Stats Class Frames the Art of Uncertainty

In his Dean's Seminar, Professor Hosam M. Mahmoud turns stories into statistics as he shares his passion for probability with first-year students.

Don't tell Professor of Statistics Hosam M. Mahmoud that numbers aren't beautiful. The white board in his Dean's Seminar on The Science of Uncertainty at George Washington University may look like a scrawl of fractions and formulas. But where many of us see only indecipherable equations, Mahmoud sees philosophy, music, politics, even sports.

Leading his class of 13 first-year students through columns of binomial distributions, he sprinkles in words like "elegance" and "art." As he points to one stream of variables and coefficients, he steps back from the board and beams, "Isn't that pretty?"

"You have to admit-mathematical formulas can be very pretty," Mahmoud said. "A mathematical formula often starts out ugly. But as you go through it and reduce all the sums and polynomials to very simple symbols, at the end, it is a thing of beauty."

On one level, Mahmoud's course serves as an introduction to probability and the calculus of chance. Like all Dean's Seminars within the Columbian College of Arts and Sciences, it offers first-year students an in-depth look at topics relevant to the issues of our time. In Mahmoud's classroom, his students gain a strong foundation in the laws of probability and the elements of stochastic behavior. But they're also as likely to hear about Aristotle and LeBron James as Isaac Newton and Erwin Schrödinger.

It's all part of his strategy to make statistics less intimidating and more accessible. Mahmoud creates concrete scenarios-stories-as entry points for theoretical equations. "There are two parts to a study like this: First, there's a story. Then it's up to us to extract the science out of it," he said.

In his Dean's Seminar on The Science of Uncertainty, Statistics Professor Hosam M. Mahmoud teaches students that even the most complicated mathematical formula is "a thing of beauty."

In one recent lecture, Mahmoud quoted Winston Churchill, Voltaire and Mr. Spock from "Star Trek." A typical hour may find students calculating the probabilities of scoring a hattrick in soccer, rolling snake eyes with dice or striking the opening notes of "Frère Jacques" on random piano keys. At the students' request, he recently spent a class and a half drawing the odds of every possible poker hand.

In his lessons, he frames probability less as a complex formula than a series of paths that can lead to different outcomes. "There's a past that brought us to this point. But there are many futures ahead of us," he explained. "What are the different chances of this future versus another future? That's what probability is."

With a heavy math background, political science student Charles Calvert said it took him time to adjust to Mahmoud's "storytelling approach." Eventually, he appreciated how Mahmoud moved the class beyond mechanical problem solving into "seeing the beauty in numbers and visualizing the way they are affecting us in real life, seeing the evolution in not only theory, but the very methods of human thought."

Uncertain outcomes

Mahmoud takes full advantage of the CCAS Dean's Seminars emphasis on lively and engaging discussions. In the four years he's taught the class, he's frequently tailored his curriculum to fit his students' interests. A past sports-obsessed class calculated L.A. Laker LeBron James' free throw percentage. When another class included several biology students, Mahmoud created scenarios around lab animals' dietary habits. With this year's class featuring political science and history majors-but no math or statistics students-Mahmoud designed a politics-heavy lesson plan, leaning on election probability lessons such as projecting results before the votes are counted.

Over a 42-year teaching career at GW, Mahmoud has frequently shared his passions in his classroom. His uncle, famed Egyptian philosopher Zaki Naguib Mahmoud, introduced him to thinkers like David Hume and Bertrand Russell-many of whom show up in his lessons on logic and paradoxes. A Real Madrid fan, he often teaches soccer stats like World Cup-winning odds. When one class showed an interest in basketball, Mahmoud, who admits to not knowing a Nugget from a Knick, gave himself a crash course on the NBA Draft, learning the probabilities of each lottery team securing the top pick.

"Every class is an opportunity to learn something new-for my students and myself," he said. "I find joy in learning."

Mahmoud stresses his teaching method isn't designed to make statistics easier. Sharp math skills are still required to work through his white board. But rather than focusing on simply solving equations, he encourages students to reduce the probability of a host of outcomes-until only the most likely one is left.

"It's certainly been a learning curve for me in Professor Mahmoud's class," first-year student Calvert said. "But then you understand that through the anecdotal stories and Voltaire references, [he] is inspiring us to see statistics and probability in the same way he does."

Indeed, Mahmoud hopes students will embrace not just the uncertainty of statistics, but also the beauty behind them. In one of his favorite anecdotes, he imagines a conversation between "A Tale of Two Cities" writer Charles Dickens and physicist Schrödinger, author of a famous uncertainty principle. In Mahmoud's telling, Dickens repeats his classic first line: "It was the best of times, it was worst of times." Schrödinger nods knowingly at the duality and smiles, "Nice."

Students "can walk away hating everything about my class-the desks, the furniture, the facilities, the instructor," Mahmoud said. "But they can't walk away hating the subject. I want them to love the subject."

The CCAS Department of Statistics is celebrating its 90th anniversary this year, marking nearly a century of significant contributions to statistical education and research at GW. To mark the occasion, the department is hosting a conference, "The Past, Present and Future of Statistics in the Era of AI" from May 9-10, which will focus on contemporary statistical challenges and opportunities.