Industry is not something earlycareer mathematicians often think of when considering their career options, but perhaps they should. Industry can offer a good remuneration package and applied problems that have become more challenging and fulfilling as products and processes have gained in complexity. Occasionally, industrial mathematicians even push the frontiers of knowledge, as in the mathematical description of surfaces made by Paul de Casteljau, a researcher at Citroën, and later Pierre Bézier, a researcher at Renault, for the modelling of car bodies.
Using mathematics to find solutions to applied problems isn't new, of course. The tradition goes all the way back to the Greek mathematician, physicist, and engineer Archimedes, who built a machine consisting of two poles and a pulley system that was able to lift a ship from water using the physical principle of the lever.
Mathematicians in industry often work on optimising products and processes. At IBM [1], for example, mathematicians may work at reducing the company's costs in time and resources of transporting goods. Corporate logistics requires the coordination of many production and corporate sites, so it can get very complex, says Gunter Dueck, chief technologist at IBM in Mannheim, Germany, where about 8% of the degree holders in his department are mathematicians. At Shell Research [2], mathematicians are working to extract underground gas and oil reservoirs more efficiently, says Hennie Poulisse, a senior mathematician at the Gas & Oil Exploration division in Rijswijk, the Netherlandsone of the four Shell research labs.
Along with the increasing complexity of technical devices produced by industry comes increased risk, and mathematicians may also contribute to the management of that risk. At Siemens Corporate Technology [3], mathematicians (who also constitute about 8% of degree holders) tackle risk through computer modelling, according to Albert Gilg, Competence Center department head at Siemens in Munich. Industries that produce electromagnetic products can save money by checking the compatibility of various components before launching a product into production, by using mathematical analysis in place of the more traditional benchtop experiments.
At Philips Research [4], mathematicians also work on data encryption as well as data compression and signal processing, says Jan ter Maten, a senior scientist at the Philips site in Eindhoven, the Netherlands.
Mathematicians are in demandincreasing demandwherever there is a need to visualize calculations and phenomena through graphics, simulate real systems, optimize and analyze complex systems, work with "virtual" products, or design miniaturised products. The latter, in particular, is a challenging field of research that often requires new algorithms and mathematical models and novel approaches in both mathematics and physics.
Computer scientists, physicists, engineers, and even chemists must study mathematics during their years at university. So what's so special about mathematicians? According to the chief executives that were interviewed, although topics like cryptology are only taught to mathematicians, the differences in knowledge and expertise among candidates from these different fields are often small. In the last 3 decades or so, as universities created new mathematicsbased institutions that bring together the different disciplinesinstitutes of technomathematics (with computer science and engineering) and interdisciplinary centers for computational mathematics (which include the methods used in industrial research in their focus)these differences have shrunk still further. Mathematicsrelated employment in industrial R&D, consequently, requires not training in a particular discipline but experience and training in a suite of mathematical skills.
As in academia, mathematicians working in industry need to be able to identify the main issues within a complex problem and formulate an approach to a solution. They must, of course, have command of the mathematical methods needed to solve the problem. But understanding problems and solving them requires not just a set of skills but the right frame of mind; mathematicians need to be patient, according to Gilg of Siemens, and drill deep into a problem until a solution is found. Shell's Poulisse says that mathematicians also have to understand that these problems may not be precisely posedthe exact location of an oil reservoir within an oil field, for example, may not be exactly knownand work with this uncertainty.
One key to industrial research is the ability to translate a reallife problem into a mathematical one and then to translate the mathematical solution back into forms that can be applied to the real world. The ability to work with abstract frameworksand to translate between these frameworks and the real worldis what distinguishes mathematicians from researchers who are merely involved in computations, according to Poulisse. Industry, he says, needs mathematicians with imagination and mathematical talent.
As with any science, there are differences in the way people work in industry as opposed to academia. "The targets of mathematics are different in industry," says Gilg. Whereas in academia one may work on finding an elegant approach to a problem, the focus in industry is on coming up with a solution that works. There are also differences of motivation: Whereas an aesthetic appreciation for mathematics is desirable, in industry the staff needs to be motivated to create value for the company, says Dave Masson, Shell's global skillpool manager in the department of petroleum engineering in Rijswijk.
There are also differences in the time frame and the degree of collaboration. In academia, important problems can take years or even decades to solve, whereas in industry, one always has to work by a deadline, says one earlycareer mathematician. Another big difference is that in academia, mathematical achievements are often made by a single researcher working alone. In industry, most of the work is collaborative, so successful industrial mathematicians need to contribute to a multidisciplinary team. Shell's Masson adds that listening and constructively discussing ideas may be a challenge for those used to academic mathematics and emphasises the need for mutual respect. Teamwork is a new experience for many young graduates; companies are usually looking for an indication that candidates have an affinity for both industrial mathematics and teamwork.
A few mathematicians are recruited by industry at the master's level, but most are hired on with a Ph.D. More advanced training, however, means more specialisation, so mathematicians with a postdoc may have more difficulty finding employment than those with less training, unless they have a speciality that is rare and in demand.
Mathematicians willing to stay in industrial R&D will have the opportunity to progress from junior to senior scientist and eventually to principal researcher. Large companies like IBM and Philips also provide a few "fellow" positions, which confer a certain amount of freedom in selecting and approaching research problems. Shell even gives some researchers sabbaticals and free time to work on their own research projects.
Still, many scientists choose to move on to corporate or business units after a few years in corporate R&D. At Philips, for example, fewer than 50% of R&D staffincluding all disciplines, not just mathematicsare still in R&D after 5 years, according to ter Maten of Philips Research. It's also worth noting that most mathematicians remain in industry once they have made the move; unless one has continued to publish in scientific journals, kept contacts in academia, and maintained a reputation within the academic community, it is very difficult to move back.
The importance of industrial mathematics has been acknowledged by national and European mathematical societies [5]. Many networks have been created to promote cooperation between companies and universities, as well as recruitment, such as the E.U.funded Mathematics, Computing, and Simulation for Industry (MACSI [6]) project, the European Consortium for Mathematics in Industry (ECMI [7]), the European Community on Computational Methods in Applied Sciences (ECCOMAS [8]), the Network on Computations in Commutative Algebra [9], and the newly established MarieCurie Research Training Network in Coupled Multiscale Simulation and Optimization in Nanoelectronics (COMSON [10]) project. According to ter Maten, these networks are necessary to overcome a shortage of qualified personnel and to provide graduates and companies the opportunity to learn more about each other and make good contacts.
Positions in industrial R&D are rarely advertised solely for mathematicians; companies want to attract the people with the best skills, so they choose to cast their net wide. Gilg recommends that mathematics graduates apply for positions that are posted for researchers generally, or that specify training in engineering or computer science as well as mathematics. A qualification from a technomathematics or interdisciplinary institute may provide an advantage, but excellent pure mathematicians with interesting curriculum vitae may also land an industrial job if they demonstrate eagerness to work on industrial topics. Programming experience is often a prerequisite to employment in industry. And for Gilg, some research experience abroad and in industry, and participation in an activity that shows good social and organisational skills, is particularly valuable.
Unlike chemists, mathematicians don't have a whole industrial sector in their speciality that they can count on for employment. Mathematicians, rather, seekand findemployment in a wide range of sectors. Large technologybased corporations, in particular, are hiring more mathematicians these days. Wherever there's a need to evaluate risk or make something work better, you're likely to find a mathematician or a company seeking one.
Further literature: Berufs und KarrierePlaner Mathematik, ViewegVerlag, 2003 [11]. This book (in German) provides a lowdown on training and job opportunities for students and mathematicians. Management by Mathematicians [12] by Gunter Dueck, Vieweg, 2002. This book provides an insight on how successful mathematicians used their mathematical background in the management world. 

The author is a consultant in industrial R&D based in Europe. Albert Michels is a pseudonym. 
Comments, suggestions? Please send your feedback to our editor [13]. 
Links:
[1] http://www.research.ibm.com/
[2] http://www.shell.com/home/Framework?siteId=home
[3] http://w4.siemens.de/ct/en/home/index.html
[4] http://www.research.philips.com/
[5] http://www.ems.org
[6] http://www.macsinet.org/
[7] http://www.ecmiindmath.org/
[8] http://www.cimne.upc.es/eccomas/html/about.htm
[9] http://cocoa.dima.unige.it/
[10] http://www.comson.org/index.php?cat=whatis
[11] http://www.amazon.de/exec/obidos/ASIN/3528131578/qid=1134514414/sr=81/ref=sr_8_xs_ap_i1_xgl/02826606520258931
[12] http://www.amazon.de/exec/obidos/ASIN/3528031875/qid=1134409177/sr=89/ref=sr_8_xs_ap_i9_xgl/02826606520258931
[13] mailto:snweditor@aaas.org