February 6, 1905 - July 22, 1977
Alice Roth was born on February 6, 1905, in Bern, Switzerland, the middle child of Conrad Roth and Marie Landolt Roth. When she was six, the family moved to the Zürich area. Alice attended the Höhere Töchterschule der Stadt Zürich, a municipal school for higher education for girls. There she studied mathematics, physics, chemistry, Latin, and foreign languages, passing the examination in 1924 that would allow her to be admitted to a university.
From 1925 to 1929, Alice studied mathematics, physics, and astronomy at the Swiss Federal Institute of Technology (ETH) in Zürich. In 1930 she finished her Master's thesis on "Extension of Weierstrass's Approximation Theorem to the complex plane and to an infinite interval" under the direction of George Polya.
For the next 10 years Roth worked as a teacher at various girls' schools in the Zurich area, including the one she attended as a child. She taught a variety of subjects such as mathematics, geometry, arithmetic, and accounting. During this time she also continued her work on function theory with Polya at ETH. In 1938 she became the second woman to earn a Ph.D. in mathematics at ETH when she completed her thesis on "Properties of approximations and radial limits of meromorphic and entire functions." This thesis was of such excellent quality that Roth was awarded a monetary prize and the ETH Silver Medal, the first woman to earn this distinction from ETH.
From 1940 until her retirement in 1971, Alice Roth taught mathematics and physics at a private school in Bern. Her teaching load was quite heavy and her salary less than what she could have earned at a public school, yet she was an influential and successful teacher. Outside of the classroom she enjoyed playing the piano, hiking, skiing, and travel. She was also a strong advocate of women's right to vote.
It was upon her retirement after a long career in teaching that Roth once again had the time and energy to return to research in the area of complex approximation theory. In addition to publishing 3 papers of her own during this time, she also did work with Paul Gauthier at the University of Montreal leading to a 1976 joint publication in the Canadian Journal of Mathematics. Roth gave an invited lecture at the University of Montreal at the age of 70. In 1976, however, she developed the first stages of cancer. She was hospitalized in Bern in 1977, and died on July 22, 1977, still working on her mathematics while ill.
One of the main results of Roth's 1938 thesis was an example of a compact set on which not every continuous function can by approximated uniformly by rational functions. But this set, now known as the "Swiss cheese," was soon forgotten. The example was rediscovered in the 1950's and proper credit was restored by 1969. The following excerpt by her former student, Peter Wilker, appeared in an obituary he wrote after her death :
"In Switzerland, as elsewhere, women mathematicians are few and far between.... Alice Roth's dissertation was awarded a medal from the ETH, and appeared shortly after its completion in a Swiss mathematical journal....One year later war broke out, the world had other worries than mathematics, and Alice Roth's work was simply forgotten. So completely forgotten that around 1950 a Russian mathematician re-discovered similar results without having the slightest idea that a young Swiss woman mathematician had published the same ideas more than a decade before he did. However, her priority was recognized."Roth developed other important results during her brief return to research at the end of her life. As the article  by Daepp, Gauthier, Gorkin, and Schmieder claims, "Roth's past as well as future work was to have a strong and lasting influence on mathematicians working in this area [rational approximation theory]. Her Swiss cheese has been modified (to an entire variety of cheeses).... Roth's fusion lemma, which appeared in her 1976 paper...influenced a new generation of mathematicians worldwide."