His mother's foresight saved mathematician Heini Halberstam from the Holocaust and brought him to England, where chance led to a career in number theory and a focus on the puzzle of prime numbers, whole numbers like seven and 13 that can be divided only by one and themselves.
Mr. Halberstam, 87, died of congestive heart failure Saturday, Jan. 25, in his Champaign home, according to his daughter Judith.
"He was a distinguished researcher," said Harold Diamond, a former colleague at the University of Illinois at Urbana-Champaign, where Mr. Halberstam headed the mathematics department from 1980 until 1988, and retired as emeritus professor in 1996.
"It's an intellectual and academic pursuit," Diamond said of the work he, Mr. Halberstam and others did in the field of number theory.
But this theoretical work has some real-world applications in fields like cryptography, for example, Diamond said. Prime numbers are an important ingredient in an encryption protocol called public key cryptography, used around the world for secure communications in some financial and defense-related applications.
Mr. Halberstam, an only child, spent his early years in Most, a small town in an area called the Sudetenland that is now part of the Czech Republic. His father, a rabbi, died when he was 10 and he moved with his mother to Prague.
His mother recognized the rising danger of anti-Semitism and sent him to England on one of the Kindertransport trains that carried thousands of mostly Jewish children to the relative safety of the United Kingdom. None were accompanied by parents.
Mr. Halberstam was 12 when he arrived in England. His mother died three years later of typhus in a Nazi work camp.
Although he had relatives in England, it was the foster parent who took him in and with whom he stayed for the duration of the war, Anne Welsford, who recognized his intellectual abilities. She encouraged him to go to university and paid for the portion of his education that wasn't covered by scholarships.
He studied number theory at the University of London, getting a doctorate there in 1952, according to Diamond.
"His research was in a field his adviser was working on and it seemed like an interesting area," Diamond said. "When he took it up, number theory was a field of pure study done by academics, just pure mathematics with no obvious applications."
After two years at Trinity College Dublin, Mr. Halberstam moved to the mathematics department of the University of Nottingham in 1964. His time there included two stints as head of the department and one period as dean of the faculty.
He left Nottingham in 1980 to come to the U. of I. as head of the mathematics department.
"The school was known for number theory, and it was a really good career move," his daughter said.
Mr. Halberstam relished the intellectual challenge of studying prime numbers. "There are many, many unsolved problems. It's a premier area of study in theoretical mathematics," his daughter said.
Diamond, who collaborated with Mr. Halberstam on a book as well as a number of articles, said his colleague's specialty was what is called sieve theory, a way of attacking some problems involving prime numbers.
In 1974, with another colleague, Mr. Halberstam published "Sieve Methods," which remains a major book in the field. He was a fellow of the American Mathematical Society and of University College, London.
In addition to his research, Mr. Halberstam was an effective teacher, generous in his support for students who met his high standards, according to his son Michael.
"My father made a point of helping students he believed in and helping them to advance in securing positions and jobs and getting their papers published," his son said.
In a short memoir he wrote for his children and grandchildren, Mr. Halberstam reflected on the strange twists and turns his life had taken, recalling a quote from a Vladimir Nabokov novel about the "mysterious thing, this branching structure of life" being as mysterious as the prime numbers he studied.
Mr. Halberstam's first wife, Heather, died in an auto accident in 1971. His second wife, Doreen, survives him; as do three other daughters, Lucy, Naomi Strachan and Jean Smith; another son, John Smith; and eight grandchildren.
Plans for a memorial service are pending.