Witold Hurewicz facts for kids

Witold Hurewicz (June 29, 1904 – September 6, 1956) was a Polish mathematician. He made very important discoveries in a field of mathematics called topology. Topology is like studying shapes and spaces, but focusing on properties that don't change even if you stretch or bend them.

Early Life and Education

Witold Hurewicz was born in Łódź, Poland, on June 29, 1904. At that time, Łódź was a big industrial city, especially known for making textiles. His father, Mieczysław Hurewicz, was an industrialist.

Schooling During Wartime

Hurewicz went to school in Poland when it was controlled by Germany. When World War I started in 1914, Poland saw many changes. In 1915, Russian forces left Poland, and Germany and Austria-Hungary took control.

During this time, the University of Warsaw was reopened as a Polish university. A strong group of mathematicians grew there, focusing on topology. Even though Hurewicz knew about the topology being studied in Poland, he chose to go to Vienna, Austria, for his university studies.

University Studies and Early Career

In Vienna, Hurewicz studied under famous mathematicians like Hans Hahn and Karl Menger. He earned his PhD in 1926.

After his PhD, Hurewicz received a special scholarship from the Rockefeller Foundation. This allowed him to spend a year, from 1927 to 1928, in Amsterdam, Netherlands. From 1928 to 1936, he worked as an assistant to another important mathematician, L. E. J. Brouwer, in Amsterdam.

He took a year off to study in the United States. He visited the Institute for Advanced Study in Princeton, New Jersey. He liked it so much that he decided to stay in the U.S. and not return to his job in Amsterdam.

Contributions to Mathematics

Hurewicz first worked at the University of North Carolina at Chapel Hill. During World War II, he used his math skills to help with the war effort. He did research in applied mathematics, which is about using math to solve real-world problems.

Wartime Research

One of his important projects during the war involved servomechanisms. These are devices that help control machines, like in airplanes or radar systems. His work on these was kept secret because it was important for the military.

Work at MIT

From 1945 until his death, Hurewicz worked at the Massachusetts Institute of Technology (MIT). This is a very famous university known for science and technology.

Key Discoveries in Topology

Hurewicz's early work focused on set theory and topology. He made a remarkable discovery in 1930. He found a way to "embed" certain types of spaces (called separable metric spaces) into smaller, more compact spaces, while keeping their "dimension" the same. Dimension theory is about how we measure the "size" of spaces.

He also wrote an important book called Dimension Theory with Henry Wallman in 1941. This book is considered a classic because it explains the theory of dimension so clearly and completely.

Hurewicz is best known for three amazing contributions to mathematics:

• He discovered the higher homotopy groups between 1935 and 1936. These groups help mathematicians understand the "holes" and "connections" in shapes in a deeper way.
• He found the long exact homotopy sequence for fibrations in 1941. This is a powerful tool that connects different mathematical structures.
• He developed the Hurewicz theorem. This theorem links homotopy groups with homology groups, which are other tools used to study shapes.

His work helped create a new field of math called homological algebra. Even though the idea of higher homotopy groups wasn't completely new, Hurewicz was the first to truly explore them and show how useful they were.

Later Work and Legacy

In the late 1940s, Hurewicz guided Yael Dowker as she earned her PhD.

Another one of his textbooks, Lectures on ordinary differential equations, was published in 1958, after he passed away. This book also showed how clearly he thought and wrote about math.

How He Passed Away

Witold Hurewicz died on September 6, 1956, in Uxmal, Mexico. He had been at a math conference in Mexico City. During an outing to see ancient Mayan ruins, he accidentally tripped and fell off the top of a step pyramid in Uxmal. Some people who knew him said he was often very absentminded, and this might have led to his accident.

See also

• Zygmunt Janiszewski