This article reviews the Society for Industrial and Applied Mathematics (SIAM)’s Report on Mathematics in Industry (MII) 2012 which surveys the use of mathematics in industry and the jobs taken by recent Ph.D.’s in mathematics, applied mathematics, statistics, biostatistics, and some related mathematical fields. This article is a follow-up to What is Really Hot in STEM jobs?

The key findings of the SIAM report are:

- 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.

# Trends and Case Studies

The bulk of the forty-eight page report ( an Adobe Acrobat PDF version is available at the SIAM web site) consists of a discussion of eight trends and eighteen case studies in the use of mathematics in industry. In a number of ways the trends and case studies can create a rather different impression than the results of the survey above.

The report lists eight trends:

- Business Analytics
- Mathematical Finance
- Systems Biology
- Oil Discovery and Extraction
- Manufacturing
- Communications and Transportation
- Modeling Complex Systems
- Computer Systems, Software, and Information Technology

Keep in mind that a trend can be a prediction — a speculation — of what will happen in the future. In fact, only the first “trend” is clearly supported by the results of the SIAM report’s actual survey of recent Ph.D. recipients who have gone into industry. The other categories are extremely rare; the case studies are quite rare types of industry projects (e.g. IBM’s Watson, Boeing’s currently-grounded Dreamliner, and HP Labs memristor). Indeed, as discussed below, it is likely that mathematical finance jobs are quite rare.

To compare the report’s trends with the current job market, I looked at job listings on the popular LinkedIn job board “in or near the USA” on Sunday, Feb 3, 2012.

First, to establish the context (normalize the data), I searched for job posts with a range of common technical and business words and phrases.

**Note:** A “quoted phrase” means than LinkedIn searched for an exact match to the phrase. The words *quoted phrase* without enclosing quotes mean LinkedIn searched for job posts with the words *quoted *and *phrase* somewhere in the post. LinkedIn treats hyphens as spaces so that “finite element” matches both “finite element” and “finite-element”. The searches are not case sensitive. STEM is an abbreviation for Science, Technology, Engineering, and Mathematics.

Word/Phrase Number of Job Posts Notes Database SQL 11,677 (Structured Query Language for databases) database 13,541 Programming Languages java 8,522 C++ 6,103 C# 4,945 Python 3,372 Perl 3.157 PHP 2,717 Javascript 6,171 (not the same as java) Types of STEM Workers "software engineer" 4,485 programmer 1,256 software engineer 13,402 electrical engineer 3,871 "electrical engineer" 633 mechanical engineer 3,155 "mechanical engineer" 641 chemical engineer 1,128 "chemical engineer" 83 scientist 964 (mostly biotech and some data scientist) petroleum engineer 331 "petroleum engineer" 15 aerospace engineer 718 "aerospace engineer" 7 chemist 136 biologist 29 Credentials PHD 2,303 doctorate 523 Bachelors 9,995 "Bachelors Degree" 20,633 Masters 5,590 "Masters Degree" 3,015 "Master's degree" 3,743 MBA 6,829 (abbreviation for Master of Business Administration) CPA 5,939 (abbreviation for Certified Public Accountant) JD 1,683 (abbreviation for Juris Doctor -- lawyer) MD 2,973 (abbreviation for Medical Doctor -- a lot of non-doctors turned up in this search) Statistics statistics 4,233 statistician 134 SAS 2,485 insurance SAS 328 marketing SAS 774 pharmaceutical SAS 269 medical SAS 402 finance SAS 501 (only a handful are quantitative finance jobs "quants") "real estate" SAS 26 biotechnology SAS 144 aerospace SAS 16 "market research" SAS 83 economics SAS 408 econometrics SAS 83 policy SAS 190 "policy maker" SAS 14 signal processing SAS 7 "statistical programmer" 50 statistical programmer 157 SPSS 633 "R programming" 14 stochastic 96 stochastic calculus 15 (all quant -- quantitative finance -- jobs) Insurance insurance 20,515 insurance analyst 1,682 insurance MBA 951 Insurance and Statistics actuary 165 actuarial 654 insurance statistics 481 insurance statistician 6 insurance "machine learning" 27 insurance statistical 477 insurance SAS 328 High School and College Math geometry 240 trigonometry 74 algebra 181 calculus 53 theorem 8 "differential equation" 1 (quant job)

## Business Analytics

The key words and phrases from this trend retrieved many job posts — several thousand in fact.

business analytics 6,637 "business analytics" 3,347 analytics 9,041 data driven 6,913 "data driven" 1,602 (this will match data-driven also) predictive analytics 1,121 "predictive analytics" 629 Markov 11 Markov decision process 1 (Software Architect - Data Analytics (Healthcare), lots of statistics jargon, job for major multinational company in India) "Markov decision process" 0

## Mathematical Finance

This turned up very few job posts — about one hundred. While these jobs get a lot of publicity and reportedly pay very well by most people’s standards, they actually appear to be quite rare.

mathematical finance 9 quantitative finance 28 financial engineering 44 financial engineer 8 algorithmic trading 35 high-frequency trading 29

## Systems Biology

The SIAM report features a case study in this section of a protein folding research company funded by David Shaw (of D.E. Shaw hedge fund fame) as an example of industry interest in this area. In fact, this is an extremely exceptional case.

"systems biology" 16 "molecular dynamics" 9 "molecular dynamics simulation" 1 (R&D Engineer(TCAD) at chip design software company in SF Bay Area, not a biology job) "whole-patient model" 0

## Oil Discovery and Estimation

The SIAM report spends several pages on basin modeling for oil and gas discovery. At least based on job posts on LinkedIn, this appears to be a genuine industry activity, but quite rare.

basin model 29 (mostly at oil and natural gas companies) "fluid-flow model" 2 (both safety analysis at a nuclear power plant, not basin modeling) fluid flow model 29 (5 for oil companies, 1 a post-doc on "fracking", others non-oil)

## Manufacturing

This trend/category actually turned up about 800 job posts, still not very large and much less than business analytics.

multidisciplinary design optimization 1 (at a major car company) "computational fluid dynamics" 80 "finite element analysis" 197 robotics 301 robot 191 volumetric error compensation 0 linear program 1 linear programming 26

## Communications and Transportation

This category mostly discussed load balancing for computer networks. Curiously, there was no mention of video compression where there have been dramatic advances making feasible widely used services such as Netflix, YouTube, and Skype.

"probabilistic algorithm" 1 "probabilistic algorithms" 1 (same as previous search) "combinatorial optimization" 10 "load balancing" 694 (many network engineer positions -- mostly non-mathematical) "load balancing" mathematics 12 "load balancing" statistics 10 "load balancing" probability 1 "load balancing" algebra 3 (3D graphics accelerator chip design at a major semiconductor company) "load balancing" trigonometry 0 "load balancing" calculus 3 (same three as algebra above) "load balancing" matlab 2 (both at MathWorks which makes MATLAB) "graph theory" 16 "discrete mathematics" 5 "operations research" 406 "operations research" matlab 31 (many data scientist/business analytics type jobs, 1 quant) "operations research" SAS 132 (many data scientist/business analytics jobs) "operations research" analytics 178 ('nuff said) "operations research" "big data" 31 "operations research" finance 95

The operations research jobs overlap heavily with business analytics/data science. Only a few jobs that mention “load balancing” appear to have high mathematical content.

## Modeling Complex Systems

This trend/category turned up only a small number of jobs. The “biometrics” jobs appear to fall into the category of health/medical statistics. Only a few are algorithms for fingerprint recognition, face recognition, etc.

"Modeling Complex Systems" 4 "nonlinear dynamics" 2 "Nonlinear dynamical systems" 1 (R&D Fluid Mechanics) "mathematical modeling" 65 "complex systems engineering" 4 biometrics 122 (somehow in this category, most of these seemed to be biostatistics jobs)

## Computer Systems, Software, and Information Technology

This category included quite a number of topics that probably should be included under “business analytics”.

"pattern recognition" 74 "computer vision" 141 "natural language processing" 289 (analytics/big data jobs often) "information retrieval" 411 (analytics/big data jobs often) "machine learning" 1017 (analytics/big data jobs often)

# Conclusion

The SIAM Report on Mathematics in Industry 2012 confirms a very strong present-day industry interest in statistics, primarily statistical analysis of business and sometimes medical/health data. Seven of the eight trends identified in the report are actually rather speculative. Actual demand today in these areas appears to be quite small. Most of the case studies are not representative of the vast majority of industry jobs that utilize mathematics to a significant degree. Curiously the report says little about several areas where there is widespread industry use of mathematics: video compression (e.g. YouTube, Netflix, Skype, etc.), speech recognition (those annoying help lines), the global positioning system, and computer graphics for games and video effects. It spends a surprising amount of time on mathematical finance, much of which is rather dubious and where there are actually few jobs, rather than emphasizing the many real advances and even genuine breakthroughs (in video compression in 2003) in the practical use of mathematics, often in combination with today’s powerful computers.

It is worth noting that the actual demand for workers with strong mathematical skills based on the LinkedIn job postings is not particularly high. According to the National Science Foundation, the United States alone produced about 33,000 Ph.D’s in science and engineering in 2009. This includes almost 8,000 biologists, many of whom are trained in statistics for analyzing their experiments or field observations, over 1,700 computer science PhD’s, 1,400 Math PhDs, over 4,000 PHD’s in the physical sciences — including almost 1,600 physicists. The United States produced 7,862 Ph.D.’s in Engineering in 2009. Most of the jobs listed on LinkedIn use mathematics taught in the first two years of a strong science and/or engineering program at a college or university.

© 2013 John F. McGowan

**About the Author**

*John F. McGowan, Ph.D.* solves problems using mathematics and mathematical software, including developing video compression and speech recognition technologies. He has extensive experience developing software in C, C++, Visual Basic, Mathematica, MATLAB, and many other programming languages. He is probably best known for his AVI Overview, an Internet FAQ (Frequently Asked Questions) on the Microsoft AVI (Audio Video Interleave) file format. He has worked as a contractor at NASA Ames Research Center involved in the research and development of image and video processing algorithms and technology. He has published articles on the origin and evolution of life, the exploration of Mars (anticipating the discovery of methane on Mars), and cheap access to space. He has a Ph.D. in physics from the University of Illinois at Urbana-Champaign and a B.S. in physics from the California Institute of Technology (Caltech). He can be reached at jmcgowan11@earthlink.net.

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A minor correction.

The survey of LinkedIn was performed on Sunday, Feb. 3, 2013 (not 2012).

John

Great post and very informative.