A.N. Kolmogorov, 84, a Soviet mathematician credited with making a major contribution to one of the most important fields of modern mathematics by creating the formal foundations of the theory of probability, died Oct. 20 in Moscow, the Soviet news agency, Tass, reported. No cause of death was given.

Dr. Kolmogorov's obituary was signed by Soviet leader Mikhail S. Gorbachev, and noted that in addition to his contributions to a variety of areas in pure mathematics, the scholar and teacher was the author of the work known in its 1950 English edition as "Foundations of the Theory of Probability."

That work, based on research Dr. Kolmogorov had done in the 1920s and early 1930s, sets out the axioms and postulates that provide a rigorous logical basis for what has become one of the most active and useful fields of modern mathematics.

Just as geometry is said to have originated in the efforts of ancient farmers to survey their fields, probability theory also sprung from rough-and-ready efforts to answer questions of everyday life -- in particular from attempts to predict the outcome of games of chance or to determine life expectancies.

One of the earliest published works in probability theory appeared in the 17th century and concerns the logical analysis of games of dice. But just as the celebrated axioms and postulates of Euclid made possible vast advances in geometry by transforming it from an agricultural tool into a formal branch of mathematics, Dr. Kolmogorov is credited with revolutionizing probability theory by rooting it in an axiomatic foundation.

From its origins in questions of heads and tails and hearts and diamonds, probability theory became an area of modern abstract mathematics, involved with sets and functions in their mathematical sense.

This development and work based on it made possible the application of probability theory to new areas of science and technology, and permitted the creation of increasingly sophisticated mathematical tools to solve problems in these areas. Also, despite the often highly abstruse nature of the mathematics that underlies it, probability theory has come to play an important role in many other areas of modern life, from economics to public opinion polling.

In addition to becoming a member of the Academy of Sciences of the USSR, Dr. Kolmogorov was recognized for his achievement by being elected to membership in many western scholarly bodies, including the U.S. National Academy of Sciences.

Andrei Nikolayevich Kolmogorov was born April 25, 1903, in Tambov, in central Russia, the son of an agronomist.

He showed formidable gifts early in his career. As a student at Moscow State University while still in his teens, he did work that stunned the mathematicians of the period.

After his graduation in 1925, he launched into his work on the foundations of probability theory.

By 1931 he was a professor at Moscow State University, and two years later he was made a director of the Institute of Mathematics there. He is credited with training many other important Soviet mathematicians as well as making contributions to such areas as topology, the theory of turbulent flows and the theory of stochastic processes.


95, a retired vice president and bookkeeper in her family business, a lifelong area resident and a member of Holy Redeemer Catholic Church in Kensington, died of congestive heart failure Oct. 24 at Holy Cross Hospital.

She and her husband, John H. Mace, founded the J.H. Mace trucking company in 1937. She closed the business after his death in 1977. Mrs. Mace, who lived in Kensington, was a native of Washington.

Her survivors include a daughter, Dorothy M. Dean of Kensington, and four grandchildren.


68, a retired travel specialist at the federal Department of Transportation and a member of Pilgrim Baptist Church, died Oct. 15 at her home in Washington after a heart attack.

Mrs. Howard was born in New Orleans and graduated from Dillard University there.

She moved to Washington during World War II and began her career as a travel specialist at the Treasury Department. She later worked at the Department of Housing and Urban Development and then at Transportation, where she retired in 1976.

At her church she had headed the Deaconess Board and taught Sunday school. She also was a member of the Phillis Wheatley YWCA and the Ivy City Citizens Association.

Her husband, Clarence Lionel Howard, died in 1979.

Survivors include one daughter, Army Capt. Audrey Howard Carswell of Fort Dix, N.J.; one stepson, Norman L. Howard of Alexandria, and five grandchildren.