Alice Roth facts for kids

Alice Roth (born February 6, 1905 – died July 22, 1977) was a brilliant Swiss mathematician. She invented a special math idea called the "Swiss cheese set." She also helped a lot with something called approximation theory. Alice Roth was born, lived, and passed away in Bern, Switzerland.

Her Early Life and Studies

Alice Roth went to a special school for girls in Zürich called the Höhere Töchterschule. After finishing there in 1924, she studied math, physics, and astronomy. She went to ETH Zurich, a famous university, and learned from a well-known professor named George Pólya.

In 1930, Alice earned her diploma. Her big project was about extending a math rule called "Weierstrass's Approximation Theorem." After that, she taught at several high schools for girls near Zurich. She also kept working with Professor Pólya at ETH.

Earning Her PhD

In 1938, Alice Roth became only the second woman to earn a PhD from ETH. A PhD is a very high university degree. Her PhD paper was titled "Properties of approximations and radial limits of meromorphic and entire functions." It was so good that she received a money prize and a special silver medal from ETH. Her supervisors were George Pólya and Heinz Hopf.

Teaching and Later Research

From 1940, Alice taught math and physics at Humboldtianum in Bern. This was a private school. She retired from teaching in 1971. After retiring, she went back to doing math research. She focused again on complex approximation, which is a part of math.

She wrote three math papers by herself. She also wrote one paper with Paul Gauthier and Joseph L. Walsh, who were professors at other universities. In 1975, when she was 70 years old, she was asked to give a public talk at the University of Montreal.

Alice Roth passed away in 1977.

Her Contributions to Mathematics

One of Alice Roth's most important discoveries was in her 1938 PhD paper. She created an example of a special math set. On this set, not every continuous function could be easily approximated by rational functions. This set is now known as the "Swiss cheese."

For a while, her discovery was forgotten. Then, in 1952, a Russian mathematician named Mergelyan found similar results on his own. But by 1969, people realized that Alice Roth had discovered it first. She received proper credit for her work.

Peter Wilker, one of her former students, wrote about her after she passed away. He said that women mathematicians were rare in Switzerland and elsewhere. He mentioned that her PhD paper won a medal and was published. But then World War II started, and her work was forgotten. He explained that a Russian mathematician later found similar ideas without knowing Alice Roth had published them years before. However, her original discovery was eventually recognized.

Alice Roth also developed other important ideas when she returned to research later in her life. Her work, especially her "Swiss cheese" idea, had a big impact on mathematicians. The "Swiss cheese" has even been changed and used in many new ways. Her "Roth's Fusion Lemma," which appeared in a paper in 1976, also influenced many new mathematicians around the world.

See Also

In Spanish: Alice Roth para niños