## Life After the PhD

- 3.1 Background and Demographics
- 3.2 Role of Recent Graduates in Their Companies
- 3.3 Qualifications and Skill Sets

**Results from the MII Survey**

The job market for PhD mathematicians has fortunately improved considerably since the 1996 MII survey, which was conducted at a time when unprecedented numbers of new PhDs were unable to land an academic position or any job at all. By comparison, very few people in this survey were forced into taking industrial jobs because they couldn’t get a job in academia.

A detailed discussion of the findings of the survey follows below. Here are some of the highlights:

- Roughly half of all mathematical scientists hired into business and industry are statisticians. The second-largest group by academic specialty is applied mathematics.
- By far the strongest employers of mathematicians are the finance and insurance sector and the pharmaceutical/medical device sector. Pharmaceutical hires are almost exclusively statisticians, while in the financial sector the majority of the hires are mathematicians.
- As reported in 1996, almost none of the mathematicians have “mathematics” in their job title. By contrast, the title of statisticians often refers to their specialty.
- The job satisfaction of the survey respondents was quite high, with nearly 90 percent reporting satisfaction with their compensation and benefits. Median pay for the respondents was about $100,000 for both men and women.
- Compared to the 1996 survey, fewer graduates reported “modeling and simulation” as an important academic specialty for their jobs, and more reported “statistics.”
- However, in a somewhat contradictory finding, the most important item evaluated in performance reviews was reported to be mathematical models.
- Programming and computer skills continue to be the most important technical skill that new hires bring to their jobs.

### 3.1 Background and Demographics

As mentioned in the introduction, a major difference between this survey and the one conducted in 1996 was the inclusion of graduate students from statistics or biostatistics departments. We felt that this provided a more realistic and inclusive view of the job market for students in the mathematical sciences. However, in cases where we have compared the two surveys, for consistency, we have only used data on the mathematics and applied mathematics students.

The four groups covered by this survey are the 2004-05, 2005-06, 2006-07, and 2007-08 hiring cohorts. Some basic demographic information on these cohorts is provided by the annual AMS-IMS-SIAM survey of doctoral candidates. Of all the PhD graduates in the mathematical sciences from 2004-2008, 787 (15%) took jobs in industry. Of these, 426 (54%) did their thesis work in statistics and 361 (46%) in mathematics. The areas of mathematics most frequently represented were applied mathematics (10%) and probability (9%). (See Table 1). Note that these are figures for the total set of PhDs hired by industry in the AMS-IMS-SIAM data.

Our intention was to conduct an e-mail survey of all PhDs in the above data set. However, we could find working e-mails for only 40% of the PhDs using the data provided or using search on the web. Our web-based survey attained a 30% response rate which is typical of such surveys. As a result, we make no claims of statistical significance for our results. However, the distribution of specialties for our survey respondents is similar to the population as a whole (see Table 1), and this gives us some confidence that we obtained a representative sample. Statisticians are slightly underrepresented and applied mathematicians are slightly overrepresented in our sample.

The respondents to our survey included 19 women and 37 men. With such small sample sizes it is difficult to do any serious comparative analysis between the two groups. We will simply report that a majority of the statisticians in our survey were female (12 women, 10 men), while the applied mathematicians were overwhelmingly male (1 woman, 9 men). We do not offer any interpretation for this disparity, but it bears watching in the future.

A large majority (81%) of the PhDs in our survey work for companies with at least 250 employees. Thirteen percent work for small companies, with fewer than 50 employees. The median salary ($100,000) was identical for men and women. The variation about the median was also extremely similar, with the first quartile at $90,000 for both genders and the third quartile at $115,000 for men and $123,000 for women.

Using the data from the AMS-IMS-SIAM annual survey, we classified employers by broad industrial category. The top employers were finance and insurance (30%) and pharmaceuticals and medical devices (28%). These sectors employ about twice as many recent graduates as the next leading category, business services (14%). (See Table 2.) Nearly every major company in the pharmaceutical industry hired several PhDs per year, and nearly all of these hires worked in statistics. Most of the major financial firms hired about 2two PhDs per year. The companies not in these two categories that also hired on average two PhDs per year were the SAS Institute, Google, IBM, and Microsoft Research. The last column of Table 2 compares the full population data to our survey recipients. Some discrepancies arise because we under-sampled statisticians, and also because the survey asked respondents to classify the division of the company in which work (which may be different than the company itself).

We analyzed the cohorts 2008-2009 and 2009-2010, asking whether or not the leading employers or the number of hires changed during the recession years 2009 and 2010. The answer was essentially no change. The leading employers hired between 87% and 94% of all PhDs in the same proportions.

Although we did not survey PhDs who took jobs in government, the AMS-IMS-SIAM data for these graduates allowed us to analyze their research backgrounds and employers. The areas of research were similar to those PhDs who went into industry, with strong concentrations in statistics, applied mathematics, numerical analysis, differential equations, and discrete mathematics (in that order). The top employers were the FDA, NSA, NIH, Los Alamos National Laboratory, Sandia National Laboratories, the other national laboratories taken as a group, and the Veterans Administration. These employers accounted for 81% of government PhD hires. The PhDs who took jobs in government from 2004-2008 accounted for 3% of all PhDs. Interestingly, while the financial industry was bulking up on PhDs from the mathematical sciences, the government hired only one such PhD into its financial agencies, in this case to the Federal Deposit Insurance Agency.

For the years 2004-2008, we analyzed the 25 departments that graduated the most PhDs who took industrial jobs. The top 25 programs in statistics send, on average, twice as many of their graduates into industry (on a percentage basis) as the mathematics programs. The range for statistics programs is 15% to 70%, while the range for mathematics programs is 10% to 40%.

We also extracted data on PhD advisors and the number of PhD graduates they supervised who went into industry. Of the PhDs who took a job in industry, 82% of their advisors had only one such PhD over the four-year period, while 11% had two, 6% had three, and 1% had four or more. These data suggest that for a large majority of graduate students, the decision to enter industry is more of a personal choice than one resulting from pressure or expectations from the advisor. Many of the students in our survey completed internships or had some other formal interaction with industry, e.g. industrial workshops or mentoring by an industrial scientist. In such cases the advisors may have facilitated or encouraged the students’ interaction with industry, even if they themselves did not collaborate with industry.

### 3.2 Role of Recent Graduates in Their Companies

*(The job is) intellectually stimulating without all the built-in failure of academic research. Academia necessitates a “publish-or-die” mindset in early career to make tenure. Work-life balance is not respected or encouraged.*

The reasons given by the PhDs in our survey for joining industry were topped by expectations of higher compensation and better opportunities for career advancement, (see Table 3). Nearly half mentioned their experience with industrial internships and roughly a third already had jobs in industry; both of these figures suggest that in most cases the decision to take an industrial job was not a last-minute choice, and the students were well-prepared. Not surprisingly, an undercurrent of dissatisfaction with academia runs through the comments, as exemplified by the above quote. Only two students reported that they took a job in industry because they could not get one in academia or government.

A high percentage of the PhDs in our survey were very satisfied or satisfied with compensation and benefits (88%) and lifestyle (80%), even if those were not stated as a primary reason for choosing a job in industry. (See Table 4). The jobs did not require them to sacrifice intellectual challenge, which was highly rated. However, not as many were satisfied with the opportunities for scientific growth. This contrast is likely due to the more project-oriented focus of industrial jobs, particularly in the first few years after graduate school.

The survey collected information on the primary mission of the groups that employ PhD mathematical scientists. (See Table 5). There are no clear leaders, but one noteworthy trend is the reduction in percentage, compared to the 1996 survey, of groups whose primary mission is software (35% in 1996 versus 13% in the current survey). Except in some cases of small groups of 5 or fewer people, the groups were interdisciplinary, including some mixture of engineers, computer scientists, physical scientists, or graduates in finance and economics.

As we pointed out in 1996, mathematicians rarely have job titles that are specific to their degree. (See Table 6a). The exception is statistics, for which titles like “senior statistician” or “biostatistician” are more common, especially in the pharmaceutical sector.

A mathematician is much more likely to be identified as an “analyst,” a “modeler,” or simply a “researcher.” The practical significance is that mathematical scientists who are not statisticians are likely to face competition from graduates with strong quantitative skills from other disciplines, and they may need to convince their employers of the relevance of their mathematical background. In Table 6b, we also list actual job functions, as reported by the respondents. In job functions, we see an even stronger emphasis on statistics, software, programming, and computer science.

An impressive 15% of our respondents were already identified as “managers,” and 21% reported management as one of their job functions. In view of the fact that many students choose industrial careers because they expect to advance more rapidly than in academia, it is encouraging to see that, for a significant fraction, these expectations are being rewarded.### 3.3 Qualifications and Skill Sets

*Computation is not enough. Our recruits need to understand algorithms, mathematical modeling, and the application. Perhaps 20 percent is implementation on computers, but 80 percent of the work involves understanding the physics and engineering.*

The skill set of graduates encompasses technical depth in a relevant discipline, breadth of knowledge across the mathematical and computational sciences, interest in and experience with the scientific or business focus of the employer, enthusiasm for varied challenges, the flexibility and communications skills required to work in an interdisciplinary team, the discipline to meet time constraints, and a sense for a reasonable solution.

The technical skill set has not changed dramatically since 1996, but continues to depend very much on the industrial sector and the group in which a graduate is employed, (see Table 7). Compared to the earlier survey, fewer respondents cited “modeling and simulation” as essential or important. However, this last finding seems to contradict the answers we received to a question on what metrics were important to the respondents’ annual performance reviews. The leading answer to that question was “mathematical models,” at 67%, followed closely by “presentations to management” at 64%, (see Table 8). Perhaps the apparent contradiction means that mathematical models remain crucial for job performance, but the pedagogy of mathematical modeling is in some way not keeping current.

In the 1996 survey, advanced computation was rated essential or important by 83% of graduates. In the current survey, we explored this in more detail. Programming (86%), computational science (57%), data mining (40%) and software engineering (34%) were the computational disciplines rated as essential or important. Overall, 65% of the respondents rated the mathematical or computational sciences as highly important to the success of their group.

In our 1996 report, we clearly emphasized the importance of communication skills. Table 8 shows that outputs related to communication skills (“presentations to management,” “preparation of internal reports”) are at least as important for advancement as technical accomplishments (“mathematical models,” “software development”).

Likewise, our on-site interviews returned again and again to the theme of soft skills such as communication, teamwork, flexibility, and willingness to listen. Some of the comments we received are given below.

*“Soft skills make the difference.”*

*“You often can’t guess who can’t make the transition [to industry]. After the fact, you can see that the successful ones are good listeners, who are tolerant of other people’s ideas and willing to make incremental improvements.”*

*“You have to be able to explain projects to non-experts. PhDs often have more flexibility than MSs, because they have been required to think outside the box.”*

*“Must be willing to ‘get hands dirty’ to help the firm meet its business imperatives.”*

*“Must be able to attack and solve unstructured problems.”*

Our survey also asked the recent graduates for advice that they would give to graduate students who are now considering careers in industry. We received 21 responses, such as these:

*“In banking, the current challenge is to sieve through huge amounts of customer data. Any training in mass data manipulation would be a plus.”*

*“Be open-minded, attend practitioners’ seminars, learn to program, and you’ll be fine.”*

*“Pursue internships. Follow your interests. Acquire database skills.”*

*“PhDs tend to underestimate the quality of science done in industry. You will get to solve challenging problems in industry, too.”*

*“Get internships and learn to program a computer. From my perspective, programming is essential for almost any industrial mathematician.”*

*“Seek internships in industries you are interested in. Do not focus so much on the degree. Think outside the academia box. Work on people skills. It does you no good to be smart if you can’t communicate or work in teams.”*