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Playing the numbers game

Pure mathematicians sometimes look down snobbishly on applied mathematicians because they deal in practical matters rather than pure science. This has never worried Mary Wheeler, legendary professor at the University of Texas. In her 40-year career she has found a lot of interesting maths problems in the real world and, in any case, she has had another, more important battle to fight.

It is easy to forget that, 40 years ago, women were not supposed to get involved in the practical world of engineering. It took extraordinary women such as Wheeler to break the mould. Today, she breaks the mould that says that you are finished at 60, as she continues to find new and exciting topics for research in applied computational mathematics.

Her chosen subjects are finite element analysis and porous media problems. Great mathematics, but with applications in engineering, oil-field exploitation, and the cleaning up of environmental pollution.

Clint Dawson, Professor of Aerospace Engineering and Engineering Mechanics at the University of Texas at Austin and a former research student of Wheeler, said: 'Mary has had to fight a lot of issues. She was probably the first woman to get a PhD at Rice in engineering, and the first woman to hold a chair in engineering. I don't think the battle between pure and applied mathematics has been the toughest battle she has faced. Her husband has a PhD and worked for Exxon, so she even had to put up with the snobbery of the Exxon wives, who were all 'stay at home moms'.

'Mary is as tough as nails. She is driven, yet she doesn't run roughshod over people. She has a certain fire in her belly that a lot of people don't have. She has a passion for research and teaching; she loves what she does. She expects a certain level of commitment from her students, but she doesn't ask anyone to work any harder than she does herself. She is probably the most energetic person that I know. I'm 20 years younger than her, and she runs me ragged sometimes.

'Mary is highly recognised for her contributions in mathematics and computational science. Early in her career, she did a lot of fundamental work in finite element methods and numerical analysis, and then she started working on porous media where she made a lot of contributions on things like oil reservoir modelling. She has now branched out into environmental problems. She has also made fundamental contributions to parallel computing, linear solvers, domain decomposition methods and applications in porous media, multiphase flow, and she has started doing work in geomechanics, which is fundamentally important.'

Wheeler was born in a small town near San Antonio in Texas, better known for its turkey ranching than for academic excellence. She comes from an old Texan ranching family. Unusually for those times, all her aunts had college degrees and her mother was a teacher with a Masters degree, so this small-town girl had plenty of role models in her ambitions. When she first went to college she studied pharmacy, but eventually decided to switch to government and had ambitions to become a lawyer. She had always been interested in mathematics and took a course in it 'just for fun'. She ended up with enough courses to graduate in mathematics as well.

She had chosen to go to the University of Texas at Austin because she was asthmatic and she had an uncle in Austin who was a doctor and could take care of her. As it happened, the drier climate of Austin meant she had little trouble.

She stayed at Austin for her Masters degree, initially thinking she could combine government and mathematics by studying econometrics. But her college roommate was taking a course based on engineering problems from a professor called David Young, and Wheeler said the problems sounded so interesting. She started getting interested in numerical analysis, and worked on the new-fangled computer that the university had just acquired. So eventually she gained a Masters in numerical analysis.

Soon after this she met and married her husband, who was a PhD chemical engineer. He had been recruited by Exxon, which was based in Houston.

Wheeler had done her Masters thesis on the Peaceman-Rachford Method, and the eponymous Henry Rachford was working at Rice University in Houston so Wheeler thought this might give her an entrée into similar work there. She was accepted to do a PhD under Rachford. While she was there she met Jim Douglas, another legendary figure in numerical analysis, and it was Douglas who spotted her potential and encouraged her throughout her career - 24 years of which was to be at Rice.

The oil industry looms large in Houston and it was not long before oil industry applications were included in her work. As she moved into porous media problems, she started working with the oil industry on managing oil-field extraction. She has also won friends in the environmental movement, by applying the same kind of expertise and personal energy to problems of cleaning up underground reservoirs and spills of toxic waste. More recently, she has been working on carbon dioxide sequestration. She has also discovered biomedical engineering and decided that tissue is just another porous medium looking her methods.

She said: 'My work has always been on the numerical algorithms for solving partial differential equations, and these algorithms apply to a collections of problems like finite-element analysis and finite-different methods. A lot of this analysis has been applied in many of the commercial packages.

'I like to gain knowledge, but it is also important to see it applied. My husband was the project leader in designing a pipeline, and I saw how numerical methods played such an important role. These calculations were validated by experiment, but seeing the way that mathematics played a part in design, showed how your work could have a real impact. We have done a lot of work in reservoir engineering and environmental bioremediation, and we have done a lot of work with the Corps of Army Engineers on environmental impact in Chesapeake Bay, Delaware Bay and Florida Bay.

'To me it is important to see your work used. I do abstract things as well, and I don't know if I will live to see them applied.

'Today, in virtually every aspect of our society, people are using numerical models to develop physical models. But I can remember a period from the 1950s through to the 1980s, when mathematicians didn't feel it necessary to do numeric, or that they should be interested in physical problems - you had to be doing something pure. But if you look back in history, mathematics has always been driven by physical problems. Why not create something that can be used by somebody, rather than have it just sit there in a book to look at?'

Wheeler steadily rose through the ranks at Rice to become a full professor, even though many colleagues looked down on numerical methods as just simple integration.

Wheeler had not moved around much in her career, and it was starting to show. She was beginning to feel that she was not being appreciated and was just part of the furniture. Her husband was still at Exxon at the time, so she did not want to leave the Houston area. She was therefore delighted when the University of Houston approached her with an offer of a Chair. Rice decided they did not want her to leave, so they offered her a two-year leave of absence to work at Houston. She also got the chance to work again with Roland Glowinski, who had joined Houston. They had previously collaborated on work in domain decomposition algorithms.

She was tempted back to Rice after that two-year period, when it started up a new centre for parallel computation. She was granted a named chair and played a major role in setting up the new centre, after being promised there would be an emphasis on the kind of research she had been doing.

In 1995 she was approached to come back to the University of Texas in Austin. Wheeler loved Austin and had always thought of going back - for the climate if nothing else. The university was about to invest in TICAM - the Texas Institute for Computational and Applied Mathematics.

They made her an offer she could not refuse, so she moved with the 13 people from her group at Rice, to start afresh.

She holds positions in mathematics, aerospace engineering, engineering mechanics, and in the petroleum and geosystems engineering departments, but she spends most of her time in her computational and applied maths programme.

Apart from mathematics, her great love is history and she will digress into a treatise on Texas history at the slightest provocation. As far as colleagues are concerned, there are no signs of her slowing down as she gets older. She is always looking for new areas of interest and applications for her research; her biggest problem is having the time to do everything that she wants.

She said: 'I love what I'm doing. My only sadness is that I'm getting old and I can't go back and do it all over again.'

Curriculum Vitae

The University of Texas at Austin, Social Sciences B.S.
The University of Texas at Austin Mathematics B.A.
The University of Texas at Austin Mathematics M.A.
Rice University Mathematics Ph.D.
Instructor, Department of Mathematics, Rice University
Associate Professor, Department of Mathematical Sciences, Rice University
Professor, Department of Mathematical Sciences, Rice University
M.D. Anderson Professor of Mathematics, University of Houston
Noah Harding Professor of Computational and Applied Mathematics (formerly Mathematical Sciences), Rice University
The University of Texas at Austin
The Ernest and Virginia Cockrell Chair in Engineering; Professor, Department of Mathematics; Professor, Aerospace Engineering and Engineering Mechanics; Professor, Petroleum and Geosystems Engineering.


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