A few months ago, I was talking to a client in Johannesburg, South Africa, when we were stymied by a telecom bandwidth economics and modeling issue.
The client has a capacity and business-planning team whose role it is to predict, given unit pricing of various bandwidth circuit types (155 mbps, 622 mbps, 2.5 Gbit/s, and 10 Gbit/s), the optimal basket of circuits that will simultaneously reduce overall cost and handle the rapidly accelerating traffic growth.
Historically, such decisions were made infrequently, they were static in nature, and calculations could be approximated manually, meaning with simple Excel formulas. But this time, the client was contemplating a major investment and needed to run various options to account for long-term traffic growth and price compression scenarios.
When I reviewed the client’s model and issues, the problem and required techniques seemed to fit something I had learned years ago in a course in operations research at the Ecole des Mines in France. Back at my hotel, I took out paper and pencil and jotted down what I thought was the problem:
Minimize \(F = 100^*x + 300^*y + 700^*z + 1000^*w\), where the variables \(x\), \(y\), \(z\), and \(w\) are the units of capacity to purchase and the coefficients 100, 300, 700, and 1000 the given price for each capacity, subject to the constraint that \(x\), \(y\), \(z\), and \(w\) are integers (you cannot purchase half circuits) satisfying the inequality \(155x + 622y + 2480z + 9920w \geq T\), where \(T\) is the given traffic need. A complicating factor was that pricing changed over time and with the length of the circuit, and that traffic was growing each year.
I realized that this was a classic optimization problem, requiring use of a simplex algorithm. Indeed, this simple but powerful method helped the client’s forecasting team solve the problem once and for all.
Math is powerful, even with only a fraction of its potential tools applied in business and management. This is not to say that every question should be turned into a mathematical model to solve. Quite the opposite: With intuition, basic analytical skills, and experience, we can for the most part address problems with simple calculations and logic.
Career Options for a Mathematician
Growing up in Mauritania, West Africa, I always enjoyed mathematics. The subject was logical and did not require costly tools or textbooks; moreover, the country’s educational system rewarded the study of mathematics and engineering, as these skills were scarce and needed. (Mauritania was known as the country of a million poets!) Yet, because of the country’s lack of resources, the math curriculum emphasized abstract mathematics.
When I ended up in France for my undergraduate studies, I discovered applied mathematics and started to develop a taste for it, which led me to a graduate program in engineering at the Ecole des Mines de Saint-Etienne. Still uncertain about my future career, I completed two master’s degrees—one in engineering at the Ecole des Mines and the other, to keep my options open, in applied mathematics at the University of Lyon. Adding to the mix, I developed an interest in information technology and computational science.
Without much long-term job planning, I landed in Chicago to start my career as a scientific programmer at Argonne National Laboratory. But a few years later, influenced by friends and alumni from the Ecole des Mines, I realized that with my math skills I could pursue a nontraditional professional path that might be more rewarding. To facilitate a career switch, I enrolled in an MBA program at Northwestern University. I have to admit that with my math background, many of the analytical courses seemed straightforward; however, I began to develop a passion for the soft skills of marketing, strategy, and management.
Whereas math is an important instrument for solving problems, other disciplines can provide better tools for selling the solution—which is what is required in business! Yes, the world is not as logical or Cartesian as I thought growing up in Mauritania.
Why Management Consulting? Why Strategy?
Most of my MBA classmates already had a firm idea of the careers they wanted to pursue, having arrived with several years’ experience within specific industries. I was a mathematician, and modeling complex equations to solve superconductivity problems (i.e., Ginzburg–Landau equations) was my strength. I thought my options were limited, but realized when I began to look for a position that for many recruiters, analytical and quantitative skills are among the key criteria. Employers can teach us business, but math skills are harder to acquire on the job. One profession—management consulting—stood out for me as providing the greatest long-term flexibility.
Management consulting is the practice of helping organizations improve their performance. A relationship with an organization generally starts with a review of a specific problem the organization would like to solve. This is followed by the development of hypotheses or assertions of a possible answer, after which those hypotheses are either substantiated or disproved via rigorous data-driven analysis.
Based on their experience, management consultants are often hired to provide advice or an external industry perspective, or for benchmarking. They are sometimes viewed as neutral and external to the organization’s internal politics. They can bring a fresh perspective and intellectual horsepower to tackle complicated issues.
Generally, the consulting industry hires from top programs and gives preference to candidates with strong analytical backgrounds. The recruiting interview process sometimes involves case studies that can take the form of a math or logic quiz; for example:
- Estimate the number of golf balls you can fit in a 747 plane (not that you’re likely to do it)
- Estimate the number of garbage cans in New York City. Some may ask you to go further and estimate the number of rats living in New York City (do you see the correlation?)
- Estimate the number of Wi-Fi connections in London
Obviously, we don’t expect you to know the exact answer to any of these questions. What the recruiter is looking for is your level of comfort with uncertainty, and your ability to structure a methodology, follow through with calculations, and come up with an answer that can then be debated.
Other important skills in consulting are communication (oral, written, and with PowerPoint); research, both primary (involving interviews and discussions with customers, and more) and secondary (desktop studies only); and economic modeling (mostly in Excel, but sometimes with MATLAB).
The consulting industry comprises key specialties, such as Strategy Consulting, Operational Improvement, Changing Management, Audit/Finance, and Information Technology. It can also focus on specific industries, such as consumer products, media, entertainment & communication, transportation & logistics, health care, financial services, and manufacturing, to name a few.
Strategy consulting, which tackles strategic issues of growth, expansion, divestiture, and profitability, is sometimes considered the crème de la crème of consulting. It is, however, among the most volatile segments, especially during downturns. The work is a bit more abstract—it often requires identifying business patterns and devising innovative solutions. You often need intuition (preferably backed by experience) to come up with answers. Strategy consulting is where the frontier of business modeling is pushed and where your decision can have the strongest impact (can make or break a company).
Many consulting firms have global operations with domestic or international clients. The latter segment has been growing rapidly in recent years, driven in part by the growth of emerging markets, where many infrastructure projects are in progress.
Consulting in Emerging Markets
Practically speaking, no country, company, stock, or index can grow indefinitely and deliver above-average performance. Developed markets have had a great run historically, but we cannot expect countries like the U.S., with less than 5% of the world population, to continue to command more than 20% of the total gross domestic product. This is not to suggest that the U.S. will not continue to grow, but rather that other countries are likely to develop faster in the future. This may already be the case for emerging markets, and Africa could actually be the surprising story over the next few decades.
One of the key skills you acquire as a consultant is the ability to transfer and apply knowledge across companies, industries, and countries. Having witnessed the explosion of communication, storage, and computing infrastructure and applications in the U.S., I found it natural to apply this experience to emerging markets. In most cases, the problems you address in that part of the world are classic (they have already been solved in developed markets), and the answers are known. All that is generally required is strong and disciplined execution.
Infrastructure development in emerging markets is an expanding area. Implementation of all these large projects requires skilled and experienced people—especially those with analytical skills. Consulting is not the only route, however, for someone hoping to participate in the development of infrastructure in emerging markets. Among the many other avenues are NGOs, the World Bank, international institutions, and universities. Junior mathematicians, statisticians, and computer scientists can participate and provide tremendous value in emerging markets. You need not be afraid to seek experience “far away from home”; the proliferation of phone and Internet connections has made the world a small village.
Opportunities for Mathematicians
The management consulting industry is always competing for top talent. The good news is that analytical and other hard skills are the first thing a recruiter is likely to seek in a résumé. Most companies hire at several educational levels: bachelor’s, master’s, and PhD. The recruiter will want to see that you have the ability to combine your analytical skills with common-sense business approaches in tackling practical problems.
You need to demonstrate that you can go beyond research papers and publications—not that these are unimportant—and can quickly grasp the problem at hand and draw from your scientific toolkit a methodology that will lead to a practical solution.
Opportunities for math and science majors have always been abundant, but I believe that they are even more so now. The needs are enormous as the world shifts to digital economies. For instance, an emerging field like Big Data, with its data sets too large and complex for analysis by standard tools, can probably absorb significant numbers of mathematicians, scientists, economists, financial modelers, statisticians, computer programmers, and others in related professions.
Conclusion: You Have the Option
Each period of development brings new types of careers, along with a reduced need for others. Some even risk extinction. With the growth of technology and communications, the cycles of change are more pronounced. It is difficult to predict where the next wave of careers will emerge, but the underlying factors that will prepare you for the future remain the same: your ability to think and solve complex problems.
Your math and science skills provide you with the option to change and adapt. They may also give you the basic building blocks for efficiently and confidently solving what may seem to be odd or unusual problems.
When I walked into my client’s office in Johannesburg a few months ago, I did not expect that an old mathematical algorithm in my toolkit would save the day, let alone that it would elegantly address a real headache for the customer.
Sue Minkoff (email@example.com) of the University of Texas at Dallas is the editor of the Careers in the Math Sciences column.