Mathematicians generally work in theoretical mathematics or applied mathematics, and their daily routine is determined by which of these specialties they’ve chosen. Theoretical mathematicians work with mathematical theory in research and academic settings, rarely with a practical application in mind. Applied mathematicians apply mathematical principles to practical problems, such as cryptography, economic analysis and data-interference patterns. Both theoretical and applied mathematics are important in the real world; advances in both disciplines have led to breakthroughs.
Theoretical mathematicians are generally mathematics professors or graduate students, with stipends or grants to work on mathematical problems that concern them. The majority use computers in their analysis, and most work alone a large part of the time. “You don’t really notice that you’re alone,” wrote one respondent about the solitude this profession maintains, “because you’re focusing on the problem.” Professional communication takes up the other large block of time in the theoretical mathematician’s life; some estimate that they spend over thirty percent of their time reading professional journals, talking on the telephone with other mathematicians, and attending conferences on related topics. The applied mathematician works in a business setting, usually on a specific task. He is paid to use mathematical concepts to analyze behavior and improve existing systems. This can involve a lot of guesswork: “About ninety-nine percent of the time you’re wrong,” said one mathematician, “so you try again. Every now and then you get something right.” Those with low failure-tolerance levels should think long and hard before entering this end of the profession. Many applied mathematicians said interpersonal skills are quite important in mathematics positions, and many wished they had taken more writing courses in college as their jobs require regular reports on progress and development.
Mathematicians said the best feature of their profession is the intellectual challenge of struggling with these numbers on an everyday basis. No mathematician thought he would ever solve all the problems—most of our responders would agree with the theoretical mathematician who wrote: “You can struggle with an equation for ages, trying to get it to tell you something, but if it doesn’t want to, there’s nothing you can do.”
There are strict academic requirements for mathematicians. Over 180 schools offer Ph.D. programs in mathematics. About 97 percent of theoretical mathematicians have a Ph.D. For entry-level positions in applied mathematics, most employers accept candidates with only a bachelor’s degree in mathematics, but many ask that those candidates have cross-disciplinary experience, such as math/computer science, or math/economics. These new hires input data, write simple analysis programs, and do basic mathematical modeling. To progress to a level of significant responsibility or leadership, many mathematicians find it helpful to earn an advanced degree not in mathematics, but in a related discipline, such as computer science, statistics, or materials engineering. A curious mind, sound deductive reasoning skills, and a willingness to approach difficult (and sometimes unsolvable) problems are all characteristics of the successful mathematician.
Many areas are open to mathematicians who leave their profession. Computer programming, cryptology, teaching, financial analysis, and economics all provide sound homes for those with mathematical training. In the course of their work, many mathematicians come into contact with these professions and find one of them more appealing.