Profiles of Professional Mathematicians and Computational Scientists
| Dimitris Agrafiotis | Barbara Hamilton |
| Kimberly J. Drake | Mark Zandi |
| Anshul Gupta | Wu Li |
| Bill Mawby | Peter Norvig |
| Ed Moylan | Craig Trost |
| Nancy Heinschel | Katya Scheinberg |
| Edmond Chow | Karim Azer |
Dimitris Agrafiotis
Vice President of Informatics
Johnson & Johnson Pharmaceutical Research & Development
Exton, PA
Adjunct Professor of Informatics
Indiana University School of Informatics, Bloomington
B.S. chemistry, University of Patras, Greece
Ph.D. theoretical organic chemistry, Imperial College, University of London
Background
I pursued computational chemistry as a graduate topic based on my undergraduate advisor's recommendation, but the turning point was my postdoctoral tenure at Harvard, where I was introduced to the beauty of expert systems, computer programming, and algorithm and software development. I converged on informatics and software development because I found them extremely fulfilling. It was the practical use of computers and modeling that ultimately defined my career; I pursued an industrial career because several opportunities presented themselves.
To get to where I am today, I developed many innovative algorithmic methods and published extensively. Most importantly, I embedded these algorithms into software that appealed to end users, who were not computationally inclined.
Job Characteristics
In my position, I develop algorithms and visualization techniques for analyzing and mining large data sets, with special emphasis on chemo- and bio-informatics. During a typical day, there are a lot of management duties and relentless email. The best parts of my job are algorithm development, software engineering, and working on projects that have real impact. My least favorite parts are the administrative duties that come with a managerial position. My work schedule consists of 40 hours per week in theory, 70 in practice; I never leave my job.
I believe the future of math in the pharmaceutical industry will involve mining of large data and heterogeneous sets and information integration. Someone looking to get involved in this field should expect to do algorithm and software development as it applies to drug discovery projects.
I am very happy with my career. I have managed to do the things I enjoy and make an impact within my organization and the broader scientific community. Balancing utility with innovation has been the key.
Salary Range
Salary range varies greatly. For Ph.D.-level positions, it could range from $80,000 to over $200,000 for managerial positions.
Kimberly J. Drake
Mathematician
Naval Surface Warfare Center, Carderock Division
Machinery Research and Silencing Division
Philadelphia, PA
B.S. mathematics and computer science (double major with a teaching certificate), Montclair State University, NJ
M.S. mathematics, North Carolina State University
Ph.D. applied mathematics, concentration in computational science, North Carolina State University
Background
During college, I participated in a semester-long internship at the Lawrence Livermore National Laboratory (LLNL) sponsored by the Department of Energy. The intern program was extremely well-run and students were exposed to all kinds of science and technology in the northern California area. I was exposed to world-class scientists who were using their scientific skills to solve problems that could really impact people’s lives. By the time I left LLNL, my career plans had changed: I’d planned on studying pure math as a graduate student and then teaching, but after my time there, I decided to pursue a career in applied math instead.
Job Characteristics
I develop algorithms and technologies to solve problems related to diagnostics and prognostics on machinery systems typically used by the Navy. Much of the work that I do on a daily basis relates to using computers to solve problems. Once we develop or find an interesting algorithm for solving problems, we have to actually implement and test the algorithm. This usually involves running experiments and analyzing the results. I also have a small test project, where we are implementing algorithms that have already been developed on real machinery systems to evaluate their usefulness to the Navy. Finally, I’m building a video and image processing laboratory, which will have the 12 different varieties of video cameras used by the Navy. We will have state of the art computing power and will be working on the development and implementation of video and image processing technologies of interest to the Navy.
People working in these areas should expect to work in interdisciplinary groups. While my work is mathematical, I work with engineers, chemists, and physicists to solve problems. There are many opportunities for mathematicians in our area. Mathematical modeling is an area that the Navy invests more time, energy, and money in every year.
Salary Range
Salaries range from $70,000 to $150,000 or more for starting, mid-level, and senior positions. It really depends on education level, length of service, and location.
Anshul Gupta
Research Staff Member
Mathematical Sciences Department
IBM T. J. Watson Research Center
Yorktown Heights, NY
Bachelor of Technology (B.Tech), computer science, Indian Institute of Technology, New Delhi
Ph.D. computer science, University of Minnesota
Background
I did not start out with a major in mathematics; instead, my background is in computer science. During my undergraduate years, parallel computing (using several processors simultaneously to run a large computer program faster) was an emerging and exciting new area of computer science. In graduate school, I learned that some of the most challenging problems requiring parallel computing are numerical in nature. I therefore focused my attention on applying parallel computing to numerical problems.
Job Characteristics
I do basic research and develop algorithms and software to solve problems in science, engineering, and optimization. Many of these problems involve simulating a physical system using a computer program, where real-world experiments might be too costly or impractical. For example, with the help of software, an automobile company can simulate a large number of crash scenarios to improve the safety of a vehicle. Real crash tests may be expensive and not accurate enough. These problems are usually so complex that they are often solved either on clusters of several computers or on supercomputers containing several processors. The algorithms and software that I develop help solve some of the underlying mathematical equations involved in these simulations efficiently on a large number of processors.
The stress level and the number of hours worked fluctuate a lot; however, a typical research career affords a lot of flex time, which helps keep stress levels down even during long days.
I believe the future of math in the computer industry lies in computer chip technology. Interestingly, just like a lot of other things, computer chips and the circuits laid out on them are also simulated to detect possible defects before a chip goes into manufacturing. In order to build faster processor chips, one needs to create larger and more complex simulations, which in turn, requires faster processors.
Salary Range
Starting: around $80,000 to $100,000; mid-level: $150,000 to $200,000; senior positions $250,000 or more.
Bill Mawby
Manager of Statistical and Mathematical Support Services
Michelin America Research and Development Corporation
Greenville, SC
B.S. natural systems, The Defiance College, Defiance, OH
Ph.D. biomathematics, North Carolina State University, Raleigh
Background
I arrived at my career path through a mixture of chance and necessity. My undergraduate training and interest was in biology, but I soon concluded that this field would require mathematics if any progress in understanding biological processes and systems was ever going to be made, and so I went to graduate school for biomathematics in order to pursue this dream. There were two professors, Dr. Bernie Mikula at Defiance and Dr. Harvey Gold at NCSU, who nurtured my interest, but it was the book series on "Towards a Theoretical Biology" that probably did the most to convert me. Work-study experiences at Argonne National Laboratory and Roswell Park Memorial Institute also largely influenced my choices.
After graduate school I tried being an independent consultant, but, mostly due to my distaste for the business end of the endeavor, I chose a more mainstream job as a statistician at Michelin Tire Corporation. I found that mathematics, like quickness in sports, can find profitable application in any field. Over the last 25 years, I have held positions as Principal Statistician for Research and Development, Corporate Statistician, and Manager of STATMATH (statistical and mathematical support services).
Job Characteristics
In my role as manager of statistical and mathematical support, I help create proposals, lead projects, guide technical personnel, contribute technically to projects, and evaluate results.
My position has two features that really motivate me to do better work: a constant variety of problems and a direct impact on business results. Workload and schedule are dictated entirely by project needs, but this does not typically involve a lot of overtime. Daily work is split rather evenly between administrative work, project meetings, creating documents, and doing mathematical research. Employees without the managerial role spend most of their time doing mathematical research, with perhaps 25% of the remaining time spent on meetings and documentation.
The applications of mathematics, including quality control statistics, design of experiments, sampling plans, finite element work, physical modeling via differential and partial differential equations, reliability, forecasting, data mining, optimization, and stochastic processes can be seen in all manner of research, industry, and commercial and administrative processes.
Salary Range
Salaries range from about $75,000 to about $150,000.
Ed Moylan
Research Engineer, Methods & Systems Analyst, Project Leader, Supervisor, and Manager (retired)
Ford Motor Company, Dearborn, MI
B.S. mathematics, University of Detroit
M.S. mathematics, University of Detroit
M.B.A. University of Michigan
Background
I earned my B.S. in mathematics in 1962 and M.A. in 1964, taught full-time for three years, and joined Ford Motor Company in 1967 as a member of the team that developed Computer Aided Design (CAD). CAD was being developed simultaneously at Ford, General Motors, Boeing, and other large companies; computer graphics technology was in its infancy. My initial contributions at Ford were to analyze what earlier developers had achieved, to evaluate what methods and technologies were available, to learn the theory of automotive design, to create additional methods, and to implement software that teamed the skill of the designer with the speed of the computer. My knowledge of calculus, differential geometry, linear algebra, and numerical analysis, was critical in doing this work.
Computer aided design, computer aided manufacturing, and computer aided engineering simulation systems began to be used worldwide throughout Ford for developing vehicle exteriors, interiors, structures, electrical circuitry, and powertrains. Data exchange standards and software for communication with suppliers had to be established. Plans had to be coordinated with counterparts in Europe and other international locations. My title evolved along with my career: Research Engineer, Methods & Systems Analyst, Project Leader, Supervisor, and Manager.
Having management responsibility involves not only being able to oversee technology development, but also being able to build business cases for technology investments or process changes. It was essential to communicate effectively with business partners in other departments, including finance, human resources, purchasing, and engineering. I needed to better understand their viewpoints, tenets, needs, and constraints. I felt that a formal education in these areas would be a good complement to my on-the-job education. I therefore went to night school, and earned an MBA in 1989; I retired in 2000.
The most satisfying aspects of my experiences were interacting with research mathematicians, working with people in other fields, contributing to joint solutions, seeing those solutions implemented worldwide, and teaching others what I learned.
Job Characteristics
I was not a researcher, but rather a “productionizer”; that is, I was able to read and comprehend published mathematical articles and adapt the results to an industrial environment. By adapting the theory and applying new methods to improve an existing production process, the impact can be significant, such as reducing costs by hundreds of millions of dollars.
Most important industrial problems initially are ill-defined and are rarely posed in mathematical terms. The critical first steps are to employ one’s “mathematical mindset” by defining terms, distinguishing between independent variables and dependent variables, and understanding the relationships among those variables. The next steps are to employ one’s “mathematical toolset” by testing assumptions against data and, if possible, using classical solution techniques. However, if new tools are needed, a literature search may be appropriate. Once sources are found, their assumptions need to be adapted to the problem at hand, applied, and validated. They then become part of one’s expanded “mathematical toolset.”
Salary Range
Salary range: $75,000 to $150,000.
What is important to industry?
Mathematical training enables one to identify and analyze intricate relationships among various aspects of complex problems. This capability is marketable if it is documented and communicated in language that is understood outside of the mathematics classroom. Mathematics majors can augment their communications skills if they develop the ability to listen and continually ask deeper questions in order to define the structure of a problem or a process, to identify the most highly leveraged variables, to develop pragmatic solutions, and to carry them through to implementation. One must be willing to continue learning and taking on additional diverse tasks. Mathematical methods and thought processes are universally applicable. For the future, much groundbreaking mathematics can be done in life sciences, data mining, supply chain management, agent-based modeling, network analysis, and many other areas and fields.
Nancy Heinschel
Applied Research Mathematician
National Security Agency (NSA)
Fort Meade, MD
B.S. mathematics, University of California, Davis
M.A. and Ph.D. mathematics, University of California, Santa Barbara
Background
The National Security Agency (NSA) is the agency of the Defense Department responsible for solving cryptographic problems for the federal government, and is the biggest employer of mathematicians in the U.S. The NSA sponsors several paid summer internship programs for undergraduate and graduate students. I first became aware of the NSA through one such program that allowed me to spend two summers as an intern during graduate school, working on real problems with intelligent and enthusiastic Agency mentors. Summer internships are a great way to learn firsthand what the NSA does and what it is like to be an Agency employee.
Like nearly all NSA mathematicians, I spent my first three years at NSA in a training program, during which I worked in five different offices. I also took courses in cryptography, statistics, and math, and attended a variety of talks and conferences to improve my technical skills. The training program allowed me to gain experience in a wide variety of project areas, to develop a network of valuable contacts, and to find an office that best fit my interests and strengths.
My graduate research was in pure mathematics, but the idea of applying mathematics to important real world problems always appealed to me and working at the NSA has given me the opportunity to do just that. NSA mathematicians use tools from diverse areas including number theory, Fourier analysis, and statistics, but being an expert in these areas is not a requirement to become an NSA mathematician, nor is having a Ph.D. Working at the NSA, I have utilized essential problem-solving skills gained by working on problems involving diverse math disciplines. I have also seen potential to apply these abilities to new challenges. The complex problems we work on generally require computers to solve, and because of this, some computer programming experience can be helpful. However, I have learned most of my programming skills on the job.
Job Characteristics
Much of my day is spent working on a computer, but it is far from solitary work. With such challenging problems to solve, I work on project teams with mathematicians, computer scientists, engineers, and many other colleagues. Some of my projects have tight deadlines, but others are longer range. In addition to computer work, I do a fair amount of writing and speaking in order to communicate my results to coworkers. Due to the classified nature of what I work on, I'm not allowed to take any work home, so I have evenings and weekends to recharge, pursue other interests, and return to work refreshed and prepared for new challenges.
Salary Range
In 2008, math and statistics positions at the NSA had starting salaries of $49,685 for those with bachelor’s degrees, $59,811 for master’s, and $83,720 for Ph.D.’s. The best place to find out more about careers at NSA is on the website, www.nsa.gov.
Edmond Chow
Computational Scientist
D. E. Shaw Research
New York, NY
Bachelor of Applied Science (B.A.Sc.), systems design engineering, University of Waterloo, Ontario
Ph.D. computer science, University of Minnesota
Background
I've always liked math, but it was computers in junior high school that triggered the math questions I would pursue for a long time afterward. Questions like "how do computers know how to compute sin(x)?" were the beginnings of applied math for me. I was lucky to have encouraging teachers, particularly one in high school who arranged a number of meetings for me with Professor Tom Hull at the University of Toronto, with whom I did a small project on computing elementary functions. Later, I participated in Lawrence Livermore National Laboratory's high school program and got a chance to try programming on Cray supercomputers. By then, I was hooked.
In addition to math, I was also interested in science, and I decided very early on that I wanted to apply numerical methods to science by doing computer simulations. Unfortunately, as an engineering undergraduate at that time, I didn't find anyone doing this until my senior year, when I took three courses in numerical analysis and did a project in the computer science and applied math department. Professor Wei-Pai Tang was my project advisor. He took me under his wing and introduced me to numerical linear algebra. He also introduced me to Yousef Saad, who later became my Ph.D. advisor.
Job Characteristics
In my current position, I work on the algorithms and software used in molecular dynamics simulations. It is a highly varied and interdisciplinary role. Almost daily, I talk to chemists about their scientific problems, as well as hardware and software engineers who want to find accurate and efficient ways to implement chemistry algorithms. In computational science, math and algorithm problems pop up everywhere. Often these are very specific problems that require specialized solutions. There may be a complicated potential energy function we want to minimize, and we may want a minimizer tailored for a specific computer architecture. Sometimes the problems seem easy, but they're made difficult because of constraints, even if the constraint is that the solution is robust yet easy to implement.
Salary Range
Starting about $100,000, depending on location and company (urban areas of California and New York are higher).
Barbara Hamilton
Manager, Information Support Services
Institute for Defense Analyses (IDA)
Center for Communications Research Division, Princeton, NJ
B.S. mathematics (computer science), Central Michigan University
M.A. mathematics, Central Michigan University
M.L.S. library science, Rutgers University, NJ
Background
I was always good in math and enjoyed it. I had excellent math teachers in both the sixth and seventh grade who made math fun and showed me there were many areas of math to study. In sixth grade, my teacher told us we could work as much or as little as we wanted and what we did would be reflected in our grade. The first day of class in seventh grade, my teacher gave us a test to see where everyone was, after which she broke the class into two groups based on ability. However, I wasn’t put in either group. She took me to a filing cabinet and told me, “You’re going to work your way through this.” I had my first independent study, doing beginning statistics, probability, and all sorts of other interesting mathematical things. I took math as an undergraduate and graduate student because I found it fun, but I think my career path decided on me.
I worked as a cryptologic mathematician for the Department of Defense and as a documentation specialist for Renaissance Technologies, a commodities trading firm. Both jobs required understanding and implementing mathematical models to real world problems. When I was offered the library job, I was looking for something new and I thought it would be interesting. I took the job with the condition that I complete a library degree.
Job Characteristics
I supervise the running of our mathematics research library and oversee our production of research reports and the paper publication process. I help the research staff find information that they need, which sometimes means obtaining a hard-to-find book or article, or doing searches on the internet or in subscription databases such as MathSciNet. Because I have a degree in mathematics, it is easier for the research staff to explain to me what it is they are looking for because we speak the same language.
Salary Range
Starting: $40,000-50,000; mid-level: $64,000-$82,000; senior positions $104,000 or more
Mark Zandi
Moody’s Economy.com
Chief Economist
West Chester, PA
B.S. economics, Wharton School at the University of Pennsylvania
Ph.D. economics, University of Pennsylvania
Background
I knew I wanted to be an economist just a couple of weeks into my Econ 101 class as a freshman at the University of Pennsylvania. The course made clear to me that economics is an intriguing combination of mathematics and the social sciences. I wasn’t completely enamored with the abstraction of pure math nor the casual empiricism of most social sciences. Economics is grounded in mathematical theory and comes alive when the theory is tested against data and empirical analysis.
I have been a professional economist since leaving graduate school. I briefly worked for Wharton Econometrics (an economic consulting firm), started my own economic consulting firm, and sold that firm to Moody’s two and half years ago.
Job Characteristics
As Chief Economist for Moody’s Economy.com, I set the research agenda for a staff of approximately 60 economists located in the U.S., London, and Sydney. We produce analyses and forecasts for economies ranging from India to Indianapolis, and for clients ranging from the U.S. State Department to New York hedge funds. I spend much of my time assessing the global economy’s growth prospects, considering different economic policy proposals, and evaluating different risks to the economy and financial system.
My job entails a substantial amount of research, writing, and speaking. I also travel extensively, giving speeches and talks at conferences and to clients. The most interesting thing about my job is that nearly each day brings a new economic issue or concern that I must work to understand and evaluate and then to articulate what I’ve learned to my clients. I suspect that, like for most professions, as an economist if you are right just a bit more than you are wrong, you will be successful.
Salary Range
Salaries range widely for economists depending on the industry and region of the country. The best place to find out more about salaries for business economists is to go to the National Association of Business Economics www.nabe.com.
Wu Li
Senior Research Engineer
Aeronautics Systems Analysis Branch
NASA Langley Research Center
Hampton, VA
B.S. in mathematics from Zhejiang Normal University, China
M.S. in mathematics, Zhejiang University, China
M.S. in computer sciences, Pennsylvania State University
Ph.D. in mathematics, Pennsylvania State University
Background
I wanted to do something that would have a lasting influence on the science or society. My best ability was in mathematics, and so that determined my career path. I believe mathematics has its own elegance and beauty, just like arts or music, but in an intellectual and logical sense.
Before working for NASA, I was a professor of applied mathematics at Old Dominion University in Norfolk, Virginia. While there, I also worked as a consultant at the Institute for Computer Applications in Science and Engineering (ICASE) on a multidisciplinary research project (robust optimization under uncertainties) funded by NASA Langley Research Center, which led to my career change from a university professor to a civil servant at NASA.
It was when I started working as a consultant for NASA, that I and began to understand the huge gap between mathematical research and practice. The paper titled “Real Life Mathematics” by Bernard Beauzamy (Irish Math. Soc. Bulletin, 48 (2002), 43-46) struck a chord in my heart and best described my conversion from mathematical research to mathematical practice; it gave me some confidence that real life mathematics could make a difference.
Job Characteristics
I am currently a NASA senior research engineer working on the supersonic research project, under the Fundamental Aeronautics Program of NASA Aeronautics Mission Directorate, as the technical lead to develop a low-boom and low-drag supersonic configuration design optimization process. Our objective is to help the research and development of economically and environmentally viable supersonic aircraft. The low-boom and low-drag design goal requires a seamless integration of low-fidelity low-boom design tools and high-fidelity computational fluid dynamics (CFD) analysis/design tools. One of the design challenges is to use optimization methods for finding a low-boom supersonic configuration using high-fidelity CFD analysis.
I usually work on a vertical integration from theory to practice: discussing with customers to understand the required technical capabilities, developing a practical solution strategy based on as much theoretical foundation as possible, implementing the solution by using a computer code, and building an easy-to-use interface for the customers. This process usually goes through a few iterations because of potential miscommunications between developers and customers about the requirements.
Some of my daily activities include developing mathematical models, solution algorithms, or user interfaces; discussing modeling or solution issues with customers or team members; planning future research tasks or activities; researching relevant literature; and documenting research results. I also evaluate proposals funded by NASA, serve as technical monitor for funded proposals, and supervise graduate students working on NASA projects.
Someone in this type of position should expect to use computational mathematics, software development skills, and communication skills to develop system-level analysis and design capabilities for technology development.
Salary Range
At NASA, the pay is based on civil servant grade and step. The salary range from Grade 9 (Step 1) to Grade 15 (Step 10) is $45,040 to $140,355. You can find more information about jobs at NASA at www.nasa.gov.
Peter Norvig
Director of Research
Google, Inc.
Mountain View, CA
B.S. applied mathematics, Brown University, RI
Ph.D. computer science, University of California, Berkeley
Background
I was always interested in math; I thought it was one of the most fun subjects in school, and my dad was a math professor. As I progressed through school, I found that the computer science courses were more fun and much easier for me. In college the computer courses always seemed to be easy, and while I liked my math courses, I remember my number theory final exam as a turning point – it was a take-home final and after working on it for at least five hours, I had zero out of ten problems answered. I kept working on it, and eventually did fine, but I realized that it made more sense for me to concentrate on computer science, which I found easier, rather than the areas of math where I had to struggle. I also remember that teaching was a great experience for me. Brown had a program of undergraduate teaching assistants (TAs), instituted by Andy van Dam, and I learned a lot from having to explain things to other students. I also learned a lot from being a TA at Berkeley.
Job Characteristics
In previous jobs, I was more involved in hands-on software development and I’ve been lucky to have had a number of exciting jobs. I worked at NASA, where my team developed the first artificial intelligence program to control a spacecraft. Continuations of that work now schedule operations for the Mars rovers and several other space missions. I worked at a small startup doing integration of Internet job and shopping ads where we built the company up from nothing and eventually sold it to Amazon.com. I worked at Sun Microsystems Laboratories doing search/information retrieval – a precursor to Google today. And I also taught at USC and at Berkeley.
My current job is overseeing research projects at Google. That means working with the team to help decide strategic directions; which projects are important now, and which can wait until later; finding connections between technologies and products (e.g. this algorithm for clustering looks like it would be useful for Google News); and directing others to the right people to talk to about problems. To do this job I needed to develop intuitions about what will work and what won’t, something that I continue to do. There are so many things to try; so much data available, so many alternative ways to process the data, build learning algorithms for it, and deploy the results, that you need a feel for what is likely to work – and you need a lot of bright colleagues who sometimes prove you wrong.
What I like best is solving problems that help people – we can develop a better algorithm and immediately see that we’ve helped hundreds of millions of people in their daily lives. What I like least is being overwhelmed with too much email – but we’re working on that, too.
Salary Range
I think it is about $70,000 starting; twice that mid-level, and potentially many millions for the lucky ones at successful companies. To find out more about this field, read the news, Internet groups, and journal articles. There’s no shortage of information.
Mathematics in the software development and research technology fields
It is a fantastic time to be involved in this field. The Internet has made so much information available, and now we need smart people to help make sense of it all – to get the right data to the right people at the right time with the right presentation. And if that’s not enough work, so many other fields require an increasing amount of computational sophistication. For example: biology, genomics, and synthetic biology are all at heart information sciences; the challenges we face in climate modeling will require better computational models and methods; the entertainment industry increasingly relies on computer graphics for animation and special effects, and on artificial intelligence for games. The field of robotics is just starting to emerge; it has the potential to address major societal issues, for example autonomous cars can allow for a more efficient transportation system that helps with the energy crisis and home service robots can help care for the elderly. There are tremendous opportunities for exciting work that matters to society, and new students and graduates are needed to do the work.
Craig Trost
Independent Quantitative Research Consultant
Physician/Statistician, Senior Director, Translational and Molecular Medicine
Pfizer Global Research and Development (retired)
B.S. General Science, University of Iowa
M.D. University of Iowa
M.S. Preventive Medicine and Environmental Health, University of Iowa
Ph.D. Biostatistics, University of North Carolina – Chapel Hill
Post Doc, Cardiovascular Biostatistics, National Heart, Lung, and Blood Institute, NIH
Residency, Clinical Pathology, University of Florida
I grew on a farm in the Midwest and really didn’t consider going to college until sometime in high school. While in junior high school, I was introduced to the “new math,” which no one seemed to like except me. Since I liked solving puzzles, I found this fascinating. After taking geometry in high school, I decided that proving theorems didn’t interest me, and it still doesn’t. In the small high school I attended, the most advanced course was pre-calculus. During that class, I discovered functions and had the epiphany that they might be useful in modeling the real world, which lead me to finding something in applied mathematics. I decided to pursue mathematical physics.
Soon after I arrived on campus, the market for physicists hit bottom. My major then changed from physics to chemistry to biochemistry and then to early admission to medical school after my junior year. Although I took math and computer science courses to raise my GPA, at that time I had given up on using mathematics in my career. While in the middle of medical school, I discovered that biostatistics and computers were being used in medical research and I immediately gravitated in this direction. It also became obvious that physicians did not know anything about math or computer science and that massive amounts of data were being generated for patient care, literally untapped mathematically. In my third year of medical school, I decided to devote my career to creating computer algorithms to provide better care to patients. In particular, I wanted to take an applied mathematics approach since most others were trying this through artificial intelligence. Unfortunately, there were essentially no programs in biomathematics or mathematical biology at that time and certainly no career path, even in academia. I had to settle for biostatistics instead.
Over the years I have taken many paths to find a home for my ideas working for six different entities: a pathology faculty, a medical software startup company, and clinical IT, management, statistical research, and computational medicine in pharmaceuticals. Although the financial reward has been good, all of these paths have been uphill.
Over the past decade, I have been gravitating toward mathematical biology studying diagnostic patterns in clinical data, which is abundant in the pharmaceutical world. Most of the mathematics that I currently use have been self-taught and often I have had to write my own computer code, in varying hardware and software environments. My approach combines stochastic processes and stochastic calculus with parameter estimation procedures and confidence regions, and my medical training has been helpful. An inordinate proportion of my career has been spent finding or generating and restructuring data for analysis and modeling. The minority of time has been spent thinking about, developing, or testing models.
Mathematics in biology fields
Mathematical biology will be an important field in the coming decades. Consider that even non-math majors or double-majors in fields such as a quantitative discipline and a biological discipline may provide the skills you need to get the job and do the work.
Katya Scheinberg
Research Staff Member
IBM T. J. Watson Research Center,
Business Analytics and Mathematical Sciences Department
Yorktown Heights, New York,
B.S. (equivalent) applied mathematics and computer science, Moscow University
M.S. and Ph.D. operations research, Columbia University
Background
I grew up in Russia and my parents both have Ph.D.s in mathematics, so from early childhood I was surrounded by mathematicians. I attended a special mathematical high school, which I loved not simply because of the good academic program, but because of outstanding fellow students, many of whom became life-long friends. Ultimately what really made me choose mathematics for a career was simply the fact that I enjoyed it, found it fascinating, and it was easily my best subject in school. In fact, I was considering medical school during my junior year in high school, and it was my math teacher who told my parents that it would be a shame if I didn't go into mathematics. In those days in Russia, it was not a very common thing to tell the parents of a girl! I am very grateful for his encouragement.
In college one of my favorite courses was a course on general optimization. I decided that I liked the field and wanted to work in it and so I chose the professor of the class as my college advisor. As it turned out, even though the course covered little of the modern state of optimization, it did introduce me to the fundamental mathematics involved.
Job Characteristics
I develop theoretical and computational algorithms to solve difficult continuous optimization problems. These problems may arise in engineering design (such as tuning of circuits), in production planning (such as optimization of production in an industrial lab), in biology applications (such as constructing models of the human brain response), and in finance (such as portfolio optimization). I study general problems of optimizing linear and nonlinear functions subject to linear and nonlinear constraints. Various applications result in different structures of the underlying functions and I develop algorithms that target this structure to be able to find the optimal solution efficiently. Theoretical aspects involve proving that the resulting algorithms have convergence guarantees. The computational aspect involves developing software that can handle large scale and difficult cases in practice and in reasonable time.
I became a research staff member at IBM after I finished my Ph.D. Before I was hired for this position, I was a recipient of a special IBM student fellowship and spent two summers working at T. J. Watson Research Center. This fellowship and the work that I did during those summers were central to my joining IBM after graduation.
On a daily basis, I think about new ideas and prove theorems, write them down for a scientific publication, write code to test ideas or to generate software and numerical results supporting my ideas, referee papers, organize conferences, and perform other duties in the scientific community. When I am working on a project with a customer, I attend regular meetings where the application and possible solutions are discussed in various levels of details. I also perform internal administrative duties, such as participating in or running various committees. A typical day is spent in front of my computer with an occasional meeting to discuss ideas with colleagues. The best aspect of my profession is the flexibility and creativity involved. Even though I have superiors, I am able to decide what and how to work on something and when to do it. Another very important benefit is the amazingly intelligent people around me. My least favorite part is that I never feel smart enough! Something always seems too difficult to understand or to solve.
My work hours are dictated by my own commitment to different projects and deadlines and to my colleagues both inside and outside IBM. No one tells me that I have to work a certain number of hours and I can take a day off very easily if I need to. On the other hand work is never out of my mind and is always ongoing, as in any other creative process.
Career Expectations
Unless a researcher has administrative aspirations, the scientific career at IBM is quite straightforward. One expects to grow as an important contributor to the scientific community and as an experienced problem solver. Those from our department who choose to move on outside IBM typically go on to academia or another research lab. A few people go to Wall Street.
Salary Range
Starting $115,000; mid-level $170,000; senior positions $200,000 or more. The best place to find out about this field is at conferences on optimization and mathematical programming (ISMP and SIAM in Optimization and ICCOPT, INFORMS). Also, the IBM Research website, http://www.research.ibm.com is a good place for more information.
Importance and future of math in industry
I expect the applications and use of optimization in industry to grow for many years to come. Industry has only now started to accept sophisticated approaches to linear and integer programming problems. There are still many possibilities for other kinds of optimization and the applications are becoming more challenging with the growth of available data.
IBM started as a computer company and it is obvious why mathematics is important in computer industry. Math is still extremely important to hardware business like IBM for product design, manufacturing, and the distribution of products. Also, applied mathematics and specifically optimization have become extremely important to the IBM services industry. Optimization is used to model and address clients' business problems, which involve scheduling, workforce management, project management, supply chain management, and other common professional needs.
Karim Azer
Senior Research Associate
Applied Computer Science and Mathematics Department
Merck Research Laboratories
Rahway, NJ
B.S. mathematics and computer science (double major), Rutgers University, NJ
M.S. applied mathematics, Courant Institute of Mathematical Sciences, New York University
Ph.D. applied mathematics, Courant Institute of Mathematical Sciences, New York University
Background
One of the running jokes in my family is that I was born with a special interest in mathematics. It was my dream as a child to grow up to be a mathematician.
I started working full time at Merck developing object-oriented software libraries in the information technology department while I was enrolled as a part-time Ph.D. student at the Courant Institute. When Dr. Jeffrey Saltzman arrived at Merck and established the applied computer science and mathematics department, I started learning about applications of mathematics in industry and became very excited about applying the skills I was learning in school to projects at work.
I became interested in modeling blood flow in arteries after reading an article that was given to me by Dr. Jeff Sachs, my current boss at Merck. For my Ph.D. thesis, I worked with Dr. Charles Peskin at the Courant Institute on developing a fluid dynamical model of blood flow in the systemic circulation. My thesis work set the stage for me to work on cardiovascular modeling coupled with vascular imaging here at Merck, which is the main topic of research in my current position.
Job Characteristics
As an applied mathematician, I interface with people with a very diverse set of educational backgrounds, including imaging scientists, biologists, physiologists, physicians, and others. My primary function is to work closely with these scientists to provide mathematical solutions that address the medical and business needs as defined by decision makers within Merck. Once the problem is identified, I work with my team on formulating a mathematical model and delivering the solution within agreed upon timelines and expectations.
Salary Range
Median starting salary: $90,000; increases with level and expertise; mid- and senior-level salaries differ depending on career path. Merck's website, www.merck.com, provides useful information regarding current events and resources as well as job opportunities.
Mathematics in the pharmaceutical field
In the future, I see applied mathematics as being as integral to drug development as is basic biology and chemistry, and being critical not only for development of innovative medicine, but also for survival in the business of drug development. This will be especially true as we find new ways and technologies to probe the human body and collect native information about how our body functions, how it is designed, and how it is altered with age, disease, or drug intervention.
What I like best about my profession is that I can contribute to improving people's quality of life by being part of a large body that strives and thrives to provide improvements in human health. Not only can I contribute to this great cause, but I can do so in an environment where I'm continually learning, I'm on the cutting-edge of research, and I'm surrounded by brilliant researchers, many of whom are principal thought leaders in their fields.
Next Page: Advice from Professionals