By Tracy James
The Southern Illinoisan
[Sun Oct 24 1999]SIU mathematics professor engaged in groundbreaking work

(Southern Illinoisan photo by JOE JINES)

[Sun Oct 24 1999]A visitor opened the door into Salah Mohammed's office in the Neckers building at Southern Illinois University at Carbondale and was surprised to find it would open only partly. 

The door bumped into a fan, which pushed against a tall black filing cabinet, which was surrounded by an amply filled bookshelf and more books stacked on the floor. Along the opposite wall of the office, roughly 8 or 9 feet square, ran two desks. 

Oh, what would his father think? 

As a bright, promising teen-ager, Mohammed was encouraged by his father to go into medicine or engineering because of the financial security it would bring. 

Money was no small matter then. As a youngster, his parents probably earned about $200 a year. But in the Sudan, where deserts stretched from one side of his home in Rufaa and the Blue Nile flowed along the other side, even the poorest children had access to good schools and universities. 

Mohammed received a government scholarship to the University of Khartoum, the Harvard of the Sudan at the time, but instead of going into medicine or engineering, he pursued his love of mathematics, and geometry in particular. 

To many people, mathematics truly is a four-letter word. 

To Mohammed, a math professor at SIUC, it's exciting, challenging and representative of life itself. Over the years, his research interests have evolved from geometry and probability to stochastic analysis, a mathematical discipline that strives to fit a general pattern to the evolution of random events. His sophisticated form of mathematics involves evolution, chance and now, memory. 

Stochastic "systems," which involve random events occurring over time, are such things as the weather, the stock market and human, animal and other populations. They change over time and are bombarded by a variety of random events or occurrences that influence how the systems evolve. 

"Everything around us has a fairly strong stochastic component," he said, pointing to the chance encounters and acquaintances that can nudge a person's life in a different direction. 

A coin toss, for example, is a classic case of probability. There is a 50-50 chance that the coin lands heads up. No evolution here. Just heads or tails. 

An investment into a certificate of deposit, on the other hand, involves evolution -- in the form of interest over a specified amount of time. But there is nothing random about it. The investor is able to calculate, or predict with certainty, the interest earned over the evolution of the investment. 

The stock market takes this to another level, combining both evolution and random influences. It is impossible to predict with certainty what will happen with an investment. But stochastic analysis can help provide a pattern of development over time that considers the unknown. 

Stochastic analysis is a relatively young mathematical discipline first written about in published works in the 1940s. The Black and Scholes stochastic formula, first published in 1973, is readily used by analysts to study options pricing. The study helps scientists filter "clutter" noise as they listen for signals from space, among other applications. 

Mohammed's research is focusing more on the influence of memory these days. The gestation period before childbirth is an example of memory in regards to human populations, whose evolution is influenced both by the unpredictable pairings of men and women and the immigration of others. 

The idea of memory also has applications to mechanical systems in engineering. Xue-Mei Li, an assistant professor of mathematics at the University of Connecticut, describes Mohammed as a pioneer and expert in the area of stochastic delay equations, which involve the idea of memory. 

David Elworthy, director of the Mathematics Research Centre at Warwick University, said Mohammed is the expert when it comes to equations that involve memory and random influences. Elworthy said Mohammed's work is especially notable in regard to systems' stability or instability. 

"His latest work with his long-time collaborator M.K.R. Scheutzow from Germany has some very fundamental results about this stability, and it is fine mathematics," Elworthy wrote to The Southern Illinoisan. 

Mohammed's work has been funded by the National Science Foundation for the last 10 years. He was invited to serve during the 1997-1998 school year as a mentor and guest speaker and researcher at the prestigious Mathematical Sciences Research Institute in Berkeley. 

"It was like paradise for a mathematician," he said. 

Despite any misgivings on his father's part, mathematics appears to have served Mohammed, who first arrived at SIUC in 1984, very well. 

It has taken him from the arid Sudan and given him the opportunity to travel extensively throughout the U.S., where he is a U.S. citizen, and Europe. He communicates and collaborates with scientists around the world. He uses his powerful office computer, which uses a dual processor, to post his work even before it gets published so other mathematicians can see what he is up to and provide him with feedback. He also uses the computer for his research and to communicate with his students at SIUC. 

Mohammed is described by Elworthy and Li as honorable, dedicated, warm and full of energy. When you meet him, he has a quick smile and is enthusiastic, particularly about math. 

While not making as much money as he could as a doctor or engineer, he says his life is rich and challenging. 

He built a home that is surrounded by trees -- something in short supply in the Sudan. The trees and rural nature of the region provide a peacefulness that Mohammed said is very conducive to mathematical thought. 

He proudly refers to himself as an African-American and describes the excitement of exploring the American culture as an immigrant. He is proud of his African heritage. He said his whole family speaks Arabic. 

He notes, however, that poverty in the U.S. poses obstacles that he was able to avoid as a kid in Sudan. He said poverty is an issue that really needs to be addressed in the U.S. because it keeps many people from developing their full potential because of the education available, or rather not available, to them in grade and high school and higher education.