By Sven Leyffer, Volker Mehrmann, Jill Pipher, Ami E. Radunskaya, Wil Schilders, and Carlos Vázquez
The 9th International Congress on Industrial and Applied Mathematics (ICIAM 2019) in Valencia, Spain, featured a special panel on mathematical science careers in academia and industry. Panelists Sven Leyffer (Argonne National Laboratory), Volker Mehrmann (European Mathematical Society (EMS) and Technische Universität Berlin), Jill Pipher (American Mathematical Society and Brown University), Ami E. Radunskaya (Association for Women in Mathematics and Pomona College), and Wil Schilders (European Consortium of Mathematics in Industry (ECMI) and Eindhoven University of Technology) represented a wide range of backgrounds and institutions. Carlos Vázquez (University of A Coruña) organized the panel.
Panelists engaged in hearty discussion about the present and future role of mathematicians in academia and industry, as well as possible improvements in the training of applied mathematicians to ensure successful careers in both sectors.
Pipher opened the panel by reporting on AMS data pertaining to numbers and field distribution of Ph.D.s, career trajectories, demographic dispersion, and tendencies in the mathematical and statistical sciences. Notable trends included the slight but possibly significant decline in the percentage of Ph.D.s awarded to women over the last decade; the continued dearth of advanced degrees in mathematics among underrepresented minorities in the U.S.; the growth in non-research faculty positions at research universities; and increased student demand for mathematics, computational/statistical, and computer science education relevant to data science careers.
For some years, the U.S. job market for newly-minted Ph.D.s has offered many more postdoctoral positions in academia than follow-up, tenure-track jobs. Pipher briefly discussed ways in which mathematics departments can prepare students for the various rewarding non-academic careers accessible to them. SIAM’s career resources page is a terrific repository of information for students looking to learn about specific fields, job openings, and companies that routinely hire mathematicians.
Mehrmann spoke about the substantial inhomogeneity that currently exists in Europe for both the academic and industrial job markets. In some countries, companies have trouble filling positions because many options are available for industry careers. In other countries, no job openings are available. A similar situation is occurring in academia; some European countries offer ample opportunities at the assistant professor level but fewer prospects for higher positions, while others have almost no reasonably-paid openings. The EMS and the European Service Network of Mathematics for Industry and Innovation (EU-MATHS-IN) provide job portals for prospective employees. Many national societies also actively involve more young scientists in the organizations themselves, and work to rectify the gender imbalance. However, the asymmetrical situation in Europe causes much south-north movement among early-career professionals.
Radunskaya reminded attendees that mathematicians are needed in all facets of society. For example, teaching mathematics to young students is critical and should be considered a valued career trajectory. Mathematicians also play a role in policymaking and decision-making for nearly every area and endeavour, including medicine and energy. Professional societies and individual mathematicians must expose the broader community—from neighbors to politicians and business owners—to the utility and joyful playfulness of mathematics. A better awareness of mathematics’ role in society might also encourage heightened participation from groups that are currently underrepresented in the field.
Leyffer reported on careers within the U.S. and European national laboratories networks. 14 Department of Energy labs exist in the U.S., and a similar number of institutes—such as the Max-Planck and Fraunhofer institutes and research units in Germany, the National Institute for Research in Computer Science and Automation (INRIA) in France, and the Rutherford Appleton Laboratory in the U.K.—operate in Europe. The U.S. laboratories offer a range of opportunities for young mathematicians, like student internships and prestigiously-named postdoctoral fellowships that allow participants to pursue independent research agendas within the labs for up to two years. These positions are open to applicants from most countries, and many labs often hire new employees from the pool of former students and postdocs. Staff members tend to work on 100 percent soft-money projects and collaborate with domain and computer scientists. These projects are often large, multi-institutional, and multidisciplinary, thus requiring participants who can both assimilate new information quickly and communicate well with other domain scientists. Current applications include the power grid in addition to data analysis for physics experiments and beamlines.
Unlike academic job environments, the labs specifically emphasize the development of open-source, production-quality software that runs on high-performance computing systems. Leyffer expects future projects to pivot towards artificial intelligence and machine learning for physics-based models, as well as heterogeneous and emerging computer architectures like quantum, neuromorphic, and low-precision devices.
Laboratories typically require that their employees have Ph.D.s as evidence of independent thinking and the ability to serve as principal investigators on research grants. Communication and negotiation skills are important when working in a multidisciplinary environment, as is overall confidence when searching for and inquiring about job opportunities. Companies often hire mathematicians for their analytical abilities, not for specific knowledge in a narrow area. Over time, applied mathematicians in national labs become jacks-of-all-trades and branch out into new fields. Leyffer observed that lab salaries are typically competitive with industry; this is especially true for applied mathematicians, whose salaries are on par with computer scientists.
Schilders discussed ways in which EU-MATHS-IN supports mathematics careers within industry. The aforementioned job portal on its website is dedicated to maths appointments in the industrial sector. Students can browse job opportunities and industrial companies can post open positions. Appointments related to the European Union’s European Industrial Doctorates program are also posted here; these positions require that Ph.D. students spend at least 50 percent of their time in industry. Schilders, who spent 30 years in industrial environments (first at Philips in Eindhoven and then at NXP Semiconductors), also explained the dual ladder system that makes it possible for researchers to pursue careers as managers and experts.
The ECMI, which is closely related to EU-MATHS-IN, organizes so-called European Study Groups with Industry (ESGI) in many European countries. These weeklong workshops begin with presentations of five or six industrial challenges. The participating mathematicians then split into groups, work on the challenges all week, and present their final results to the industrial participants. ESGI is one of the best ways to get involved with industry, and can even lead to job offers and industrial careers.
Schilders also provided information on the yearly “Speed Dating with Industry” event at the Dutch Mathematical Congress, which provides a space for students to ask questions and converse with industry representatives about job opportunities. The Agency for Interaction in Mathematics with Business and Society—the French network within EU-MATHS-IN—organizes career fairs each year that draw 50 to 60 companies and 1,200 to 1,400 students from all across France.
Following their initial presentations, the panelists engaged with an active audience on a range of questions about mathematical science careers in academia and industry, and a comparison between the two.
Addressing a question about the number of mathematics positions at universities and research centers, Leyffer cited the growth in artificial intelligence and machine learning at Google, Microsoft, and U.S. schools like the Georgia Institute of Technology and Lehigh University. He also added that applied mathematicians can find relevant opportunities in industrial engineering, statistics, operations research, and computer science departments.
Mehrmann spoke about the European Union’s industrial mathematics professorships, which frequently attract candidates with industrial experience. He talked specifically about the transition between sectors, noting that postdoctoral researchers from labs often move back to academia, and even hold joint appointments with an emphasis on industry.
Schilders admitted that moving from industry to academia is generally difficult and usually happens late in one’s career. In many cases, academic appointments in the Netherlands involve only one or two days per week. If one hopes to return to academia from industry, he/she must maintain an updated academic profile by attending conferences and publishing papers whenever possible. Leyffer added that transitioning to academia is typically easier in industrial engineering departments or national labs, whose cultures are most similar to industry.
During his closing remarks, Mehrmann shared a telling statistic; several recent studies have estimated that applied mathematics’ contribution to a country’s gross domestic product is between 15 and 25 percent, which is a strong base for a healthy profession. He encouraged the audience to urge ICIAM member societies to foster applied math by putting more effort into support, advertisement, and education of young scientists.
Sven Leyffer is a senior computational mathematician at Argonne National Laboratory who works on nonlinear optimization. He currently serves as secretary of the International Council for Industrial and Applied Mathematics. Volker Mehrmann is a professor of numerical mathematics at the Technische Universität Berlin, president of the European Mathematical Society, and co-founder of the European Service Network of Mathematics for Industry and Innovation (EU-MATHS-IN). Jill Pipher is Vice President for Research and Elisha Benjamin Andrews Professor of Mathematics at Brown University. She began her term as president of the American Mathematical Society in February 2019. Ami E. Radunskaya is a professor of mathematics at Pomona College. She is the most recent past-president of the Association for Women in Mathematics and is a co-director of the EDGE Program (Enhancing Diversity in Graduate Education). Wil Schilders is a professor of scientific computing for industry at the Eindhoven University of Technology, director of the Dutch Platform for Mathematics, and co-founder and current president of EU-MATHS-IN. Carlos Vázquez is a full professor of applied mathematics at the University of A Coruña and a member of the organizing committee for the 9th International Congress on Industrial and Applied Mathematics (ICIAM 2019).