By Rick Vacek | June 13, 2024
Many students believe that studying mathematics is not worth the effort.
That attitude doesn’t rate with Dr. Alain Bensoussan, Lars Magnus Ericsson chair and professor of management in the Naveen Jindal School of Management at The University of Texas at Dallas. He has built his multifaceted career around the value of math and understanding how to use it.
“Mathematics is fantastic,” he said. “It provides tools to solve real problems.”
In April, the former head of the French and European space agencies showed how to use those tools with a fascinating inside look at the race to the moon when he delivered the 2024 Polykarp Kusch Lecture, “Research in Management Science and the Importance of Mathematics.” (Watch the lecture on YouTube.)
Bensoussan’s love of mathematics is accompanied by his love of history, and in a subsequent interview he stressed the importance of learning from a historical fact: Words and sounds often differ vastly between cultures and across generations within each culture, but mathematics is universal. In math, no translation is needed.
“Mathematics improves, but the core does not change. It’s not a new language; it’s like the evolution of the language,” he said. “That’s why, if you learn it, it’s a win-win because it will be helpful all your life. And if you don’t learn it, you will never learn it because you need to learn it when you’re young, like any language.
“The resilience explains why learning mathematics is an extremely good investment. This, unfortunately, is something many students don’t realize, and because it’s difficult they are not interested.”
Bensoussan began his Kusch lecture with President John F. Kennedy’s declaration in an address to a joint session of Congress on May 25, 1961:
“I believe that this nation should commit itself to achieving the goal, before this decade is out, of landing a man on the moon and returning him safely to the earth. No single space project in this period will be more impressive to mankind, or more important for the long-range exploration of space; and none will be so difficult or expensive to accomplish.”
At the time, Bensoussan was a 21-year-old student whose astrophysics professor said the task was impossible.
That assessment was proved wrong when the mission was accomplished on July 20, 1969, but it was every bit as costly as Kennedy predicted. At the time, Bensoussan said, the National Aeronautics and Space Administration (NASA) swallowed up 5.5% of the U.S. budget; now that figure is only 0.4%.
Space travel also was inherently wasteful until SpaceX launched the Falcon 9 in 2010. Its most costly parts are reusable.
“Space is the worst possible way of transporting goods or humans,” Bensoussan said. “It’s totally ridiculous. It would be like taking a plane from New York to Paris, destroying the plane and taking another one.”
From World War II until the 1980s, the focus of business was on efficiency – minimizing expenses and maximizing profits.
“Now it is completely different,” Bensoussan said. “If you are efficient and you die the next day, what does it mean to be efficient? We see it quite often – companies do very well and are very efficient but die because of unforeseen risks.
“All of this is good news for mathematicians. Decision-making under uncertainty requires new mathematics. You cannot optimize everything. You try to optimize the mean, the average. The spread is very big. Then you take into account risk, which brings new mathematical problems.
“The problems of today are much more complex. They deal with randomness and conflicts.”
Bensoussan’s Kusch talk, in honor of the Nobel Prize winner who was a member of the UT Dallas physics faculty from 1972 to 1982, emphasized how complex problems were solved in the space race.
He told of the story of Wernher von Braun, creator of the Saturn V launch vehicle, which ultimately propelled Apollo 11 to the surface of the moon. He was determined to test it stage by stage, never implementing more than one change between flight tests, which was the traditional way to manage space missions.
Bensoussan made plain his admiration for systems engineer George Mueller, who bravely told von Braun he would fail unless he changed his management practices and switched to “all-up testing,” involving all three stages of the Saturn V at once.
When von Braun argued that the all-up approach would make it difficult to pinpoint failures, Mueller countered by insisting stage by stage simply spread the risks among many tests.
Mueller also knew that Kennedy’s declaration wouldn’t be fulfilled unless all-up was implemented. He got his way.
“In retrospect it is clear that without all-up testing the first manned lunar landing could not have taken place as early as 1969,” von Braun wrote before his death in 1977. “It sounded reckless, but George Mueller’s reasoning was impeccable.”
In other words, it all came down to management. Bensoussan began his talk by declaring, “Management science is a gold mine for mathematicians,” and math is life, in his view.
“The principle of mathematics is that all problems are extremely complex,” he said later. “The number one principle is how to simplify the problem. To simplify, you have to cut it into pieces. ‘OK, I cannot solve everything, so I’m going to solve this problem that is relevant.’ It’s not the solution to the large problem, but it does solve some aspect that has relevance. Doing that, I learn, and maybe I can solve the more complex problem.
“The principle of simplification is the key to succeeding in mathematics – and in the world, in your own life. People would not think this is true, but mathematics is extremely useful for real life because the principles that you implement are exactly the same as what you should use in your life.”
The interview with Bensoussan included a colleague, Dr. Viswanath Ramakrishna, assistant department head and professor of mathematics in the School of Natural Sciences and Mathematics, and two mathematics PhD students.
Manjula Mahesh Ranpati Dewage is studying the effect of production on environment, using mathematics to produce models and explain the implications in management science.
Jyoti Hasija is focusing on clients working together, largely with cellphones, to keep data private. Again, it’s all about math and models.
The conversation eventually developed into a back-and-forth between Ramakrishna and Bensoussan, which was like listening to two eminent historians discuss the major talking points of the last century.
“The best way to model is to use mathematics. As soon as you have a mathematical model, you’re in good shape.”
DR. ALAIN BENSOUSSAN
Ramakrishna:
“Mathematics is ultimately about eliciting patterns from different situations in the moment. You try to abstract what is common from various things, so you build a model around it. Even in pure mathematics, you build models.
“You build a mathematical model and you analyze it with the tools of mathematics; all of a sudden it suggests new questions that probably would not have arisen if you had just studied it on a case-by-case basis. In that sense, mathematics is universe. It’s in your head, but it plays a huge role.”
Bensoussan:
“A model is an approximation of reality. It does not exist. It’s not true. The reality is different. But the model is a simpler representation. If it is close to reality, it is relevant, and because it is simpler you can handle it.
“The best way to model is to use mathematics. As soon as you have a mathematical model, you’re in good shape.”
Artificial intelligence isn’t the ultimate answer, Bensoussan warned. In his view, combining big data and the power of computers with mathematical tools is the good strategy.
Bensoussan then explained the difference between pure and applied mathematics:
“Compare writing an important report and a play of Shakespeare. Both use the same tool, the English language. The first one corresponds to a real problem. The second one does not correspond to a specific need, but when it is written it has a huge impact because it is a masterpiece.
“It is essential that students understand the importance of mathematics. It is a very fruitful investment.”