A Mathematician Gets Out of the Box

Darren Crowdy (pictured left), an applied mathematics lecturer at Imperial College London, says he always tells his undergraduate students to "get out and see the world."

Crowdy is not encouraging his students to take an extended vacation, though at a mere 34 years old he himself has indeed seen a fair share of the world. Now that he has secured an international research reputation and established a firm grip on the rungs of the academic career ladder, Crowdy encourages young mathematicians to take off the blinders, put on their metaphorical backpacks and hiking books, and seek career opportunities far and wide instead of just sticking close to some comfortable disciplinary home.

Crowdy has himself taken the initiative on many occasions, leaving behind the familiar comforts of his own country during his Ph.D. training, searching out a unique and daring research niche, and investing time in communicating the results of his work to researchers well outside his field. Crowdy believes he has created his own career opportunities by doing this; such a proactive approach, says Crowdy, is fun and rewarding and can greatly enhance your career prospects. Now sitting at the other side of the interview table, Crowdy has become an advocate for his approach. "Having the initiative to glean experience," he says, "counts for a lot."

Leaving the Trail at the Trailhead

Embarking on his mathematics career, Crowdy didn't choose the U.K. standard route for researcher training of 3 years of undergraduate studies plus 3 years of doctoral training. When he completed his undergraduate degree in mathematics at the University of Cambridge, Crowdy opted to stay on at Cambridge do a diploma in Advanced Mathematical Studies. The course offers mathematics graduates the chance to be exposed to fundamental research areas in the mathematics faculty at a more profound level than undergraduate. "Maths requires maturity of understanding; you need more exposure after your undergrad. The difference between undergraduate and graduates studies is in understanding, mastering [mathematical concepts]," he explains.

Meanwhile, Crowdy was busy working out options for his doctoral training which he wished to conduct abroad. A faculty member at Cambridge recommended he hook up with Professor Philip Saffman, who is based at the California Institute of Technology (Caltech). Crowdy arranged to visit Caltech and also the Massachusetts Institute of Technology (MIT) in Boston. He was offered Ph.D. positions in both institutions and decided that Caltech was a better academic fit. The Caltech position had the additional and considerable advantage of being fully funded. When probed about his success in obtaining positions at such prestigious research centres, Crowdy once again credits his proactive approach. "Having the initiative to travel that distance and visit makes you stand out."

A Solid Theoretical Education

Despite having obtained extra qualifications in maths back in Cambridge, Caltech required Crowdy to take another year of course work. "At the time I was resentful," says Crowdy, but he later changed his view. "The course work was crucial to consolidate what I already knew." Crowdy considers those 2 extra years of course work--one seeking his advanced diploma at Cambridge and the other at Caltech--to be time very well spent. "It formed the structure I built my research career on," he notes.

Crowdy commenced that research career in Saffman's lab where he pursed applied mathematics research in fluid mechanics. He recalls the intellectual environment at Caltech as rich and horizon-broadening: "The student body was very diverse. I got a new perspective." On completing his Ph.D. in 1998, Crowdy moved to the east coast when he was offered a position as a mathematics instructor at MIT. This was a 2-year research-and-teaching post that, in contrast to most postdocs, was not attached to a particular grant. The pay-off was two fold, says Crowdy: "I was immediately treated like a faculty member, given courses to teach, but was not tied to any particular research area. I couldn't believe what I had been given."

Two years later, with teaching experience at a prestigious institution under his belt, he started to apply for independent positions and obtained a lectureship in mathematics at Imperial College London. In 2003 he moved into his current, more senior position, as a Reader in Applied Mathematics.

Daring to Find Your Own Research Niche

Crowdy's research record also went from strength to strength. He has more than 40 publications to his name, half of which are single author papers. His research interests lie in applied mathematics: the application of complex mathematical analysis in physical systems, like the interface between fluids such as water and oil. Crowdy attributes his research success to "taking risks; I didn't jump on the bandwagon." Mathematics researchers, he says, need to "develop [their] own style. Follow your heart. Don't be afraid to go out on your own."

This attitude was influenced by his mentors, especially Saffman at Caltech and Saleh Tanveer, a former student of Saffman who is now based in Ohio. Crowdy concedes that embarking on unknown territory in mathematics is perhaps less dangerous than in other sciences because mathematics provides it's own certainty, and it's own cairns and blazes marking out even the least-traveled trails. Mathematics research, he says, is "beautifully unequivocal. It's either right or wrong, there is nothing to argue about."

Still, those internal markers aren't sufficient for the applied mathematician, Crowdy maintains. He believes that top-quality research in applied mathematics--where mathematical solutions are sought for "real" (read non-mathematical) quandaries--can only result when mathematicians energetically engage scientists from the disciplines the scientific problems arise from. "Speak with them [the researchers], find out what their questions are, and translate this to: "how can I solve this with maths?' " In contrast to some "pure" mathematicians, Crowdy is emphatic that mathematicians need to take care their work is not esoteric, and that communicating its relevance within mathematics and to the other science communities as paramount to succeeding. "You have to convey what is important about your work. There is no point giving a presentation that no one understands."

Crowdy's research achievements are well recognised. Last year, he was awarded the prestigious, £50,000 Philip Leverhulme Prize, an award that aims to support young British academics whose work has received international recognition. A few months ago, Crowdy secured an Advanced Fellowship Award from the U.K.'s Engineering and Physical Sciences Research Council. This award guarantees salary funding for 5 years without administrative or teaching commitments. Crowdy intends to use this opportunity to concentrate on his research and to partly travel overseas to pursue his research. He has already planned a 9 month stay at MIT next year.

Advice From the Other Side of the Interview Table

With a flourishing research and academic career and experience on hiring committees under his belt, Crowdy is now in a position to advise early career mathematicians. While serving on hiring committees, he says, "I see how decisions are made". He advocates going abroad or at least moving institutions for both graduate studies and postdoc positions as opposed to staying at your old institution, even for the brightest students. "I encourage students to look elsewhere for their Ph.D and talk to different people. I never forgot the fact that someone told me about opportunities abroad."

Crowdy is still reaping the rewards of his early audacity, as the contacts he has made at various institutions continue to yield research collaborations. Further down the line, he says, these same relationships with researchers at home and abroad, are likely to yield further dividends. "People sponsor you and recommend you for the next stage."

Crowdy's future plans include devoting more time to his research thanks to his EPSRC fellowship and taking sabbaticals to work directly with researchers on far-off shores. Crowdy believes many opportunities exist for early career mathematicians who are willing to be proactive. "You have only one life," says the researcher who was never hesitant to get out of his own box.

Get out and Meet Fellow Applied Mathematicians!

Darren Crowdy would highly recommend attending the annual British Applied Mathematics Colloquium. The next one will be held in Keele, U.K., in April 2006.

He also recommends joining the U.K. based Institute of Mathematics which is a professional and learned society for mathematicians.

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