## Advice from Professionals

“I strongly encourage undergraduates and high school students to take as many mathematics courses as possible, even if they do not choose mathematics as their major. The role of math in almost every field is expanding and will continue to expand in the near future. In addition to giving your career a boost, strong quantitative skills come in handy in ways that are not always obvious, but nevertheless have a strong impact on your everyday life. For example, an understanding of probability and statistics makes you a better decision-maker when faced with uncertainty. A strong mathematical background may also help you make smarter savings and financial planning decisions.”

**– Anshul Gupta, IBM T. J. Watson Research Center**

“Be voracious in your appetite for applying your mathematical skills to real problems, be careful not to become narrow in your skills, and constantly remind yourself that others in the company may not see your skills as critical.

“There is no doubt that a sound mathematical basis is more sought-after than ever in all areas of business, but the requirement of achieving measurable gains more quickly does lead to the need for more than sheer mathematical skill. In addition, the successful mathematician must be results-oriented, must prefer workable over ideal solutions, must work well in teams as both member and leader, and must be willing to adapt quickly to new needs. Generally, the most valuable employees are those that can identify a useful tool and adapt it to company’s needs rather than creating something from scratch.

“I foresee that the tendency to ‘share’ resources between industry and academia will accelerate more quickly. Also, since most customers of mathematics cannot distinguish between the mathematical idea and the software in which it is embedded, it is critical to have a working knowledge of various packages, databases, and delivery systems.”

**– Bill Mawby, Michelin America Research and Development Corporation**

“Learn the language of other disciplines by ‘going to where they hang out,’ especially during junior and senior years of college. For example, attend seminars sponsored by other academic departments to gain awareness of their nomenclature and topical issues. Attend professional conferences and trade shows to view the latest technologies and applications. Engage in conversations with the other attendees and listen to how they describe their processes and problems.

“Practice structuring problems encountered in other fields. Start with simple examples; describe algebraically the relationships among a few variables. What would it mean to the application if one of the variables changed slowly? Quickly? How well does the mathematical model fit or predict the data from the problem? What insights does it offer that are not as readily available via physical experimentation? Discuss the solutions and interpretations with practitioners in the subject field. This will hone both mathematical skills and the ability to communicate with non-mathematicians.

“Draft a résumé as early as freshman year and periodically update it in terms of goals, credentials, and experiences; compare the phrasing of your résumé with the words used in job descriptions found in placement offices and on job boards.”

**– Ed Moylan, Ford Motor Company (retired)**

“Math has become a mainstay of economics. Without strong mathematical underpinnings, economics loses its rigor and thus its credibility. A necessary condition to be a good economist is thus to be at least a proficient mathematician. Math is vital to formulating economic theory, constructing accurate data sets, and applying theory to the data.

“Key advice: be sure that you are very proficient in math and statistics before going to graduate school in economics. I would also suggest working during and between undergraduate and graduate school at consulting firms, think tanks, different types of businesses, and in government to see how economics is applied to everyday problems. This is important even for those who ultimately plan to go on to academia.”

**– Mark Zandi, Moody’s Economy.com**

“My advice to mathematics students is to develop both a breadth and depth of knowledge and understanding of fundamental areas of mathematics. Do your best to take courses from other disciplines and expose yourself to a wide range of fields and applications. Get advice from academics and practitioners from different industries, and learn about their work. Finally, engage in the area of research that you enjoy most and find most fulfilling.

“As a hiring manager, I see that students coming into the workplace are extremely well prepared, having mastered more than one technical area, and with a diverse educational background. Mathematics students pursuing biomathematics careers have solid background in biology, in addition to the standard dose of mathematics taught at the Ph.D. level. Expect to be immersed in a multi-disciplinary environment alongside scientists with cross-disciplinary expertise.”

**– Karim Azer, Merck Research Laboratories**

“Get involved in projects beyond your coursework. Whether it is a pet project of your own, a research project with a professor, a contribution to an open-source project, work at a company outside of school, or a competition such as the ACM programming contests, the FIRST Robotics League, or Moody’s Mega Math Challenge, you learn a lot by doing a project: how to work with others, how to meet deadlines, to compare yourself to others, and the thrill of accomplishing something worthwhile.

“My second piece of advice (which ties in with the first) is that you tend to regress to the mean of your peers, so surround yourself with the best peers you can find, and learn from them. You definitely learn something by being the biggest fish in a small pond, and you should make sure you get that experience a few times, but you learn more from being surrounded by the best in your field.”

**– Peter Norvig, Google, Inc.**

“Students should realize that they are responsible for their own future. For those who wish to pursue an industrial career, they need to understand why they are on their company's payroll. They need to work not only on what is interesting to them, but on what is important to the company. Solve real problems, not imaginary ones. The greatest skill is to be able to package elegant solutions that appeal to a wide audience of non-experts.”

**– Dimitris Agrafiotis, Johnson & Johnson Pharmaceutical Research**

“Whatever you decide to do make sure it is something you like! Also, a friend says he always tries to work with people who are smarter than him, so that he will get smarter in turn. Look into how to network with people in your field or interest area, especially through professional societies.”

*– Barbara Hamilton, Institute for Defense Analyses, Center for Communications Research Division, Princeton*

“There are so many learning opportunities for students in engineering, science, and mathematics. I would recommend that students seek out those opportunities and apply for every one. For example, students can participate almost every year of college in summer internship programs. The Navy has an internship program that gives students a chance to work in their labs for 10 weeks in the summer. The program generally gets few applicants who are math majors.”

**– Kimberly Drake, Naval Surface Warfare Center, Carderock Division**

“In practice, mathematics is a tool. New mathematical results are only important if they have some impact in useful practical applications. Teamwork is critical for the success of mathematics in practice. Pay attention to customer needs and requirements. Students should realize that promotion is based on leadership and technical excellence. Having one special skill might not be the best option in this dynamic information age.”

**– Wu Li, NASA Langley Research Center**

“Never assume that some subject of mathematics will not be useful to you in the future. In college, I did not like statistics and decided not to study it any further since I assumed I would choose work that didn’t involve statistical methods. Now one of my biggest research interests is in applications of optimization in statistical machine learning, and I wish I knew more statistical theory.

“Choose your first subject of research carefully, so it is not too competitive but also not too obscure. Definitely learn to write code to demonstrate usefulness of your algorithmic ideas.”

*– Katya Scheinberg, IBM T. J. Watson Research Center*

“The math problems that you'll encounter at work normally will not be related to the ones you studied or wrote your thesis on. My advice is to take advantage of a wide variety of classes while you are at school, as they will help you work on diverse sets of problems later on. It is really true that the theoretical ideas you learn in school actually apply very well when you put them to work in practice.

“I cannot express enough how important it is to develop clear communication skills, both in speaking and writing. This is not just a language skill, but also a skill for clear thinking. After you've proven yourself with your technical skills, it's these communication skills that will take you farther in your career. With the increasing advantages of using computing in science and engineering, I believe the opportunities in computational science can only grow.”

**– Edmond Chow, D. E. Shaw Research**

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