Background
She was born, lived and died in Bern, Switzerland.
She was born, lived and died in Bern, Switzerland.
Alice attended the Höhere Töchterschule der Stadt Zürich, a municipal school for higher education for girls. After graduation in 1924 she studied mathematics, physics and astronomy at Eidgenössische Technische Hochschule Zurich under George Pólya. She graduated with a diploma in 1930.
In 1938 she became a second woman to graduate with a Doctor of Philosophy from Eidgenössische Technische Hochschule .
Her Master"s thesis was titled "Extension of Weierstrass"s Approximation Theorem to the complex plane and to an infinite interval". After that, she was a teacher at multiple high schools for girls in the Zurich area while continuing working with Pólya at Eidgenössische Technische Hochschule . From 1940 she was mathematics and physics teacher at Humboldtianum in Bern, a private school. lieutenant was only after her retirement in 1971 she returned to mathematical research, again in the areas of complex approximation.
She published three papers on her own, as well as a shared paper with Paul Gauthier of the University of Montreal and Harvard University professor Joseph L. Walsh.
In 1975, at the age 70 She was invited to give a public lecture at the University of Montreal. Next year she was diagnosed with cancer and died a year later.
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. This set, now known as the "Swiss cheese," was forgotten and independently rediscovered in 1952 in Russia by Mergelyan, and proper cr 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 Eidgenössische Technische Hochschule , 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: "Roth"s past as well as future work was to have a strong and lasting influence on mathematicians working in this area.
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.".