for another company, we had a large number of engineers working on a new ballistic missile system for the Navy. The schedules were aggressive, and the work multi-faceted and difficult. On one of the projects, it appeared necessary, despite the tight schedules, to spend a year running cases of flight trajectories. However, there was a PhD mathematician working on this, and he argued that since all the factors were known, mathematics could be used to perform a quick study, and come up with all the possible trajectories. He saved the company a year of effort and countless computer runs.

In these cases, Mathematics is not enough. It is important to get the information into the right hands. A junior engineer or mathematician will not be listened to, at least without concerted effort and the right arguments.

I had the opportunity to learn this first-hand. I was working on a critical program for the Air Force, and one evening before heading home, I was reading the specifications (not always easy reading). Before I went too far with this, I came upon something that stopped me in my tracks. Here, in a system where efficiency was highly emphasized, was an operation being done 80 times in one set, and then in the next set, the inverse of those operations was being done. This seemed to me something that should be fixed. So I went to my boss and pointed this out. However, I was new, and my boss did not know enough mathematics to understand my claim that eaeb = ea+b. No matter how I argued, she was not going to take my word for it. Her approach, ultimately, was to arrange a panel discussion with some scary senior analysts around the table to make me retract my story. But I did not back down. Looking back on it, the issue was a badly implemented discrete Fourier transform. I left the company soon after. It took about a month before I started getting phone calls asking for my notes. They had come around to agree with me.

The point of all this is, that mathematicians are needed outside of academia. Mathematics is used, and sometimes misused, every day in almost every industry. Mathematicians are needed for their training, but also their insights. I believe that mathematicians are able to find efficiencies, and new approaches, that others are blind to. Mathematicians are needed to prevent errors, to analyze complex problems and systems. There is no doubt in my mind that we need more mathematicians in industry.

A random walk toward a net positive

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by Derek Kane, Deka Research and Development  dgkane64@gmail.com

Today, I am investigating whether magnetic resonance imaging can evaluate cell viability as we attempt to grow replacement organs: hearts, lungs, kidneys, etc., for patients who need transplants. I believe the child I was at five would approve. Of course, I also have a two hour meeting this afternoon to read C++ code to ensure that it not only performs its intended task, but also conforms to DEKA’s formatting standards. Even the coolest job, and I have a very cool job, includes drudgery and paperwork.

Avoiding boredom was my earliest career goal. My undergraduate degree was mechanical engineering, and my brother got me a job with him at Itek Optical Systems. Itek made cameras and telescopes, largely for the Department of Defense. The engineering challenges were fascinating, but the analysis and algorithm aspects of the work excited me much more than traditional mechanical engineering. However, my lack of deep mathematical training limited the analyses and algorithm development I could handle. At this job, I also noticed two career paths: one group of older engineers became middle managers whose work looked unbearably dull and who seemed very vulnerable to layoffs. A smaller group of engineers, including my boss, served as technical experts. When a new and innovative solution was required, or when a program stalled because a physical or computational challenge could not be overcome, these experts were consulted. I wanted this job.

I decided I also wanted to attend graduate school in mathematics. The deeper understanding of mathematics would enable me to comprehend and address a wider range of analytic and algorithmic problems. Additionally, a PhD provides gravitas when working with other engineers in industry. An engineer with a bachelor’s degree must have a large volume of high quality and high visibility work, before their opinions are considered seriously outside of the company where they work. While there are a great many fools who have doctorates, when you are sitting around a table with several PhDs, it is handy to have your own so you are part of the club.

To prepare for graduate school, I took one or two undergraduate math classes every semester for two and a half years while working. In the process, I discovered that math was beautiful as well as useful. The University of Michigan accepted me into their graduate program, and I studied algebraic group theory, intending to become a professor after graduation. Graduate school also proved an ideal environment to enjoy my two small children. However, as I approached my defense the academic job market was drying up. I could look forward to a series of one or two year positions before finding a tenure-track job. With two children, this prospect was unattractive, so I decided to return to industry.

My previous experience with optics enabled me to join a laser-based project at Lockheed Martin. This project offered the opportunity to work with inertial systems, and this experience made me attractive to Deka Research & Development. Deka was developing the iBot (an inertially stabilized wheelchair capable of traversing rough terrain, curbs and stairs) and the Segway (an inertially stabilized, two-wheel vehicle).

Dean Kamen, the founder of Deka, feels that we should only be working on jobs that are hard and that positively affect many people. The range of work I get to join is varied and exciting: mobility for people who can’t walk, prosthetics for people who have lost arms, clean water for people who will never get utilities from their governments, hearing improvement, safe delivery of drugs, improved dialysis for people with kidney failure, several projects I cannot talk about, and most recently growing new organs for people in need of transplants.

The range of disciplines this allows me to sample is equally wide ranging: thermodynamics, electro-magnetics, computer modeling of liquids, exotic signal processing, statistics, optics, big data analysis, synthetic biology, human-machine interfaces, colloidal flows, causality, complexity, numerical solution of differential equations, etc. Mathematical training allows me to move from discipline to discipline, because at its core, each of these topics depends upon a quantitative approach to understanding data, modeling relationships, and predicting outcomes. Grad school supplemented this flexibility by demonstrating that hard work and research can overcome difficult technical problems. You should leave grad school feeling that if another human has managed to solve a problem and write it down, then you can read their work and understand it.

Today, it is almost twenty-one years since I defended my thesis. I anticipate another twenty-one years of professional life, although I am aiming for at least forty more years. At the beginning of my career, my primary concerns were staying employed and working on exciting projects. Now, I am becoming concerned with why I do the work I do, and whether this work is a net good for the world.

I left the defense industry seventeen years ago, primarily for the selfish reason that it had become wearing and grating to put up with the intrusiveness of security clearances, and because commercial industry was tackling more interesting technical challenges than defense. It is absolutely true that there are sound moral arguments for working for defense, but I never really thought about the ethical justification of my work. I have been extraordinarily fortunate to land at a company where I am sure that my work is contributing to society.

I am largely comfortable with what I worked on, but I regret not seriously considering the moral implications of my early projects. Young mathematicians have complex lives; they need to support families, establish reputations and orient themselves in a world bursting with opportunities. However, it is also very valuable to develop an understanding of the non-technical world: history, culture and philosophy. This helps us avoid choices that make it hard to sleep as we get older. Older mathematicians have reputations, authority and time to reflect. It is morally incumbent that we provide opportunities for young mathematicians, guide them to interesting work, and protect them from external forces who would inappropriately exploit their talents.

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Study Groups with Industry: Mathematics meets the real world

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A study group is a type of workshop which brings together mathematicians and people from industry. The meetings typically last for 5 days, Monday-Friday. On the Monday morning the industry representatives present problems of current interest to an audience of applied mathematicians. Subsequently the mathematicians split into working groups to investigate the suggested topics. On the Friday solutions and results are presented to the industry representative. After the meeting a report is prepared for the company, detailing the progress made and usually with suggestions for further work or experiments. Over the years they have proved to be an excellent way of building bridges between universities and companies as well as providing exciting new topics for mathematicians. Of course there is pressure involved in attempting to understand and solve a problem over a short time frame. This can often produce an exciting and intense atmosphere but, in general, a good time is had by all.

 

Meyers_Study_groups.jpeg

Experiments can often help guide a mathematical investigation (or cause even more confusion)

The original Study Groups with Industry started in Oxford in 1968. The format proved a popular way for initiating interaction between universities and private industry. The interaction often led to further collaboration, student projects and new fields of research. Consequently, study groups were adopted in other countries, starting in Europe to form the European Study Groups with Industry (ESGI) and then spreading throughout the world, regular meetings are currently held in Australia, Canada, India, New Zealand, US, Russia and South Africa. A vast range of topics have been covered in the meetings, including beer and wine bottle labelling, legal sale of rhino horn, spontaneous combustion, mortgaging of cows, building toys, city bike sharing strategies, determining fish freshness, etc. New forms of meeting have also evolved, such as the Mathematics in Medicine or Agri-Food Study Groups.

The popularity of study groups can be attributed to their mutually beneficial effects. For companies there is:

  1. The possibility of a quick solution to their problem, or at least guidance on a way forward.
  2. Mathematicians can help identify and correctly formulate a problem for further study.
  3. Access to state-of-the-art techniques.
  4. Building contacts with top researchers in a given field.

The academics benefit from:

  1. Discovering new problems and research areas with practical applications.
  2. The possibility of further projects and collaboration with industry.
  3. The opportunity for future funding.

An important feature of these meetings is that they can also highlight the talents of students, leading to employment opportunities with the companies. In South Africa, after attending a number of study groups, a group of students took a new direction. Noting the gap in the market for applying mathematics to real world problems they started their own company, Isazi Consulting. Now they return to the meetings this time posing their own problems, and looking for new recruits.

Information on the European Study Groups can be found on the website of the European Consortium for Mathematics in Industry. A good source of information for meetings in Europe and the rest of the world is the Mathematics in Industry Information Service, see

ECMI Study Groups https://ecmiindmath.org/study-groups/

MIIS Website http://www.maths-in-industry.org/

 

Tim Myers

Centre de Recerca Matematica

Barcelona, Spain